Mobile GUI agents can execute tasks from natural-language instructions, but their evaluation remains difficult to make both realistic and reproducible. Existing benchmarks typically trade off these goals: simplified apps lack real-world mobile complexity, whereas live commercial apps introduce uncontrolled variation from recommendations, advertisements, accounts, and changing content. We propose AppSim-Bench, which addresses this trade-off through controllable simulated apps that preserve task-relevant interaction logic while supporting deterministic evaluation. Built through a coding-agent-assisted and human-verified workflow, it contains 557 tasks across 17 high-frequency Chinese and English apps. Its controllable backend data and outcome-based verification remove major sources of environmental stochasticity, enabling reproducible cross-model comparison. Evaluating 19 GUI agents, spanning general-purpose and GUI-specialized systems, we find that autonomous mobile execution remains far from solved. The best model completes only 50.27% of tasks, and 28.55% of tasks are not solved by any agent. Further analysis shows that failures concentrate in longer workflows, numerical reasoning tasks, and inefficient trajectories marked by high action overhead and budget exhaustion. Our project is available at https://github.com/Acrab-Lab/AppSim.

The large language models (LLMs) learning framework for math problem generation (MPG) mostly performs homogeneous training in different epochs on small-scale manually annotated data. This pattern struggles to provide large-scale new quality data to support continual improvement, and fails to stimulate the mutual promotion reaction between generation and reasoning ability of math problem, resulting in the lack of reliable solving process. This paper proposes a synthetic data based continual learning framework to improve LLMs ability for MPG and math reasoning. The framework cycles through three stages, “supervised fine-tuning, data synthesis, direct preference optimization”, continuously and steadily improve performance. We propose a synthetic data method with dual mechanism of model self-play and multi-agent cooperation is proposed, which ensures the consistency and validity of synthetic data through sample filtering and rewriting strategies, and overcomes the dependence of continual learning on manually annotated data. A data replay strategy that assesses sample importance via loss differentials is designed to mitigate catastrophic forgetting. Experimental analysis on abundant authoritative math datasets demonstrates the superiority and effectiveness of our framework.