Error

Derivation

1. Initial program 0.5

   \[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]

2. Simplified0.4

   \[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(d2 - d3\right)}{\left(d4 - d1\right)}\right)}\]
3. Using strategy rm

4. Applied associate-+r-0.4

   \[\leadsto d1 \cdot \color{blue}{\left(\left(\frac{\left(d2 - d3\right)}{d4}\right) - d1\right)}\]
5. Using strategy rm

6. Applied associate-+l-0.4

   \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right)\]

7. Applied associate--l-0.4

   \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\frac{\left(d3 - d4\right)}{d1}\right)\right)}\]
8. Using strategy rm

9. Applied sub-neg0.4

   \[\leadsto d1 \cdot \color{blue}{\left(\frac{d2}{\left(-\left(\frac{\left(d3 - d4\right)}{d1}\right)\right)}\right)}\]

10. Applied distribute-rgt-in0.5

    \[\leadsto \color{blue}{\frac{\left(d2 \cdot d1\right)}{\left(\left(-\left(\frac{\left(d3 - d4\right)}{d1}\right)\right) \cdot d1\right)}}\]
11. Using strategy rm

12. Applied distribute-rgt-out0.4

    \[\leadsto \color{blue}{d1 \cdot \left(\frac{d2}{\left(-\left(\frac{\left(d3 - d4\right)}{d1}\right)\right)}\right)}\]

13. Simplified0.4

    \[\leadsto d1 \cdot \color{blue}{\left(\frac{\left(d2 - \left(\frac{d1}{d3}\right)\right)}{d4}\right)}\]

14. Final simplification0.4

    \[\leadsto d1 \cdot \left(\left(d2 - \left(d1 + d3\right)\right) + d4\right)\]

Reproduce

herbie shell --seed 2019093 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))