Error

Derivation

1. Initial program 0.3

   \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(real->posit(5)\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(real->posit(32)\right)\right)}\]
2. Using strategy rm

3. Applied *-commutative0.3

   \[\leadsto \frac{\left(\frac{\color{blue}{\left(d2 \cdot d1\right)}}{\left(\left(\frac{d3}{\left(real->posit(5)\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(real->posit(32)\right)\right)}\]

4. Applied distribute-rgt-out0.3

   \[\leadsto \frac{\color{blue}{\left(d1 \cdot \left(\frac{d2}{\left(\frac{d3}{\left(real->posit(5)\right)}\right)}\right)\right)}}{\left(d1 \cdot \left(real->posit(32)\right)\right)}\]
5. Using strategy rm

6. Applied +-commutative0.3

   \[\leadsto \frac{\left(d1 \cdot \left(\frac{d2}{\color{blue}{\left(\frac{\left(real->posit(5)\right)}{d3}\right)}}\right)\right)}{\left(d1 \cdot \left(real->posit(32)\right)\right)}\]

7. Applied associate-+r+0.3

   \[\leadsto \frac{\left(d1 \cdot \color{blue}{\left(\frac{\left(\frac{d2}{\left(real->posit(5)\right)}\right)}{d3}\right)}\right)}{\left(d1 \cdot \left(real->posit(32)\right)\right)}\]

8. Applied distribute-rgt-in0.3

   \[\leadsto \frac{\color{blue}{\left(\frac{\left(\left(\frac{d2}{\left(real->posit(5)\right)}\right) \cdot d1\right)}{\left(d3 \cdot d1\right)}\right)}}{\left(d1 \cdot \left(real->posit(32)\right)\right)}\]

9. Final simplification0.3

   \[\leadsto \left(\left(d2 + 5\right) \cdot d1 + d3 \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))