Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.7 → 23.8

Time: 5.7s

Precision: 64

Math

\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]

↓

\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b + z \cdot \left(-y\right)\right)}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Target

Original	23.7
Target	18.2
Herbie	23.8

\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

1. Initial program 23.7

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
2. Using strategy rm

3. Applied sub-neg 23.7

   \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \color{blue}{\left(b + \left(-y\right)\right)}}\]

4. Applied distribute-lft-in 23.8

   \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(z \cdot b + z \cdot \left(-y\right)\right)}}\]

5. Final simplification 23.8

   \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b + z \cdot \left(-y\right)\right)}\]

Reproduce

herbie shell --seed 2020126 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))