Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.4 → 23.4

Time: 8.9s

Precision: binary64

Math

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

↓

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

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	23.4
Target	18.2
Herbie	23.4

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

Derivation

1. Initial program 23.4

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

3. Applied sub-neg 23.4

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

4. Applied distribute-lft-in 23.4

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

5. Applied associate-+r+ 23.4

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

6. Simplified 23.4

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

7. Final simplification 23.4

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

Reproduce

herbie shell --seed 2020171 
(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)))))