Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Average Error: 10.6 → 0.0

Time: 6.7s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	10.6
Target	0.0
Herbie	0.0

\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

1. Initial program 10.6

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

2. Taylor expanded around 0 3.6

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

3. Taylor expanded around 0 3.6

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

4. Simplified 0.0

   \[\leadsto \color{blue}{\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y}\]

5. Final simplification 0.0

   \[\leadsto \left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))