Average Error: 10.3 → 0.0
Time: 4.7s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \frac{x}{z} \cdot \left(1 - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \frac{x}{z} \cdot \left(1 - y\right)
(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))
↓
(FPCore (x y z) :precision binary64 (+ y (* (/ x z) (- 1.0 y))))
double code(double x, double y, double z) {
	return (x + (y * (z - x))) / z;
}
↓
double code(double x, double y, double z) {
	return y + ((x / z) * (1.0 - y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.3
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  2. Taylor expanded around 0 3.6

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

  3. Simplified3.6

    \[\leadsto \color{blue}{y + \frac{x - x \cdot y}{z}}\]
  4. Using strategy rm

  5. Applied div-sub_binary64_212253.6

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

  6. Simplified0.0

    \[\leadsto y + \left(\frac{x}{z} - \color{blue}{y \cdot \frac{x}{z}}\right)\]
  7. Using strategy rm

  8. Applied *-un-lft-identity_binary64_212200.0

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

  9. Applied *-un-lft-identity_binary64_212200.0

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

  10. Applied times-frac_binary64_212260.0

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

  11. Applied distribute-rgt-out--_binary64_211740.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2020344 
(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))