Average Error: 10.4 → 0.0
Time: 15.0s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \frac{x}{z} \cdot \left(y - 1\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \frac{x}{z} \cdot \left(y - 1\right)
double f(double x, double y, double z) {
        double r635637 = x;
        double r635638 = y;
        double r635639 = z;
        double r635640 = r635639 - r635637;
        double r635641 = r635638 * r635640;
        double r635642 = r635637 + r635641;
        double r635643 = r635642 / r635639;
        return r635643;
}
↓
double f(double x, double y, double z) {
        double r635644 = y;
        double r635645 = x;
        double r635646 = z;
        double r635647 = r635645 / r635646;
        double r635648 = 1.0;
        double r635649 = r635644 - r635648;
        double r635650 = r635647 * r635649;
        double r635651 = r635644 - r635650;
        return r635651;
}

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

Original10.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around 0 3.7

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

  3. Simplified3.7

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

  5. Applied *-un-lft-identity3.7

    \[\leadsto y - \frac{y \cdot x - \color{blue}{1 \cdot x}}{z}\]

  6. Applied distribute-rgt-out--3.7

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

  7. Applied associate-/l*2.9

    \[\leadsto y - \color{blue}{\frac{x}{\frac{z}{y - 1}}}\]
  8. Using strategy rm

  9. Applied associate-/r/0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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))