Average Error: 9.8 → 0.0
Time: 2.2s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \frac{x}{z} \cdot \left(1 - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \frac{x}{z} \cdot \left(1 - y\right)
double f(double x, double y, double z) {
        double r713647 = x;
        double r713648 = y;
        double r713649 = z;
        double r713650 = r713649 - r713647;
        double r713651 = r713648 * r713650;
        double r713652 = r713647 + r713651;
        double r713653 = r713652 / r713649;
        return r713653;
}
↓
double f(double x, double y, double z) {
        double r713654 = y;
        double r713655 = x;
        double r713656 = z;
        double r713657 = r713655 / r713656;
        double r713658 = 1.0;
        double r713659 = r713658 - r713654;
        double r713660 = r713657 * r713659;
        double r713661 = r713654 + r713660;
        return r713661;
}

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

Original9.8
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.8

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

  2. Taylor expanded around 0 3.4

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

  3. Taylor expanded around 0 3.4

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

  4. Simplified0.0

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

  5. Taylor expanded around 0 3.4

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019356 
(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))