Average Error: 10.2 → 0.0
Time: 16.3s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} - \frac{x}{z} \cdot y\right) + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} - \frac{x}{z} \cdot y\right) + y
double f(double x, double y, double z) {
        double r23284033 = x;
        double r23284034 = y;
        double r23284035 = z;
        double r23284036 = r23284035 - r23284033;
        double r23284037 = r23284034 * r23284036;
        double r23284038 = r23284033 + r23284037;
        double r23284039 = r23284038 / r23284035;
        return r23284039;
}
↓
double f(double x, double y, double z) {
        double r23284040 = x;
        double r23284041 = z;
        double r23284042 = r23284040 / r23284041;
        double r23284043 = y;
        double r23284044 = r23284042 * r23284043;
        double r23284045 = r23284042 - r23284044;
        double r23284046 = r23284045 + r23284043;
        return r23284046;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

Enter valid numbers for all inputs

Target

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.5

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

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

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