Average Error: 10.3 → 0.0
Time: 15.4s
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 r39401046 = x;
        double r39401047 = y;
        double r39401048 = z;
        double r39401049 = r39401048 - r39401046;
        double r39401050 = r39401047 * r39401049;
        double r39401051 = r39401046 + r39401050;
        double r39401052 = r39401051 / r39401048;
        return r39401052;
}
↓
double f(double x, double y, double z) {
        double r39401053 = x;
        double r39401054 = z;
        double r39401055 = r39401053 / r39401054;
        double r39401056 = y;
        double r39401057 = r39401055 * r39401056;
        double r39401058 = r39401055 - r39401057;
        double r39401059 = r39401058 + r39401056;
        return r39401059;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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

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

  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 2019170 
(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))