Average Error: 9.2 → 0.0
Time: 11.9s
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 r38424133 = x;
        double r38424134 = y;
        double r38424135 = z;
        double r38424136 = r38424135 - r38424133;
        double r38424137 = r38424134 * r38424136;
        double r38424138 = r38424133 + r38424137;
        double r38424139 = r38424138 / r38424135;
        return r38424139;
}
↓
double f(double x, double y, double z) {
        double r38424140 = x;
        double r38424141 = z;
        double r38424142 = r38424140 / r38424141;
        double r38424143 = y;
        double r38424144 = r38424142 * r38424143;
        double r38424145 = r38424142 - r38424144;
        double r38424146 = r38424145 + r38424143;
        return r38424146;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.2

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

  2. Taylor expanded around 0 2.9

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

  4. Applied associate--l+2.9

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(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))