Average Error: 9.7 → 0.0
Time: 8.7s
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 r568512 = x;
        double r568513 = y;
        double r568514 = z;
        double r568515 = r568514 - r568512;
        double r568516 = r568513 * r568515;
        double r568517 = r568512 + r568516;
        double r568518 = r568517 / r568514;
        return r568518;
}
↓
double f(double x, double y, double z) {
        double r568519 = x;
        double r568520 = z;
        double r568521 = r568519 / r568520;
        double r568522 = y;
        double r568523 = r568521 * r568522;
        double r568524 = r568521 - r568523;
        double r568525 = r568524 + r568522;
        return r568525;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original9.7
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.7

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

  2. Simplified3.3

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

  4. Applied div-sub3.3

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

  5. Simplified2.9

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

  7. Applied associate-/r/0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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))