Average Error: 9.7 → 0.0
Time: 8.7s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\frac{x}{z} + \frac{x}{z} \cdot \left(-y\right)\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\frac{x}{z} + \frac{x}{z} \cdot \left(-y\right)\right)
double f(double x, double y, double z) {
        double r686363 = x;
        double r686364 = y;
        double r686365 = z;
        double r686366 = r686365 - r686363;
        double r686367 = r686364 * r686366;
        double r686368 = r686363 + r686367;
        double r686369 = r686368 / r686365;
        return r686369;
}
↓
double f(double x, double y, double z) {
        double r686370 = y;
        double r686371 = x;
        double r686372 = z;
        double r686373 = r686371 / r686372;
        double r686374 = -r686370;
        double r686375 = r686373 * r686374;
        double r686376 = r686373 + r686375;
        double r686377 = r686370 + r686376;
        return r686377;
}

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

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 sub-neg2.9

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

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))