Average Error: 10.5 → 0.0
Time: 14.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\frac{x}{z} + \left(y - \frac{x}{z} \cdot y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\frac{x}{z} + \left(y - \frac{x}{z} \cdot y\right)
double f(double x, double y, double z) {
        double r32351282 = x;
        double r32351283 = y;
        double r32351284 = z;
        double r32351285 = r32351284 - r32351282;
        double r32351286 = r32351283 * r32351285;
        double r32351287 = r32351282 + r32351286;
        double r32351288 = r32351287 / r32351284;
        return r32351288;
}
↓
double f(double x, double y, double z) {
        double r32351289 = x;
        double r32351290 = z;
        double r32351291 = r32351289 / r32351290;
        double r32351292 = y;
        double r32351293 = r32351291 * r32351292;
        double r32351294 = r32351292 - r32351293;
        double r32351295 = r32351291 + r32351294;
        return r32351295;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.5
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.5

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

  2. Taylor expanded around 0 3.5

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

  3. Taylor expanded around 0 3.5

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(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))