Average Error: 10.5 → 0.0
Time: 10.8s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} - y \cdot \frac{x}{z}\right) + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} - y \cdot \frac{x}{z}\right) + y
double f(double x, double y, double z) {
        double r55438039 = x;
        double r55438040 = y;
        double r55438041 = z;
        double r55438042 = r55438041 - r55438039;
        double r55438043 = r55438040 * r55438042;
        double r55438044 = r55438039 + r55438043;
        double r55438045 = r55438044 / r55438041;
        return r55438045;
}
↓
double f(double x, double y, double z) {
        double r55438046 = x;
        double r55438047 = z;
        double r55438048 = r55438046 / r55438047;
        double r55438049 = y;
        double r55438050 = r55438049 * r55438048;
        double r55438051 = r55438048 - r55438050;
        double r55438052 = r55438051 + r55438049;
        return r55438052;
}

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 3.9

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

  3. Taylor expanded around 0 3.9

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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))