Average Error: 10.2 → 0.0
Time: 2.4s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r969950 = x;
        double r969951 = y;
        double r969952 = z;
        double r969953 = r969952 - r969950;
        double r969954 = r969951 * r969953;
        double r969955 = r969950 + r969954;
        double r969956 = r969955 / r969952;
        return r969956;
}
↓
double f(double x, double y, double z) {
        double r969957 = x;
        double r969958 = z;
        double r969959 = r969957 / r969958;
        double r969960 = y;
        double r969961 = r969959 + r969960;
        double r969962 = r969959 * r969960;
        double r969963 = r969961 - r969962;
        return r969963;
}

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

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.3

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

  3. Taylor expanded around 0 3.3

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))