Average Error: 10.3 → 0.0
Time: 9.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) + \left(-\frac{x}{z} \cdot y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) + \left(-\frac{x}{z} \cdot y\right)
double f(double x, double y, double z) {
        double r764042 = x;
        double r764043 = y;
        double r764044 = z;
        double r764045 = r764044 - r764042;
        double r764046 = r764043 * r764045;
        double r764047 = r764042 + r764046;
        double r764048 = r764047 / r764044;
        return r764048;
}
↓
double f(double x, double y, double z) {
        double r764049 = x;
        double r764050 = z;
        double r764051 = r764049 / r764050;
        double r764052 = y;
        double r764053 = r764051 + r764052;
        double r764054 = r764051 * r764052;
        double r764055 = -r764054;
        double r764056 = r764053 + r764055;
        return r764056;
}

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

Original10.3
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  2. Taylor expanded around 0 3.4

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

  4. Applied sub-neg3.4

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(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))