Average Error: 10.2 → 0.0
Time: 10.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}
double f(double x, double y, double z) {
        double r903044 = x;
        double r903045 = y;
        double r903046 = z;
        double r903047 = r903046 - r903044;
        double r903048 = r903045 * r903047;
        double r903049 = r903044 + r903048;
        double r903050 = r903049 / r903046;
        return r903050;
}
↓
double f(double x, double y, double z) {
        double r903051 = y;
        double r903052 = -r903051;
        double r903053 = 1.0;
        double r903054 = r903052 + r903053;
        double r903055 = x;
        double r903056 = z;
        double r903057 = r903055 / r903056;
        double r903058 = r903054 * r903057;
        double r903059 = r903051 + r903058;
        return r903059;
}

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 3.5

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

  3. Taylor expanded around 0 3.5

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

  4. Simplified0.0

    \[\leadsto \color{blue}{y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}}\]

  5. Final simplification0.0

    \[\leadsto y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}\]

Reproduce

herbie shell --seed 2020047 
(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))