Average Error: 10.5 → 0.0
Time: 13.5s
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 r822059 = x;
        double r822060 = y;
        double r822061 = z;
        double r822062 = r822061 - r822059;
        double r822063 = r822060 * r822062;
        double r822064 = r822059 + r822063;
        double r822065 = r822064 / r822061;
        return r822065;
}
↓
double f(double x, double y, double z) {
        double r822066 = y;
        double r822067 = -r822066;
        double r822068 = 1.0;
        double r822069 = r822067 + r822068;
        double r822070 = x;
        double r822071 = z;
        double r822072 = r822070 / r822071;
        double r822073 = r822069 * r822072;
        double r822074 = r822066 + r822073;
        return r822074;
}

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 3.6

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

  3. Taylor expanded around 0 3.6

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

  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 2020042 
(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))