Average Error: 10.1 → 0.0
Time: 11.5s
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 r518175 = x;
        double r518176 = y;
        double r518177 = z;
        double r518178 = r518177 - r518175;
        double r518179 = r518176 * r518178;
        double r518180 = r518175 + r518179;
        double r518181 = r518180 / r518177;
        return r518181;
}
↓
double f(double x, double y, double z) {
        double r518182 = y;
        double r518183 = -r518182;
        double r518184 = 1.0;
        double r518185 = r518183 + r518184;
        double r518186 = x;
        double r518187 = z;
        double r518188 = r518186 / r518187;
        double r518189 = r518185 * r518188;
        double r518190 = r518182 + r518189;
        return r518190;
}

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

Original10.1
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.1

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

  2. Taylor expanded around 0 3.4

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

  3. Taylor expanded around 0 3.4

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

  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 2019305 
(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))