Average Error: 10.2 → 3.7
Time: 14.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \frac{x \cdot y - x}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \frac{x \cdot y - x}{z}
double f(double x, double y, double z) {
        double r494171 = x;
        double r494172 = y;
        double r494173 = z;
        double r494174 = r494173 - r494171;
        double r494175 = r494172 * r494174;
        double r494176 = r494171 + r494175;
        double r494177 = r494176 / r494173;
        return r494177;
}
↓
double f(double x, double y, double z) {
        double r494178 = y;
        double r494179 = x;
        double r494180 = r494179 * r494178;
        double r494181 = r494180 - r494179;
        double r494182 = z;
        double r494183 = r494181 / r494182;
        double r494184 = r494178 - r494183;
        return r494184;
}

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
Herbie3.7
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.7

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

  3. Simplified3.7

    \[\leadsto \color{blue}{y - \frac{x \cdot y - x}{z}}\]

  4. Final simplification3.7

    \[\leadsto y - \frac{x \cdot y - x}{z}\]

Reproduce

herbie shell --seed 2019303 
(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))