Average Error: 10.2 → 3.7
Time: 14.7s
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 r675995 = x;
        double r675996 = y;
        double r675997 = z;
        double r675998 = r675997 - r675995;
        double r675999 = r675996 * r675998;
        double r676000 = r675995 + r675999;
        double r676001 = r676000 / r675997;
        return r676001;
}
↓
double f(double x, double y, double z) {
        double r676002 = y;
        double r676003 = x;
        double r676004 = r676003 * r676002;
        double r676005 = r676004 - r676003;
        double r676006 = z;
        double r676007 = r676005 / r676006;
        double r676008 = r676002 - r676007;
        return r676008;
}

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))