Average Error: 10.0 → 0.0
Time: 19.7s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y
double f(double x, double y, double z) {
        double r539027 = x;
        double r539028 = y;
        double r539029 = z;
        double r539030 = r539029 - r539027;
        double r539031 = r539028 * r539030;
        double r539032 = r539027 + r539031;
        double r539033 = r539032 / r539029;
        return r539033;
}
↓
double f(double x, double y, double z) {
        double r539034 = y;
        double r539035 = -r539034;
        double r539036 = 1.0;
        double r539037 = r539035 + r539036;
        double r539038 = x;
        double r539039 = z;
        double r539040 = r539038 / r539039;
        double r539041 = r539037 * r539040;
        double r539042 = r539041 + r539034;
        return r539042;
}

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

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

Derivation

  1. Initial program 10.0

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

  2. Simplified10.0

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z - x, y, x\right)}{z}}\]

  3. Taylor expanded around 0 3.4

    \[\leadsto \color{blue}{\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity3.4

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

  6. Applied *-un-lft-identity3.4

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

  7. Applied distribute-lft-out--3.4

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(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))