Average Error: 10.5 → 0.0
Time: 10.3s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(y + \frac{x}{z}\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(y + \frac{x}{z}\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r36011610 = x;
        double r36011611 = y;
        double r36011612 = z;
        double r36011613 = r36011612 - r36011610;
        double r36011614 = r36011611 * r36011613;
        double r36011615 = r36011610 + r36011614;
        double r36011616 = r36011615 / r36011612;
        return r36011616;
}
↓
double f(double x, double y, double z) {
        double r36011617 = y;
        double r36011618 = x;
        double r36011619 = z;
        double r36011620 = r36011618 / r36011619;
        double r36011621 = r36011617 + r36011620;
        double r36011622 = r36011620 * r36011617;
        double r36011623 = r36011621 - r36011622;
        return r36011623;
}

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 3.9

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

  4. Applied *-un-lft-identity3.9

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

  5. Applied times-frac3.5

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

  6. Simplified3.5

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

  7. Taylor expanded around 0 3.9

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))