Average Error: 10.1 → 0.0
Time: 12.8s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{y}{\frac{z}{x}}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{y}{\frac{z}{x}}
double f(double x, double y, double z) {
        double r946839 = x;
        double r946840 = y;
        double r946841 = z;
        double r946842 = r946841 - r946839;
        double r946843 = r946840 * r946842;
        double r946844 = r946839 + r946843;
        double r946845 = r946844 / r946841;
        return r946845;
}
↓
double f(double x, double y, double z) {
        double r946846 = x;
        double r946847 = z;
        double r946848 = r946846 / r946847;
        double r946849 = y;
        double r946850 = r946848 + r946849;
        double r946851 = r946847 / r946846;
        double r946852 = r946849 / r946851;
        double r946853 = r946850 - r946852;
        return r946853;
}

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. Simplified10.1

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

  3. Taylor expanded around 0 3.4

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

  4. Taylor expanded around 0 3.4

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 +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))