Average Error: 10.5 → 0.0
Time: 13.5s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}
double f(double x, double y, double z) {
        double r780020 = x;
        double r780021 = y;
        double r780022 = z;
        double r780023 = r780022 - r780020;
        double r780024 = r780021 * r780023;
        double r780025 = r780020 + r780024;
        double r780026 = r780025 / r780022;
        return r780026;
}
↓
double f(double x, double y, double z) {
        double r780027 = y;
        double r780028 = -r780027;
        double r780029 = 1.0;
        double r780030 = r780028 + r780029;
        double r780031 = x;
        double r780032 = z;
        double r780033 = r780031 / r780032;
        double r780034 = r780030 * r780033;
        double r780035 = r780027 + r780034;
        return r780035;
}

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 3.6

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

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

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

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

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

  6. Applied distribute-lft-out--3.6

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(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))