Average Error: 10.2 → 0.0
Time: 11.4s
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 r785167 = x;
        double r785168 = y;
        double r785169 = z;
        double r785170 = r785169 - r785167;
        double r785171 = r785168 * r785170;
        double r785172 = r785167 + r785171;
        double r785173 = r785172 / r785169;
        return r785173;
}
↓
double f(double x, double y, double z) {
        double r785174 = y;
        double r785175 = -r785174;
        double r785176 = 1.0;
        double r785177 = r785175 + r785176;
        double r785178 = x;
        double r785179 = z;
        double r785180 = r785178 / r785179;
        double r785181 = r785177 * r785180;
        double r785182 = r785181 + r785174;
        return r785182;
}

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

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.5

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

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

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

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

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

  6. Applied distribute-lft-out--3.5

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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))