Average Error: 10.4 → 0.0
Time: 9.5s
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 r881266 = x;
        double r881267 = y;
        double r881268 = z;
        double r881269 = r881268 - r881266;
        double r881270 = r881267 * r881269;
        double r881271 = r881266 + r881270;
        double r881272 = r881271 / r881268;
        return r881272;
}
↓
double f(double x, double y, double z) {
        double r881273 = y;
        double r881274 = -r881273;
        double r881275 = 1.0;
        double r881276 = r881274 + r881275;
        double r881277 = x;
        double r881278 = z;
        double r881279 = r881277 / r881278;
        double r881280 = r881276 * r881279;
        double r881281 = r881280 + r881273;
        return r881281;
}

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

Original10.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around 0 3.3

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

  4. Applied *-un-lft-identity3.3

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

  5. Applied *-un-lft-identity3.3

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

  6. Applied distribute-lft-out--3.3

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

  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 2020046 
(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))