Average Error: 10.3 → 0.0
Time: 16.5s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \frac{x}{z} \cdot \left(y - 1\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \frac{x}{z} \cdot \left(y - 1\right)
double f(double x, double y, double z) {
        double r480295 = x;
        double r480296 = y;
        double r480297 = z;
        double r480298 = r480297 - r480295;
        double r480299 = r480296 * r480298;
        double r480300 = r480295 + r480299;
        double r480301 = r480300 / r480297;
        return r480301;
}
↓
double f(double x, double y, double z) {
        double r480302 = y;
        double r480303 = x;
        double r480304 = z;
        double r480305 = r480303 / r480304;
        double r480306 = 1.0;
        double r480307 = r480302 - r480306;
        double r480308 = r480305 * r480307;
        double r480309 = r480302 - r480308;
        return r480309;
}

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

Original10.3
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  2. Taylor expanded around 0 3.5

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

  3. Simplified3.5

    \[\leadsto \color{blue}{y - \frac{y \cdot x - x}{z}}\]
  4. Using strategy rm

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

    \[\leadsto y - \frac{y \cdot x - x}{\color{blue}{1 \cdot z}}\]

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

    \[\leadsto y - \frac{y \cdot x - \color{blue}{1 \cdot x}}{1 \cdot z}\]

  7. Applied distribute-rgt-out--3.5

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

  8. Applied times-frac3.4

    \[\leadsto y - \color{blue}{\frac{x}{1} \cdot \frac{y - 1}{z}}\]

  9. Simplified3.4

    \[\leadsto y - \color{blue}{x} \cdot \frac{y - 1}{z}\]

  10. Taylor expanded around 0 3.5

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 
(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))