Average Error: 28.7 → 0.1
Time: 18.6s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}
double f(double x, double y, double z) {
        double r382314 = x;
        double r382315 = r382314 * r382314;
        double r382316 = y;
        double r382317 = r382316 * r382316;
        double r382318 = r382315 + r382317;
        double r382319 = z;
        double r382320 = r382319 * r382319;
        double r382321 = r382318 - r382320;
        double r382322 = 2.0;
        double r382323 = r382316 * r382322;
        double r382324 = r382321 / r382323;
        return r382324;
}
↓
double f(double x, double y, double z) {
        double r382325 = y;
        double r382326 = z;
        double r382327 = x;
        double r382328 = r382326 + r382327;
        double r382329 = r382326 - r382327;
        double r382330 = r382329 / r382325;
        double r382331 = r382328 * r382330;
        double r382332 = r382325 - r382331;
        double r382333 = 2.0;
        double r382334 = r382332 / r382333;
        return r382334;
}

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

Original28.7
Target0.2
Herbie0.1
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.7

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]

  2. Simplified13.0

    \[\leadsto \color{blue}{\frac{y - \frac{z \cdot z - x \cdot x}{y}}{2}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity13.0

    \[\leadsto \frac{y - \frac{z \cdot z - x \cdot x}{\color{blue}{1 \cdot y}}}{2}\]

  5. Applied difference-of-squares13.0

    \[\leadsto \frac{y - \frac{\color{blue}{\left(z + x\right) \cdot \left(z - x\right)}}{1 \cdot y}}{2}\]

  6. Applied times-frac0.1

    \[\leadsto \frac{y - \color{blue}{\frac{z + x}{1} \cdot \frac{z - x}{y}}}{2}\]

  7. Simplified0.1

    \[\leadsto \frac{y - \color{blue}{\left(z + x\right)} \cdot \frac{z - x}{y}}{2}\]

  8. Final simplification0.1

    \[\leadsto \frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)))