Average Error: 27.0 → 0.1
Time: 17.1s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}
double f(double x, double y, double z) {
        double r32172284 = x;
        double r32172285 = r32172284 * r32172284;
        double r32172286 = y;
        double r32172287 = r32172286 * r32172286;
        double r32172288 = r32172285 + r32172287;
        double r32172289 = z;
        double r32172290 = r32172289 * r32172289;
        double r32172291 = r32172288 - r32172290;
        double r32172292 = 2.0;
        double r32172293 = r32172286 * r32172292;
        double r32172294 = r32172291 / r32172293;
        return r32172294;
}
↓
double f(double x, double y, double z) {
        double r32172295 = y;
        double r32172296 = x;
        double r32172297 = z;
        double r32172298 = r32172296 - r32172297;
        double r32172299 = r32172298 / r32172295;
        double r32172300 = r32172296 + r32172297;
        double r32172301 = r32172299 * r32172300;
        double r32172302 = r32172295 + r32172301;
        double r32172303 = 2.0;
        double r32172304 = r32172302 / r32172303;
        return r32172304;
}

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

Original27.0
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 27.0

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}}\]
  3. Using strategy rm

  4. Applied associate-/r/0.1

    \[\leadsto \frac{y + \color{blue}{\frac{x - z}{y} \cdot \left(z + x\right)}}{2.0}\]

  5. Final simplification0.1

    \[\leadsto \frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"

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

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))