Average Error: 28.9 → 0.2
Time: 9.7s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(x + z\right) \cdot \frac{z - x}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(x + z\right) \cdot \frac{z - x}{y}}{2}
double f(double x, double y, double z) {
        double r695513 = x;
        double r695514 = r695513 * r695513;
        double r695515 = y;
        double r695516 = r695515 * r695515;
        double r695517 = r695514 + r695516;
        double r695518 = z;
        double r695519 = r695518 * r695518;
        double r695520 = r695517 - r695519;
        double r695521 = 2.0;
        double r695522 = r695515 * r695521;
        double r695523 = r695520 / r695522;
        return r695523;
}
↓
double f(double x, double y, double z) {
        double r695524 = y;
        double r695525 = x;
        double r695526 = z;
        double r695527 = r695525 + r695526;
        double r695528 = r695526 - r695525;
        double r695529 = r695528 / r695524;
        double r695530 = r695527 * r695529;
        double r695531 = r695524 - r695530;
        double r695532 = 2.0;
        double r695533 = r695531 / r695532;
        return r695533;
}

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

Original28.9
Target0.2
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.9

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))