Average Error: 28.2 → 0.2
Time: 9.2s
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 r803483 = x;
        double r803484 = r803483 * r803483;
        double r803485 = y;
        double r803486 = r803485 * r803485;
        double r803487 = r803484 + r803486;
        double r803488 = z;
        double r803489 = r803488 * r803488;
        double r803490 = r803487 - r803489;
        double r803491 = 2.0;
        double r803492 = r803485 * r803491;
        double r803493 = r803490 / r803492;
        return r803493;
}
↓
double f(double x, double y, double z) {
        double r803494 = y;
        double r803495 = x;
        double r803496 = z;
        double r803497 = r803495 + r803496;
        double r803498 = r803496 - r803495;
        double r803499 = r803498 / r803494;
        double r803500 = r803497 * r803499;
        double r803501 = r803494 - r803500;
        double r803502 = 2.0;
        double r803503 = r803501 / r803502;
        return r803503;
}

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

Original28.2
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 28.2

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

  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 2020047 +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)))