Average Error: 28.2 → 0.2
Time: 9.8s
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 r673367 = x;
        double r673368 = r673367 * r673367;
        double r673369 = y;
        double r673370 = r673369 * r673369;
        double r673371 = r673368 + r673370;
        double r673372 = z;
        double r673373 = r673372 * r673372;
        double r673374 = r673371 - r673373;
        double r673375 = 2.0;
        double r673376 = r673369 * r673375;
        double r673377 = r673374 / r673376;
        return r673377;
}
↓
double f(double x, double y, double z) {
        double r673378 = y;
        double r673379 = x;
        double r673380 = z;
        double r673381 = r673379 + r673380;
        double r673382 = r673380 - r673379;
        double r673383 = r673382 / r673378;
        double r673384 = r673381 * r673383;
        double r673385 = r673378 - r673384;
        double r673386 = 2.0;
        double r673387 = r673385 / r673386;
        return r673387;
}

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)))