Average Error: 28.2 → 0.1
Time: 12.6s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{z - x}{\frac{y}{z + x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{z - x}{\frac{y}{z + x}}}{2}
double f(double x, double y, double z) {
        double r632987 = x;
        double r632988 = r632987 * r632987;
        double r632989 = y;
        double r632990 = r632989 * r632989;
        double r632991 = r632988 + r632990;
        double r632992 = z;
        double r632993 = r632992 * r632992;
        double r632994 = r632991 - r632993;
        double r632995 = 2.0;
        double r632996 = r632989 * r632995;
        double r632997 = r632994 / r632996;
        return r632997;
}
↓
double f(double x, double y, double z) {
        double r632998 = y;
        double r632999 = z;
        double r633000 = x;
        double r633001 = r632999 - r633000;
        double r633002 = r632999 + r633000;
        double r633003 = r632998 / r633002;
        double r633004 = r633001 / r633003;
        double r633005 = r632998 - r633004;
        double r633006 = 2.0;
        double r633007 = r633005 / r633006;
        return r633007;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original28.2
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 28.2

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

  2. Simplified0.1

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

  3. Final simplification0.1

    \[\leadsto \frac{y - \frac{z - x}{\frac{y}{z + x}}}{2}\]

Reproduce

herbie shell --seed 2019179 
(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)))