Average Error: 28.5 → 0.2
Time: 19.0s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}
double f(double x, double y, double z) {
        double r27730841 = x;
        double r27730842 = r27730841 * r27730841;
        double r27730843 = y;
        double r27730844 = r27730843 * r27730843;
        double r27730845 = r27730842 + r27730844;
        double r27730846 = z;
        double r27730847 = r27730846 * r27730846;
        double r27730848 = r27730845 - r27730847;
        double r27730849 = 2.0;
        double r27730850 = r27730843 * r27730849;
        double r27730851 = r27730848 / r27730850;
        return r27730851;
}
↓
double f(double x, double y, double z) {
        double r27730852 = y;
        double r27730853 = x;
        double r27730854 = z;
        double r27730855 = r27730853 - r27730854;
        double r27730856 = r27730854 + r27730853;
        double r27730857 = r27730852 / r27730856;
        double r27730858 = r27730855 / r27730857;
        double r27730859 = r27730852 + r27730858;
        double r27730860 = 2.0;
        double r27730861 = r27730859 / r27730860;
        return r27730861;
}

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

Original28.5
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 28.5

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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)))