Average Error: 26.3 → 0.1
Time: 15.3s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{x + z}}}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{\frac{y}{x + z}}}{2.0}
double f(double x, double y, double z) {
        double r29835752 = x;
        double r29835753 = r29835752 * r29835752;
        double r29835754 = y;
        double r29835755 = r29835754 * r29835754;
        double r29835756 = r29835753 + r29835755;
        double r29835757 = z;
        double r29835758 = r29835757 * r29835757;
        double r29835759 = r29835756 - r29835758;
        double r29835760 = 2.0;
        double r29835761 = r29835754 * r29835760;
        double r29835762 = r29835759 / r29835761;
        return r29835762;
}
↓
double f(double x, double y, double z) {
        double r29835763 = y;
        double r29835764 = x;
        double r29835765 = z;
        double r29835766 = r29835764 - r29835765;
        double r29835767 = r29835764 + r29835765;
        double r29835768 = r29835763 / r29835767;
        double r29835769 = r29835766 / r29835768;
        double r29835770 = r29835763 + r29835769;
        double r29835771 = 2.0;
        double r29835772 = r29835770 / r29835771;
        return r29835772;
}

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

Original26.3
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 26.3

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}}\]

  3. Final simplification0.1

    \[\leadsto \frac{y + \frac{x - z}{\frac{y}{x + z}}}{2.0}\]

Reproduce

herbie shell --seed 2019162 
(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)))