Average Error: 26.4 → 0.2
Time: 30.1s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}
double f(double x, double y, double z) {
        double r28745757 = x;
        double r28745758 = r28745757 * r28745757;
        double r28745759 = y;
        double r28745760 = r28745759 * r28745759;
        double r28745761 = r28745758 + r28745760;
        double r28745762 = z;
        double r28745763 = r28745762 * r28745762;
        double r28745764 = r28745761 - r28745763;
        double r28745765 = 2.0;
        double r28745766 = r28745759 * r28745765;
        double r28745767 = r28745764 / r28745766;
        return r28745767;
}
↓
double f(double x, double y, double z) {
        double r28745768 = y;
        double r28745769 = x;
        double r28745770 = z;
        double r28745771 = r28745769 - r28745770;
        double r28745772 = r28745770 + r28745769;
        double r28745773 = r28745768 / r28745772;
        double r28745774 = r28745771 / r28745773;
        double r28745775 = r28745768 + r28745774;
        double r28745776 = 2.0;
        double r28745777 = r28745775 / r28745776;
        return r28745777;
}

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

Original26.4
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 26.4

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019164 +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)))