Average Error: 28.2 → 0.2
Time: 12.2s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{\frac{x + z}{y} \cdot \left(x - z\right) + y}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{\frac{x + z}{y} \cdot \left(x - z\right) + y}{2}
double f(double x, double y, double z) {
        double r593773 = x;
        double r593774 = r593773 * r593773;
        double r593775 = y;
        double r593776 = r593775 * r593775;
        double r593777 = r593774 + r593776;
        double r593778 = z;
        double r593779 = r593778 * r593778;
        double r593780 = r593777 - r593779;
        double r593781 = 2.0;
        double r593782 = r593775 * r593781;
        double r593783 = r593780 / r593782;
        return r593783;
}
↓
double f(double x, double y, double z) {
        double r593784 = x;
        double r593785 = z;
        double r593786 = r593784 + r593785;
        double r593787 = y;
        double r593788 = r593786 / r593787;
        double r593789 = r593784 - r593785;
        double r593790 = r593788 * r593789;
        double r593791 = r593790 + r593787;
        double r593792 = 2.0;
        double r593793 = r593791 / r593792;
        return r593793;
}

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

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x + z}{y}, x - z, y\right)}{2}}\]
  3. Using strategy rm

  4. Applied fma-udef0.2

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

  5. Final simplification0.2

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

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)))