Average Error: 25.9 → 0.2
Time: 15.1s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}
double f(double x, double y, double z) {
        double r23275990 = x;
        double r23275991 = r23275990 * r23275990;
        double r23275992 = y;
        double r23275993 = r23275992 * r23275992;
        double r23275994 = r23275991 + r23275993;
        double r23275995 = z;
        double r23275996 = r23275995 * r23275995;
        double r23275997 = r23275994 - r23275996;
        double r23275998 = 2.0;
        double r23275999 = r23275992 * r23275998;
        double r23276000 = r23275997 / r23275999;
        return r23276000;
}
↓
double f(double x, double y, double z) {
        double r23276001 = y;
        double r23276002 = x;
        double r23276003 = z;
        double r23276004 = r23276002 - r23276003;
        double r23276005 = r23276004 / r23276001;
        double r23276006 = r23276002 + r23276003;
        double r23276007 = r23276005 * r23276006;
        double r23276008 = r23276001 + r23276007;
        double r23276009 = 2.0;
        double r23276010 = r23276008 / r23276009;
        return r23276010;
}

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

Original25.9
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 25.9

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

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}}\]
  3. Using strategy rm

  4. Applied associate-/r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(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)))