Average Error: 28.9 → 0.2
Time: 44.7s
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 r33659556 = x;
        double r33659557 = r33659556 * r33659556;
        double r33659558 = y;
        double r33659559 = r33659558 * r33659558;
        double r33659560 = r33659557 + r33659559;
        double r33659561 = z;
        double r33659562 = r33659561 * r33659561;
        double r33659563 = r33659560 - r33659562;
        double r33659564 = 2.0;
        double r33659565 = r33659558 * r33659564;
        double r33659566 = r33659563 / r33659565;
        return r33659566;
}
↓
double f(double x, double y, double z) {
        double r33659567 = y;
        double r33659568 = x;
        double r33659569 = z;
        double r33659570 = r33659568 - r33659569;
        double r33659571 = r33659570 / r33659567;
        double r33659572 = r33659568 + r33659569;
        double r33659573 = r33659571 * r33659572;
        double r33659574 = r33659567 + r33659573;
        double r33659575 = 2.0;
        double r33659576 = r33659574 / r33659575;
        return r33659576;
}

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

Original28.9
Target0.1
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 28.9

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

  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 2019165 
(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)))