Average Error: 28.3 → 0.2
Time: 19.7s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}
double f(double x, double y, double z) {
        double r28769479 = x;
        double r28769480 = r28769479 * r28769479;
        double r28769481 = y;
        double r28769482 = r28769481 * r28769481;
        double r28769483 = r28769480 + r28769482;
        double r28769484 = z;
        double r28769485 = r28769484 * r28769484;
        double r28769486 = r28769483 - r28769485;
        double r28769487 = 2.0;
        double r28769488 = r28769481 * r28769487;
        double r28769489 = r28769486 / r28769488;
        return r28769489;
}
↓
double f(double x, double y, double z) {
        double r28769490 = y;
        double r28769491 = x;
        double r28769492 = z;
        double r28769493 = r28769491 - r28769492;
        double r28769494 = r28769492 + r28769491;
        double r28769495 = r28769490 / r28769494;
        double r28769496 = r28769493 / r28769495;
        double r28769497 = r28769490 + r28769496;
        double r28769498 = 2.0;
        double r28769499 = r28769497 / r28769498;
        return r28769499;
}

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

Original28.3
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 28.3

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

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{\frac{x - z}{\frac{y}{z + x}} + y}{2}}\]

  3. Final simplification0.2

    \[\leadsto \frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}\]

Reproduce

herbie shell --seed 2019169 +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)))