Average Error: 28.8 → 0.1
Time: 40.3s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2}
double f(double x, double y, double z) {
        double r29850494 = x;
        double r29850495 = r29850494 * r29850494;
        double r29850496 = y;
        double r29850497 = r29850496 * r29850496;
        double r29850498 = r29850495 + r29850497;
        double r29850499 = z;
        double r29850500 = r29850499 * r29850499;
        double r29850501 = r29850498 - r29850500;
        double r29850502 = 2.0;
        double r29850503 = r29850496 * r29850502;
        double r29850504 = r29850501 / r29850503;
        return r29850504;
}
↓
double f(double x, double y, double z) {
        double r29850505 = y;
        double r29850506 = x;
        double r29850507 = z;
        double r29850508 = r29850506 - r29850507;
        double r29850509 = r29850508 / r29850505;
        double r29850510 = r29850506 + r29850507;
        double r29850511 = r29850509 * r29850510;
        double r29850512 = r29850505 + r29850511;
        double r29850513 = 2.0;
        double r29850514 = r29850512 / r29850513;
        return r29850514;
}

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

Original28.8
Target0.2
Herbie0.1
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.8

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}}\]
  3. Using strategy rm

  4. Applied associate-/r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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)))