Average Error: 28.6 → 0.1
Time: 13.2s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(x + z\right) \cdot \frac{z - x}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(x + z\right) \cdot \frac{z - x}{y}}{2}
double f(double x, double y, double z) {
        double r633461 = x;
        double r633462 = r633461 * r633461;
        double r633463 = y;
        double r633464 = r633463 * r633463;
        double r633465 = r633462 + r633464;
        double r633466 = z;
        double r633467 = r633466 * r633466;
        double r633468 = r633465 - r633467;
        double r633469 = 2.0;
        double r633470 = r633463 * r633469;
        double r633471 = r633468 / r633470;
        return r633471;
}
↓
double f(double x, double y, double z) {
        double r633472 = y;
        double r633473 = x;
        double r633474 = z;
        double r633475 = r633473 + r633474;
        double r633476 = r633474 - r633473;
        double r633477 = r633476 / r633472;
        double r633478 = r633475 * r633477;
        double r633479 = r633472 - r633478;
        double r633480 = 2.0;
        double r633481 = r633479 / r633480;
        return r633481;
}

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

Original28.6
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 28.6

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +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)))