Average Error: 28.5 → 0.1
Time: 16.7s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y}{2} - \frac{z - x}{y \cdot 2} \cdot \left(z + x\right)\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y}{2} - \frac{z - x}{y \cdot 2} \cdot \left(z + x\right)
double f(double x, double y, double z) {
        double r575548 = x;
        double r575549 = r575548 * r575548;
        double r575550 = y;
        double r575551 = r575550 * r575550;
        double r575552 = r575549 + r575551;
        double r575553 = z;
        double r575554 = r575553 * r575553;
        double r575555 = r575552 - r575554;
        double r575556 = 2.0;
        double r575557 = r575550 * r575556;
        double r575558 = r575555 / r575557;
        return r575558;
}
↓
double f(double x, double y, double z) {
        double r575559 = y;
        double r575560 = 2.0;
        double r575561 = r575559 / r575560;
        double r575562 = z;
        double r575563 = x;
        double r575564 = r575562 - r575563;
        double r575565 = r575559 * r575560;
        double r575566 = r575564 / r575565;
        double r575567 = r575562 + r575563;
        double r575568 = r575566 * r575567;
        double r575569 = r575561 - r575568;
        return r575569;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original28.5
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 28.5

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

  2. Simplified0.1

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

  4. Applied div-sub0.1

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

  5. Simplified0.1

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

  7. Applied associate-/r/0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))