Average Error: 28.8 → 0.1
Time: 55.0s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(z - x\right) \cdot \frac{x + z}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(z - x\right) \cdot \frac{x + z}{y}}{2}
double f(double x, double y, double z) {
        double r35424676 = x;
        double r35424677 = r35424676 * r35424676;
        double r35424678 = y;
        double r35424679 = r35424678 * r35424678;
        double r35424680 = r35424677 + r35424679;
        double r35424681 = z;
        double r35424682 = r35424681 * r35424681;
        double r35424683 = r35424680 - r35424682;
        double r35424684 = 2.0;
        double r35424685 = r35424678 * r35424684;
        double r35424686 = r35424683 / r35424685;
        return r35424686;
}
↓
double f(double x, double y, double z) {
        double r35424687 = y;
        double r35424688 = z;
        double r35424689 = x;
        double r35424690 = r35424688 - r35424689;
        double r35424691 = r35424689 + r35424688;
        double r35424692 = r35424691 / r35424687;
        double r35424693 = r35424690 * r35424692;
        double r35424694 = r35424687 - r35424693;
        double r35424695 = 2.0;
        double r35424696 = r35424694 / r35424695;
        return r35424696;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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

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

  4. Applied associate-/r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(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)))