Average Error: 28.5 → 0.1
Time: 21.8s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{z - x}{y} \cdot \left(z + x\right)}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{z - x}{y} \cdot \left(z + x\right)}{2}
double f(double x, double y, double z) {
        double r33010014 = x;
        double r33010015 = r33010014 * r33010014;
        double r33010016 = y;
        double r33010017 = r33010016 * r33010016;
        double r33010018 = r33010015 + r33010017;
        double r33010019 = z;
        double r33010020 = r33010019 * r33010019;
        double r33010021 = r33010018 - r33010020;
        double r33010022 = 2.0;
        double r33010023 = r33010016 * r33010022;
        double r33010024 = r33010021 / r33010023;
        return r33010024;
}
↓
double f(double x, double y, double z) {
        double r33010025 = y;
        double r33010026 = z;
        double r33010027 = x;
        double r33010028 = r33010026 - r33010027;
        double r33010029 = r33010028 / r33010025;
        double r33010030 = r33010026 + r33010027;
        double r33010031 = r33010029 * r33010030;
        double r33010032 = r33010025 - r33010031;
        double r33010033 = 2.0;
        double r33010034 = r33010032 / r33010033;
        return r33010034;
}

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 associate-/r/0.1

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

  5. Final simplification0.1

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

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)))