Average Error: 26.9 → 0.1
Time: 10.8s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{z + x}{y} \cdot \left(x - z\right)}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{z + x}{y} \cdot \left(x - z\right)}{2.0}
double f(double x, double y, double z) {
        double r14191027 = x;
        double r14191028 = r14191027 * r14191027;
        double r14191029 = y;
        double r14191030 = r14191029 * r14191029;
        double r14191031 = r14191028 + r14191030;
        double r14191032 = z;
        double r14191033 = r14191032 * r14191032;
        double r14191034 = r14191031 - r14191033;
        double r14191035 = 2.0;
        double r14191036 = r14191029 * r14191035;
        double r14191037 = r14191034 / r14191036;
        return r14191037;
}
↓
double f(double x, double y, double z) {
        double r14191038 = y;
        double r14191039 = z;
        double r14191040 = x;
        double r14191041 = r14191039 + r14191040;
        double r14191042 = r14191041 / r14191038;
        double r14191043 = r14191040 - r14191039;
        double r14191044 = r14191042 * r14191043;
        double r14191045 = r14191038 + r14191044;
        double r14191046 = 2.0;
        double r14191047 = r14191045 / r14191046;
        return r14191047;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original26.9
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 26.9

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{y + \frac{z + x}{y} \cdot \left(x - z\right)}{2.0}}\]

  3. Final simplification0.1

    \[\leadsto \frac{y + \frac{z + x}{y} \cdot \left(x - z\right)}{2.0}\]

Reproduce

herbie shell --seed 2019156 
(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)))