Average Error: 28.7 → 0.1
Time: 18.3s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}
double f(double x, double y, double z) {
        double r412062 = x;
        double r412063 = r412062 * r412062;
        double r412064 = y;
        double r412065 = r412064 * r412064;
        double r412066 = r412063 + r412065;
        double r412067 = z;
        double r412068 = r412067 * r412067;
        double r412069 = r412066 - r412068;
        double r412070 = 2.0;
        double r412071 = r412064 * r412070;
        double r412072 = r412069 / r412071;
        return r412072;
}
↓
double f(double x, double y, double z) {
        double r412073 = y;
        double r412074 = z;
        double r412075 = x;
        double r412076 = r412074 + r412075;
        double r412077 = r412074 - r412075;
        double r412078 = r412077 / r412073;
        double r412079 = r412076 * r412078;
        double r412080 = r412073 - r412079;
        double r412081 = 2.0;
        double r412082 = r412080 / r412081;
        return r412082;
}

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

Original28.7
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 28.7

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

  2. Simplified13.0

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

  4. Applied *-un-lft-identity13.0

    \[\leadsto \frac{y - \frac{z \cdot z - x \cdot x}{\color{blue}{1 \cdot y}}}{2}\]

  5. Applied difference-of-squares13.0

    \[\leadsto \frac{y - \frac{\color{blue}{\left(z + x\right) \cdot \left(z - x\right)}}{1 \cdot y}}{2}\]

  6. Applied times-frac0.1

    \[\leadsto \frac{y - \color{blue}{\frac{z + x}{1} \cdot \frac{z - x}{y}}}{2}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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)))