Average Error: 28.6 → 0.2
Time: 22.1s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}
double f(double x, double y, double z) {
        double r447152 = x;
        double r447153 = r447152 * r447152;
        double r447154 = y;
        double r447155 = r447154 * r447154;
        double r447156 = r447153 + r447155;
        double r447157 = z;
        double r447158 = r447157 * r447157;
        double r447159 = r447156 - r447158;
        double r447160 = 2.0;
        double r447161 = r447154 * r447160;
        double r447162 = r447159 / r447161;
        return r447162;
}
↓
double f(double x, double y, double z) {
        double r447163 = y;
        double r447164 = z;
        double r447165 = x;
        double r447166 = r447164 + r447165;
        double r447167 = r447164 - r447165;
        double r447168 = r447163 / r447167;
        double r447169 = r447166 / r447168;
        double r447170 = r447163 - r447169;
        double r447171 = 2.0;
        double r447172 = r447170 / r447171;
        return r447172;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original28.6
Target0.1
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.6

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

  2. Simplified12.5

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

  4. Applied difference-of-squares12.5

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

  5. Applied associate-/l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))