Average Error: 28.9 → 0.2
Time: 11.8s
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 r794165 = x;
        double r794166 = r794165 * r794165;
        double r794167 = y;
        double r794168 = r794167 * r794167;
        double r794169 = r794166 + r794168;
        double r794170 = z;
        double r794171 = r794170 * r794170;
        double r794172 = r794169 - r794171;
        double r794173 = 2.0;
        double r794174 = r794167 * r794173;
        double r794175 = r794172 / r794174;
        return r794175;
}
↓
double f(double x, double y, double z) {
        double r794176 = y;
        double r794177 = z;
        double r794178 = x;
        double r794179 = r794177 + r794178;
        double r794180 = r794178 - r794177;
        double r794181 = r794180 / r794176;
        double r794182 = r794179 * r794181;
        double r794183 = r794176 + r794182;
        double r794184 = 2.0;
        double r794185 = r794183 / r794184;
        return r794185;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original28.9
Target0.2
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 28.9

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

  2. Simplified12.7

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

  4. Applied *-un-lft-identity12.7

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

  5. Applied difference-of-squares12.7

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

  6. Applied times-frac0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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)))