Average Error: 28.6 → 0.2
Time: 21.4s
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 r433120 = x;
        double r433121 = r433120 * r433120;
        double r433122 = y;
        double r433123 = r433122 * r433122;
        double r433124 = r433121 + r433123;
        double r433125 = z;
        double r433126 = r433125 * r433125;
        double r433127 = r433124 - r433126;
        double r433128 = 2.0;
        double r433129 = r433122 * r433128;
        double r433130 = r433127 / r433129;
        return r433130;
}
↓
double f(double x, double y, double z) {
        double r433131 = y;
        double r433132 = z;
        double r433133 = x;
        double r433134 = r433132 + r433133;
        double r433135 = r433132 - r433133;
        double r433136 = r433131 / r433135;
        double r433137 = r433134 / r433136;
        double r433138 = r433131 - r433137;
        double r433139 = 2.0;
        double r433140 = r433138 / r433139;
        return r433140;
}

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

Original28.6
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)))