Average Error: 28.5 → 0.1
Time: 20.8s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}
double f(double x, double y, double z) {
        double r42784170 = x;
        double r42784171 = r42784170 * r42784170;
        double r42784172 = y;
        double r42784173 = r42784172 * r42784172;
        double r42784174 = r42784171 + r42784173;
        double r42784175 = z;
        double r42784176 = r42784175 * r42784175;
        double r42784177 = r42784174 - r42784176;
        double r42784178 = 2.0;
        double r42784179 = r42784172 * r42784178;
        double r42784180 = r42784177 / r42784179;
        return r42784180;
}
↓
double f(double x, double y, double z) {
        double r42784181 = y;
        double r42784182 = x;
        double r42784183 = z;
        double r42784184 = r42784182 + r42784183;
        double r42784185 = r42784182 - r42784183;
        double r42784186 = r42784181 / r42784185;
        double r42784187 = r42784184 / r42784186;
        double r42784188 = r42784181 + r42784187;
        double r42784189 = 2.0;
        double r42784190 = r42784188 / r42784189;
        return r42784190;
}

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

Original28.5
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 28.5

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

  2. Simplified12.7

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

  4. Applied difference-of-squares12.7

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

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))