Average Error: 28.3 → 0.2
Time: 20.0s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{\frac{\frac{y}{x + z}}{z - x} \cdot \left(z - x\right)}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{\frac{\frac{y}{x + z}}{z - x} \cdot \left(z - x\right)}}{2}
double f(double x, double y, double z) {
        double r36518170 = x;
        double r36518171 = r36518170 * r36518170;
        double r36518172 = y;
        double r36518173 = r36518172 * r36518172;
        double r36518174 = r36518171 + r36518173;
        double r36518175 = z;
        double r36518176 = r36518175 * r36518175;
        double r36518177 = r36518174 - r36518176;
        double r36518178 = 2.0;
        double r36518179 = r36518172 * r36518178;
        double r36518180 = r36518177 / r36518179;
        return r36518180;
}
↓
double f(double x, double y, double z) {
        double r36518181 = y;
        double r36518182 = x;
        double r36518183 = z;
        double r36518184 = r36518182 - r36518183;
        double r36518185 = r36518182 + r36518183;
        double r36518186 = r36518181 / r36518185;
        double r36518187 = r36518183 - r36518182;
        double r36518188 = r36518186 / r36518187;
        double r36518189 = r36518188 * r36518187;
        double r36518190 = r36518184 / r36518189;
        double r36518191 = r36518181 + r36518190;
        double r36518192 = 2.0;
        double r36518193 = r36518191 / r36518192;
        return r36518193;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original28.3
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 28.3

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

  2. Simplified0.2

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

  4. Applied flip-+13.0

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

  5. Applied associate-/r/13.0

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019169 
(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)))