Average Error: 28.5 → 0.2
Time: 18.4s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}
double f(double x, double y, double z) {
        double r27253267 = x;
        double r27253268 = r27253267 * r27253267;
        double r27253269 = y;
        double r27253270 = r27253269 * r27253269;
        double r27253271 = r27253268 + r27253270;
        double r27253272 = z;
        double r27253273 = r27253272 * r27253272;
        double r27253274 = r27253271 - r27253273;
        double r27253275 = 2.0;
        double r27253276 = r27253269 * r27253275;
        double r27253277 = r27253274 / r27253276;
        return r27253277;
}
↓
double f(double x, double y, double z) {
        double r27253278 = y;
        double r27253279 = x;
        double r27253280 = z;
        double r27253281 = r27253279 - r27253280;
        double r27253282 = r27253280 + r27253279;
        double r27253283 = r27253278 / r27253282;
        double r27253284 = r27253281 / r27253283;
        double r27253285 = r27253278 + r27253284;
        double r27253286 = 2.0;
        double r27253287 = r27253285 / r27253286;
        return r27253287;
}

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

Derivation

  1. Initial program 28.5

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +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)))