Average Error: 27.4 → 0.1
Time: 16.6s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y - \left(z - x\right) \cdot \frac{z + x}{y}}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y - \left(z - x\right) \cdot \frac{z + x}{y}}{2.0}
double f(double x, double y, double z) {
        double r28130268 = x;
        double r28130269 = r28130268 * r28130268;
        double r28130270 = y;
        double r28130271 = r28130270 * r28130270;
        double r28130272 = r28130269 + r28130271;
        double r28130273 = z;
        double r28130274 = r28130273 * r28130273;
        double r28130275 = r28130272 - r28130274;
        double r28130276 = 2.0;
        double r28130277 = r28130270 * r28130276;
        double r28130278 = r28130275 / r28130277;
        return r28130278;
}
↓
double f(double x, double y, double z) {
        double r28130279 = y;
        double r28130280 = z;
        double r28130281 = x;
        double r28130282 = r28130280 - r28130281;
        double r28130283 = r28130280 + r28130281;
        double r28130284 = r28130283 / r28130279;
        double r28130285 = r28130282 * r28130284;
        double r28130286 = r28130279 - r28130285;
        double r28130287 = 2.0;
        double r28130288 = r28130286 / r28130287;
        return r28130288;
}

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

Original27.4
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 27.4

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{y - \left(z - x\right) \cdot \frac{z + x}{y}}{2.0}}\]

  3. Taylor expanded around 0 12.2

    \[\leadsto \frac{y - \color{blue}{\left(\frac{{z}^{2}}{y} - \frac{{x}^{2}}{y}\right)}}{2.0}\]

  4. Simplified0.1

    \[\leadsto \frac{y - \color{blue}{\frac{z - x}{\frac{y}{z + x}}}}{2.0}\]
  5. Using strategy rm

  6. Applied div-inv0.2

    \[\leadsto \frac{y - \color{blue}{\left(z - x\right) \cdot \frac{1}{\frac{y}{z + x}}}}{2.0}\]

  7. Simplified0.1

    \[\leadsto \frac{y - \left(z - x\right) \cdot \color{blue}{\frac{x + z}{y}}}{2.0}\]

  8. Final simplification0.1

    \[\leadsto \frac{y - \left(z - x\right) \cdot \frac{z + x}{y}}{2.0}\]

Reproduce

herbie shell --seed 2019163 
(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)))