Average Error: 28.2 → 0.2
Time: 18.9s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2}
double f(double x, double y, double z) {
        double r36178384 = x;
        double r36178385 = r36178384 * r36178384;
        double r36178386 = y;
        double r36178387 = r36178386 * r36178386;
        double r36178388 = r36178385 + r36178387;
        double r36178389 = z;
        double r36178390 = r36178389 * r36178389;
        double r36178391 = r36178388 - r36178390;
        double r36178392 = 2.0;
        double r36178393 = r36178386 * r36178392;
        double r36178394 = r36178391 / r36178393;
        return r36178394;
}
↓
double f(double x, double y, double z) {
        double r36178395 = y;
        double r36178396 = x;
        double r36178397 = z;
        double r36178398 = r36178396 - r36178397;
        double r36178399 = r36178398 / r36178395;
        double r36178400 = r36178396 + r36178397;
        double r36178401 = r36178399 * r36178400;
        double r36178402 = r36178395 + r36178401;
        double r36178403 = 2.0;
        double r36178404 = r36178402 / r36178403;
        return r36178404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original28.2
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 28.2

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

  2. Simplified0.1

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

  4. Applied associate-/r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 
(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)))