Average Error: 0.4 → 0.4
Time: 8.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r2319 = 3.0;
        double r2320 = x;
        double r2321 = sqrt(r2320);
        double r2322 = r2319 * r2321;
        double r2323 = y;
        double r2324 = 1.0;
        double r2325 = 9.0;
        double r2326 = r2320 * r2325;
        double r2327 = r2324 / r2326;
        double r2328 = r2323 + r2327;
        double r2329 = r2328 - r2324;
        double r2330 = r2322 * r2329;
        return r2330;
}
↓
double f(double x, double y) {
        double r2331 = y;
        double r2332 = 1.0;
        double r2333 = x;
        double r2334 = 9.0;
        double r2335 = r2333 * r2334;
        double r2336 = r2332 / r2335;
        double r2337 = r2331 + r2336;
        double r2338 = r2337 - r2332;
        double r2339 = 3.0;
        double r2340 = sqrt(r2333);
        double r2341 = r2339 * r2340;
        double r2342 = r2338 * r2341;
        return r2342;
}

Error

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Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.4

    \[\leadsto \color{blue}{\left(1 \cdot 3\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]

  6. Applied associate-*l*0.4

    \[\leadsto \color{blue}{1 \cdot \left(3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right)}\]

  7. Simplified0.4

    \[\leadsto 1 \cdot \color{blue}{\left(\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \sqrt{x}\right)\right)}\]

  8. Final simplification0.4

    \[\leadsto \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))