Average Error: 0.4 → 0.4
Time: 25.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r332324 = 3.0;
        double r332325 = x;
        double r332326 = sqrt(r332325);
        double r332327 = r332324 * r332326;
        double r332328 = y;
        double r332329 = 1.0;
        double r332330 = 9.0;
        double r332331 = r332325 * r332330;
        double r332332 = r332329 / r332331;
        double r332333 = r332328 + r332332;
        double r332334 = r332333 - r332329;
        double r332335 = r332327 * r332334;
        return r332335;
}
↓
double f(double x, double y) {
        double r332336 = 3.0;
        double r332337 = x;
        double r332338 = sqrt(r332337);
        double r332339 = y;
        double r332340 = 1.0;
        double r332341 = 9.0;
        double r332342 = r332337 * r332341;
        double r332343 = r332340 / r332342;
        double r332344 = r332339 + r332343;
        double r332345 = r332344 - r332340;
        double r332346 = r332338 * r332345;
        double r332347 = r332336 * r332346;
        return r332347;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019323 
(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)))