Average Error: 0.4 → 0.4
Time: 36.1s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)\]
\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(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)
double f(double x, double y) {
        double r253975 = 3.0;
        double r253976 = x;
        double r253977 = sqrt(r253976);
        double r253978 = r253975 * r253977;
        double r253979 = y;
        double r253980 = 1.0;
        double r253981 = 9.0;
        double r253982 = r253976 * r253981;
        double r253983 = r253980 / r253982;
        double r253984 = r253979 + r253983;
        double r253985 = r253984 - r253980;
        double r253986 = r253978 * r253985;
        return r253986;
}
↓
double f(double x, double y) {
        double r253987 = 3.0;
        double r253988 = x;
        double r253989 = sqrt(r253988);
        double r253990 = 1.0;
        double r253991 = 9.0;
        double r253992 = r253988 * r253991;
        double r253993 = r253990 / r253992;
        double r253994 = r253993 - r253990;
        double r253995 = y;
        double r253996 = r253994 + r253995;
        double r253997 = r253989 * r253996;
        double r253998 = r253987 * r253997;
        return r253998;
}

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. Simplified0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019323 +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)))