Average Error: 0.4 → 0.4
Time: 16.9s
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 r468913 = 3.0;
        double r468914 = x;
        double r468915 = sqrt(r468914);
        double r468916 = r468913 * r468915;
        double r468917 = y;
        double r468918 = 1.0;
        double r468919 = 9.0;
        double r468920 = r468914 * r468919;
        double r468921 = r468918 / r468920;
        double r468922 = r468917 + r468921;
        double r468923 = r468922 - r468918;
        double r468924 = r468916 * r468923;
        return r468924;
}
↓
double f(double x, double y) {
        double r468925 = 3.0;
        double r468926 = x;
        double r468927 = sqrt(r468926);
        double r468928 = y;
        double r468929 = 1.0;
        double r468930 = 9.0;
        double r468931 = r468926 * r468930;
        double r468932 = r468929 / r468931;
        double r468933 = r468928 + r468932;
        double r468934 = r468933 - r468929;
        double r468935 = r468927 * r468934;
        double r468936 = r468925 * r468935;
        return r468936;
}

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 2019350 
(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)))