Average Error: 0.4 → 0.4
Time: 24.6s
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 r53394895 = 3.0;
        double r53394896 = x;
        double r53394897 = sqrt(r53394896);
        double r53394898 = r53394895 * r53394897;
        double r53394899 = y;
        double r53394900 = 1.0;
        double r53394901 = 9.0;
        double r53394902 = r53394896 * r53394901;
        double r53394903 = r53394900 / r53394902;
        double r53394904 = r53394899 + r53394903;
        double r53394905 = r53394904 - r53394900;
        double r53394906 = r53394898 * r53394905;
        return r53394906;
}
↓
double f(double x, double y) {
        double r53394907 = 3.0;
        double r53394908 = x;
        double r53394909 = sqrt(r53394908);
        double r53394910 = y;
        double r53394911 = 1.0;
        double r53394912 = 9.0;
        double r53394913 = r53394908 * r53394912;
        double r53394914 = r53394911 / r53394913;
        double r53394915 = r53394910 + r53394914;
        double r53394916 = r53394915 - r53394911;
        double r53394917 = r53394909 * r53394916;
        double r53394918 = r53394907 * r53394917;
        return r53394918;
}

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 2019173 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))