Average Error: 0.4 → 0.4
Time: 5.0s
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 r394885 = 3.0;
        double r394886 = x;
        double r394887 = sqrt(r394886);
        double r394888 = r394885 * r394887;
        double r394889 = y;
        double r394890 = 1.0;
        double r394891 = 9.0;
        double r394892 = r394886 * r394891;
        double r394893 = r394890 / r394892;
        double r394894 = r394889 + r394893;
        double r394895 = r394894 - r394890;
        double r394896 = r394888 * r394895;
        return r394896;
}
↓
double f(double x, double y) {
        double r394897 = 3.0;
        double r394898 = x;
        double r394899 = sqrt(r394898);
        double r394900 = y;
        double r394901 = 1.0;
        double r394902 = 9.0;
        double r394903 = r394898 * r394902;
        double r394904 = r394901 / r394903;
        double r394905 = r394900 + r394904;
        double r394906 = r394905 - r394901;
        double r394907 = r394899 * r394906;
        double r394908 = r394897 * r394907;
        return r394908;
}

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 2020036 +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)))