Average Error: 0.4 → 0.4
Time: 22.1s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\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 r16427986 = 3.0;
        double r16427987 = x;
        double r16427988 = sqrt(r16427987);
        double r16427989 = r16427986 * r16427988;
        double r16427990 = y;
        double r16427991 = 1.0;
        double r16427992 = 9.0;
        double r16427993 = r16427987 * r16427992;
        double r16427994 = r16427991 / r16427993;
        double r16427995 = r16427990 + r16427994;
        double r16427996 = r16427995 - r16427991;
        double r16427997 = r16427989 * r16427996;
        return r16427997;
}
↓
double f(double x, double y) {
        double r16427998 = 3.0;
        double r16427999 = x;
        double r16428000 = sqrt(r16427999);
        double r16428001 = y;
        double r16428002 = 1.0;
        double r16428003 = 9.0;
        double r16428004 = r16427999 * r16428003;
        double r16428005 = r16428002 / r16428004;
        double r16428006 = r16428001 + r16428005;
        double r16428007 = r16428006 - r16428002;
        double r16428008 = r16428000 * r16428007;
        double r16428009 = r16427998 * r16428008;
        return r16428009;
}

Error

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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. Using strategy rm

  5. Applied *-commutative0.4

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

  6. 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 2019172 +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)))