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 r409443 = 3.0;
        double r409444 = x;
        double r409445 = sqrt(r409444);
        double r409446 = r409443 * r409445;
        double r409447 = y;
        double r409448 = 1.0;
        double r409449 = 9.0;
        double r409450 = r409444 * r409449;
        double r409451 = r409448 / r409450;
        double r409452 = r409447 + r409451;
        double r409453 = r409452 - r409448;
        double r409454 = r409446 * r409453;
        return r409454;
}
↓
double f(double x, double y) {
        double r409455 = 3.0;
        double r409456 = x;
        double r409457 = sqrt(r409456);
        double r409458 = y;
        double r409459 = 1.0;
        double r409460 = 9.0;
        double r409461 = r409456 * r409460;
        double r409462 = r409459 / r409461;
        double r409463 = r409458 + r409462;
        double r409464 = r409463 - r409459;
        double r409465 = r409457 * r409464;
        double r409466 = r409455 * r409465;
        return r409466;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 2020027 +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)))