Average Error: 0.4 → 0.4
Time: 4.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)
double f(double x, double y) {
        double r396519 = 3.0;
        double r396520 = x;
        double r396521 = sqrt(r396520);
        double r396522 = r396519 * r396521;
        double r396523 = y;
        double r396524 = 1.0;
        double r396525 = 9.0;
        double r396526 = r396520 * r396525;
        double r396527 = r396524 / r396526;
        double r396528 = r396523 + r396527;
        double r396529 = r396528 - r396524;
        double r396530 = r396522 * r396529;
        return r396530;
}
↓
double f(double x, double y) {
        double r396531 = 3.0;
        double r396532 = x;
        double r396533 = sqrt(r396532);
        double r396534 = r396531 * r396533;
        double r396535 = y;
        double r396536 = 1.0;
        double r396537 = r396536 / r396532;
        double r396538 = 9.0;
        double r396539 = r396537 / r396538;
        double r396540 = r396535 + r396539;
        double r396541 = r396540 - r396536;
        double r396542 = r396534 * r396541;
        return r396542;
}

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-/r*0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 +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)))