Average Error: 0.4 → 0.4
Time: 23.5s
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 r283538 = 3.0;
        double r283539 = x;
        double r283540 = sqrt(r283539);
        double r283541 = r283538 * r283540;
        double r283542 = y;
        double r283543 = 1.0;
        double r283544 = 9.0;
        double r283545 = r283539 * r283544;
        double r283546 = r283543 / r283545;
        double r283547 = r283542 + r283546;
        double r283548 = r283547 - r283543;
        double r283549 = r283541 * r283548;
        return r283549;
}
↓
double f(double x, double y) {
        double r283550 = 3.0;
        double r283551 = x;
        double r283552 = sqrt(r283551);
        double r283553 = y;
        double r283554 = 1.0;
        double r283555 = 9.0;
        double r283556 = r283551 * r283555;
        double r283557 = r283554 / r283556;
        double r283558 = r283553 + r283557;
        double r283559 = r283558 - r283554;
        double r283560 = r283552 * r283559;
        double r283561 = r283550 * r283560;
        return r283561;
}

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 2019323 
(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)))