Average Error: 0.4 → 0.4
Time: 4.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}}\right) - 1\right)\]
\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 + \sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}}\right) - 1\right)
double f(double x, double y) {
        double r429438 = 3.0;
        double r429439 = x;
        double r429440 = sqrt(r429439);
        double r429441 = r429438 * r429440;
        double r429442 = y;
        double r429443 = 1.0;
        double r429444 = 9.0;
        double r429445 = r429439 * r429444;
        double r429446 = r429443 / r429445;
        double r429447 = r429442 + r429446;
        double r429448 = r429447 - r429443;
        double r429449 = r429441 * r429448;
        return r429449;
}
↓
double f(double x, double y) {
        double r429450 = 3.0;
        double r429451 = x;
        double r429452 = sqrt(r429451);
        double r429453 = r429450 * r429452;
        double r429454 = y;
        double r429455 = 1.0;
        double r429456 = 9.0;
        double r429457 = r429451 * r429456;
        double r429458 = r429455 / r429457;
        double r429459 = sqrt(r429458);
        double r429460 = r429459 * r429459;
        double r429461 = r429454 + r429460;
        double r429462 = r429461 - r429455;
        double r429463 = r429453 * r429462;
        return r429463;
}

Error

Bits error versus x

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 add-sqr-sqrt0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020018 +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)))