Average Error: 0.4 → 0.4
Time: 14.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \left(\left(y - 1\right) + \frac{1}{9 \cdot x}\right)\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \left(\left(y - 1\right) + \frac{1}{9 \cdot x}\right)\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r312472 = 3.0;
        double r312473 = x;
        double r312474 = sqrt(r312473);
        double r312475 = r312472 * r312474;
        double r312476 = y;
        double r312477 = 1.0;
        double r312478 = 9.0;
        double r312479 = r312473 * r312478;
        double r312480 = r312477 / r312479;
        double r312481 = r312476 + r312480;
        double r312482 = r312481 - r312477;
        double r312483 = r312475 * r312482;
        return r312483;
}
↓
double f(double x, double y) {
        double r312484 = 3.0;
        double r312485 = y;
        double r312486 = 1.0;
        double r312487 = r312485 - r312486;
        double r312488 = 9.0;
        double r312489 = x;
        double r312490 = r312488 * r312489;
        double r312491 = r312486 / r312490;
        double r312492 = r312487 + r312491;
        double r312493 = r312484 * r312492;
        double r312494 = sqrt(r312489);
        double r312495 = r312493 * r312494;
        return r312495;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 *-un-lft-identity0.4

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

  4. Applied times-frac0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019294 
(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)))