Average Error: 0.4 → 0.4
Time: 18.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right) \cdot 3
double f(double x, double y) {
        double r19823447 = 3.0;
        double r19823448 = x;
        double r19823449 = sqrt(r19823448);
        double r19823450 = r19823447 * r19823449;
        double r19823451 = y;
        double r19823452 = 1.0;
        double r19823453 = 9.0;
        double r19823454 = r19823448 * r19823453;
        double r19823455 = r19823452 / r19823454;
        double r19823456 = r19823451 + r19823455;
        double r19823457 = r19823456 - r19823452;
        double r19823458 = r19823450 * r19823457;
        return r19823458;
}
↓
double f(double x, double y) {
        double r19823459 = x;
        double r19823460 = sqrt(r19823459);
        double r19823461 = y;
        double r19823462 = 0.1111111111111111;
        double r19823463 = r19823462 / r19823459;
        double r19823464 = r19823461 + r19823463;
        double r19823465 = 1.0;
        double r19823466 = r19823464 - r19823465;
        double r19823467 = r19823460 * r19823466;
        double r19823468 = 3.0;
        double r19823469 = r19823467 * r19823468;
        return r19823469;
}

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. Taylor expanded around 0 0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111049432054187491303309798}{x}}\right) - 1\right)\]
  3. Using strategy rm

  4. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right)}\]

  5. Final simplification0.4

    \[\leadsto \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right) \cdot 3\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))