Average Error: 0.4 → 0.4
Time: 19.6s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\frac{0.1111111111111111}{x} + y\right) + \left(-1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\frac{0.1111111111111111}{x} + y\right) + \left(-1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r22446616 = 3.0;
        double r22446617 = x;
        double r22446618 = sqrt(r22446617);
        double r22446619 = r22446616 * r22446618;
        double r22446620 = y;
        double r22446621 = 1.0;
        double r22446622 = 9.0;
        double r22446623 = r22446617 * r22446622;
        double r22446624 = r22446621 / r22446623;
        double r22446625 = r22446620 + r22446624;
        double r22446626 = r22446625 - r22446621;
        double r22446627 = r22446619 * r22446626;
        return r22446627;
}
↓
double f(double x, double y) {
        double r22446628 = 3.0;
        double r22446629 = x;
        double r22446630 = sqrt(r22446629);
        double r22446631 = r22446628 * r22446630;
        double r22446632 = 0.1111111111111111;
        double r22446633 = r22446632 / r22446629;
        double r22446634 = y;
        double r22446635 = r22446633 + r22446634;
        double r22446636 = r22446631 * r22446635;
        double r22446637 = 1.0;
        double r22446638 = -r22446637;
        double r22446639 = r22446638 * r22446631;
        double r22446640 = r22446636 + r22446639;
        return r22446640;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.4
Herbie0.4
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.4

    \[\leadsto \left(3.0 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\left(y + \frac{1.0}{x \cdot 9.0}\right) + \left(-1.0\right)\right)}\]

  4. Applied distribute-lft-in0.4

    \[\leadsto \color{blue}{\left(3.0 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right) + \left(3.0 \cdot \sqrt{x}\right) \cdot \left(-1.0\right)}\]

  5. Taylor expanded around 0 0.4

    \[\leadsto \left(3.0 \cdot \sqrt{x}\right) \cdot \left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) + \left(3.0 \cdot \sqrt{x}\right) \cdot \left(-1.0\right)\]

  6. Final simplification0.4

    \[\leadsto \left(3.0 \cdot \sqrt{x}\right) \cdot \left(\frac{0.1111111111111111}{x} + y\right) + \left(-1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)\]

Reproduce

herbie shell --seed 2019168 +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)))