Average Error: 0.4 → 0.4
Time: 4.7s
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 r418479 = 3.0;
        double r418480 = x;
        double r418481 = sqrt(r418480);
        double r418482 = r418479 * r418481;
        double r418483 = y;
        double r418484 = 1.0;
        double r418485 = 9.0;
        double r418486 = r418480 * r418485;
        double r418487 = r418484 / r418486;
        double r418488 = r418483 + r418487;
        double r418489 = r418488 - r418484;
        double r418490 = r418482 * r418489;
        return r418490;
}
↓
double f(double x, double y) {
        double r418491 = 3.0;
        double r418492 = x;
        double r418493 = sqrt(r418492);
        double r418494 = y;
        double r418495 = 1.0;
        double r418496 = 9.0;
        double r418497 = r418492 * r418496;
        double r418498 = r418495 / r418497;
        double r418499 = r418494 + r418498;
        double r418500 = r418499 - r418495;
        double r418501 = r418493 * r418500;
        double r418502 = r418491 * r418501;
        return r418502;
}

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 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 2020033 +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)))