Average Error: 0.4 → 0.4
Time: 4.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\]
\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 + \frac{\frac{1}{x}}{9}\right) - 1\right)
double f(double x, double y) {
        double r392711 = 3.0;
        double r392712 = x;
        double r392713 = sqrt(r392712);
        double r392714 = r392711 * r392713;
        double r392715 = y;
        double r392716 = 1.0;
        double r392717 = 9.0;
        double r392718 = r392712 * r392717;
        double r392719 = r392716 / r392718;
        double r392720 = r392715 + r392719;
        double r392721 = r392720 - r392716;
        double r392722 = r392714 * r392721;
        return r392722;
}
↓
double f(double x, double y) {
        double r392723 = 3.0;
        double r392724 = x;
        double r392725 = sqrt(r392724);
        double r392726 = r392723 * r392725;
        double r392727 = y;
        double r392728 = 1.0;
        double r392729 = r392728 / r392724;
        double r392730 = 9.0;
        double r392731 = r392729 / r392730;
        double r392732 = r392727 + r392731;
        double r392733 = r392732 - r392728;
        double r392734 = r392726 * r392733;
        return r392734;
}

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-/r*0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(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)))