Average Error: 0.4 → 0.4
Time: 27.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\left(\frac{1 \cdot \sqrt{x}}{x \cdot 9} + \left(-1\right) \cdot \sqrt{x}\right) + \sqrt{x} \cdot y\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\left(\frac{1 \cdot \sqrt{x}}{x \cdot 9} + \left(-1\right) \cdot \sqrt{x}\right) + \sqrt{x} \cdot y\right)
double f(double x, double y) {
        double r518240 = 3.0;
        double r518241 = x;
        double r518242 = sqrt(r518241);
        double r518243 = r518240 * r518242;
        double r518244 = y;
        double r518245 = 1.0;
        double r518246 = 9.0;
        double r518247 = r518241 * r518246;
        double r518248 = r518245 / r518247;
        double r518249 = r518244 + r518248;
        double r518250 = r518249 - r518245;
        double r518251 = r518243 * r518250;
        return r518251;
}
↓
double f(double x, double y) {
        double r518252 = 3.0;
        double r518253 = 1.0;
        double r518254 = x;
        double r518255 = sqrt(r518254);
        double r518256 = r518253 * r518255;
        double r518257 = 9.0;
        double r518258 = r518254 * r518257;
        double r518259 = r518256 / r518258;
        double r518260 = -r518253;
        double r518261 = r518260 * r518255;
        double r518262 = r518259 + r518261;
        double r518263 = y;
        double r518264 = r518255 * r518263;
        double r518265 = r518262 + r518264;
        double r518266 = r518252 * r518265;
        return r518266;
}

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. Simplified0.4

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

  6. Applied distribute-lft-in0.4

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

  8. Applied sub-neg0.4

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

  9. Applied distribute-lft-in0.4

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

  10. Simplified0.4

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019351 +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)))