Average Error: 0.4 → 0.4
Time: 50.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(y + \frac{1}{9 \cdot x}\right)\right) \cdot 3 + 1 \cdot \left(\sqrt{x} \cdot \left(-3\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(y + \frac{1}{9 \cdot x}\right)\right) \cdot 3 + 1 \cdot \left(\sqrt{x} \cdot \left(-3\right)\right)
double f(double x, double y) {
        double r24193342 = 3.0;
        double r24193343 = x;
        double r24193344 = sqrt(r24193343);
        double r24193345 = r24193342 * r24193344;
        double r24193346 = y;
        double r24193347 = 1.0;
        double r24193348 = 9.0;
        double r24193349 = r24193343 * r24193348;
        double r24193350 = r24193347 / r24193349;
        double r24193351 = r24193346 + r24193350;
        double r24193352 = r24193351 - r24193347;
        double r24193353 = r24193345 * r24193352;
        return r24193353;
}
↓
double f(double x, double y) {
        double r24193354 = x;
        double r24193355 = sqrt(r24193354);
        double r24193356 = y;
        double r24193357 = 1.0;
        double r24193358 = 9.0;
        double r24193359 = r24193358 * r24193354;
        double r24193360 = r24193357 / r24193359;
        double r24193361 = r24193356 + r24193360;
        double r24193362 = r24193355 * r24193361;
        double r24193363 = 3.0;
        double r24193364 = r24193362 * r24193363;
        double r24193365 = -r24193363;
        double r24193366 = r24193355 * r24193365;
        double r24193367 = r24193357 * r24193366;
        double r24193368 = r24193364 + r24193367;
        return r24193368;
}

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 sub-neg0.4

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

  4. Applied distribute-lft-in0.4

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

  6. Applied associate-*l*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019200 
(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)))