Average Error: 0.4 → 0.4
Time: 17.3s
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 r459410 = 3.0;
        double r459411 = x;
        double r459412 = sqrt(r459411);
        double r459413 = r459410 * r459412;
        double r459414 = y;
        double r459415 = 1.0;
        double r459416 = 9.0;
        double r459417 = r459411 * r459416;
        double r459418 = r459415 / r459417;
        double r459419 = r459414 + r459418;
        double r459420 = r459419 - r459415;
        double r459421 = r459413 * r459420;
        return r459421;
}
↓
double f(double x, double y) {
        double r459422 = 3.0;
        double r459423 = x;
        double r459424 = sqrt(r459423);
        double r459425 = y;
        double r459426 = 1.0;
        double r459427 = 9.0;
        double r459428 = r459423 * r459427;
        double r459429 = r459426 / r459428;
        double r459430 = r459425 + r459429;
        double r459431 = r459430 - r459426;
        double r459432 = r459424 * r459431;
        double r459433 = r459422 * r459432;
        return r459433;
}

Error

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Bits error versus y

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Results

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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 2020046 
(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)))