Average Error: 0.4 → 0.4
Time: 3.7s
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 r444390 = 3.0;
        double r444391 = x;
        double r444392 = sqrt(r444391);
        double r444393 = r444390 * r444392;
        double r444394 = y;
        double r444395 = 1.0;
        double r444396 = 9.0;
        double r444397 = r444391 * r444396;
        double r444398 = r444395 / r444397;
        double r444399 = r444394 + r444398;
        double r444400 = r444399 - r444395;
        double r444401 = r444393 * r444400;
        return r444401;
}
↓
double f(double x, double y) {
        double r444402 = 3.0;
        double r444403 = x;
        double r444404 = sqrt(r444403);
        double r444405 = y;
        double r444406 = 1.0;
        double r444407 = 9.0;
        double r444408 = r444403 * r444407;
        double r444409 = r444406 / r444408;
        double r444410 = r444405 + r444409;
        double r444411 = r444410 - r444406;
        double r444412 = r444404 * r444411;
        double r444413 = r444402 * r444412;
        return r444413;
}

Error

Bits error versus x

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 2020036 
(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)))