Average Error: 0.4 → 0.4
Time: 4.2s
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 r483393 = 3.0;
        double r483394 = x;
        double r483395 = sqrt(r483394);
        double r483396 = r483393 * r483395;
        double r483397 = y;
        double r483398 = 1.0;
        double r483399 = 9.0;
        double r483400 = r483394 * r483399;
        double r483401 = r483398 / r483400;
        double r483402 = r483397 + r483401;
        double r483403 = r483402 - r483398;
        double r483404 = r483396 * r483403;
        return r483404;
}
↓
double f(double x, double y) {
        double r483405 = 3.0;
        double r483406 = x;
        double r483407 = sqrt(r483406);
        double r483408 = y;
        double r483409 = 1.0;
        double r483410 = 9.0;
        double r483411 = r483406 * r483410;
        double r483412 = r483409 / r483411;
        double r483413 = r483408 + r483412;
        double r483414 = r483413 - r483409;
        double r483415 = r483407 * r483414;
        double r483416 = r483405 * r483415;
        return r483416;
}

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 2020039 +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)))