Average Error: 0.4 → 0.4
Time: 5.7s
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 r406473 = 3.0;
        double r406474 = x;
        double r406475 = sqrt(r406474);
        double r406476 = r406473 * r406475;
        double r406477 = y;
        double r406478 = 1.0;
        double r406479 = 9.0;
        double r406480 = r406474 * r406479;
        double r406481 = r406478 / r406480;
        double r406482 = r406477 + r406481;
        double r406483 = r406482 - r406478;
        double r406484 = r406476 * r406483;
        return r406484;
}
↓
double f(double x, double y) {
        double r406485 = 3.0;
        double r406486 = x;
        double r406487 = sqrt(r406486);
        double r406488 = y;
        double r406489 = 1.0;
        double r406490 = 9.0;
        double r406491 = r406486 * r406490;
        double r406492 = r406489 / r406491;
        double r406493 = r406488 + r406492;
        double r406494 = r406493 - r406489;
        double r406495 = r406487 * r406494;
        double r406496 = r406485 * r406495;
        return r406496;
}

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 2020002 
(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)))