Average Error: 0.4 → 0.4
Time: 16.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)
double f(double x, double y) {
        double r1025467 = 3.0;
        double r1025468 = x;
        double r1025469 = sqrt(r1025468);
        double r1025470 = r1025467 * r1025469;
        double r1025471 = y;
        double r1025472 = 1.0;
        double r1025473 = 9.0;
        double r1025474 = r1025468 * r1025473;
        double r1025475 = r1025472 / r1025474;
        double r1025476 = r1025471 + r1025475;
        double r1025477 = r1025476 - r1025472;
        double r1025478 = r1025470 * r1025477;
        return r1025478;
}
↓
double f(double x, double y) {
        double r1025479 = 3.0;
        double r1025480 = x;
        double r1025481 = sqrt(r1025480);
        double r1025482 = r1025479 * r1025481;
        double r1025483 = y;
        double r1025484 = 1.0;
        double r1025485 = r1025484 / r1025480;
        double r1025486 = 9.0;
        double r1025487 = r1025485 / r1025486;
        double r1025488 = r1025483 + r1025487;
        double r1025489 = r1025488 - r1025484;
        double r1025490 = r1025482 * r1025489;
        return r1025490;
}

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-/r*0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(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)))