Average Error: 0.2 → 0.2
Time: 4.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r371644 = 1.0;
        double r371645 = x;
        double r371646 = 9.0;
        double r371647 = r371645 * r371646;
        double r371648 = r371644 / r371647;
        double r371649 = r371644 - r371648;
        double r371650 = y;
        double r371651 = 3.0;
        double r371652 = sqrt(r371645);
        double r371653 = r371651 * r371652;
        double r371654 = r371650 / r371653;
        double r371655 = r371649 - r371654;
        return r371655;
}
↓
double f(double x, double y) {
        double r371656 = 1.0;
        double r371657 = x;
        double r371658 = 9.0;
        double r371659 = r371657 * r371658;
        double r371660 = r371656 / r371659;
        double r371661 = r371656 - r371660;
        double r371662 = y;
        double r371663 = 3.0;
        double r371664 = r371662 / r371663;
        double r371665 = sqrt(r371657);
        double r371666 = r371664 / r371665;
        double r371667 = r371661 - r371666;
        return r371667;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))