Average Error: 0.2 → 0.3
Time: 4.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r339458 = 1.0;
        double r339459 = x;
        double r339460 = 9.0;
        double r339461 = r339459 * r339460;
        double r339462 = r339458 / r339461;
        double r339463 = r339458 - r339462;
        double r339464 = y;
        double r339465 = 3.0;
        double r339466 = sqrt(r339459);
        double r339467 = r339465 * r339466;
        double r339468 = r339464 / r339467;
        double r339469 = r339463 - r339468;
        return r339469;
}
↓
double f(double x, double y) {
        double r339470 = 1.0;
        double r339471 = 0.1111111111111111;
        double r339472 = x;
        double r339473 = r339471 / r339472;
        double r339474 = r339470 - r339473;
        double r339475 = y;
        double r339476 = 1.0;
        double r339477 = 3.0;
        double r339478 = sqrt(r339472);
        double r339479 = r339477 * r339478;
        double r339480 = r339476 / r339479;
        double r339481 = r339475 * r339480;
        double r339482 = r339474 - r339481;
        return r339482;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 div-inv0.2

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

  4. Taylor expanded around 0 0.3

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]

  5. Final simplification0.3

    \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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)))))