Average Error: 0.2 → 0.2
Time: 6.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r454463 = 1.0;
        double r454464 = x;
        double r454465 = 9.0;
        double r454466 = r454464 * r454465;
        double r454467 = r454463 / r454466;
        double r454468 = r454463 - r454467;
        double r454469 = y;
        double r454470 = 3.0;
        double r454471 = sqrt(r454464);
        double r454472 = r454470 * r454471;
        double r454473 = r454469 / r454472;
        double r454474 = r454468 - r454473;
        return r454474;
}
↓
double f(double x, double y) {
        double r454475 = 1.0;
        double r454476 = 0.1111111111111111;
        double r454477 = x;
        double r454478 = r454476 / r454477;
        double r454479 = r454475 - r454478;
        double r454480 = y;
        double r454481 = 3.0;
        double r454482 = r454480 / r454481;
        double r454483 = sqrt(r454477);
        double r454484 = r454482 / r454483;
        double r454485 = r454479 - r454484;
        return r454485;
}

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
Target0.3
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. Taylor expanded around 0 0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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)))))