Average Error: 0.2 → 0.2
Time: 9.0s
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 r473439 = 1.0;
        double r473440 = x;
        double r473441 = 9.0;
        double r473442 = r473440 * r473441;
        double r473443 = r473439 / r473442;
        double r473444 = r473439 - r473443;
        double r473445 = y;
        double r473446 = 3.0;
        double r473447 = sqrt(r473440);
        double r473448 = r473446 * r473447;
        double r473449 = r473445 / r473448;
        double r473450 = r473444 - r473449;
        return r473450;
}
↓
double f(double x, double y) {
        double r473451 = 1.0;
        double r473452 = 0.1111111111111111;
        double r473453 = x;
        double r473454 = r473452 / r473453;
        double r473455 = r473451 - r473454;
        double r473456 = y;
        double r473457 = 3.0;
        double r473458 = r473456 / r473457;
        double r473459 = sqrt(r473453);
        double r473460 = r473458 / r473459;
        double r473461 = r473455 - r473460;
        return r473461;
}

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. 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 2020024 +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)))))