Average Error: 0.2 → 0.2
Time: 7.7s
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 r358732 = 1.0;
        double r358733 = x;
        double r358734 = 9.0;
        double r358735 = r358733 * r358734;
        double r358736 = r358732 / r358735;
        double r358737 = r358732 - r358736;
        double r358738 = y;
        double r358739 = 3.0;
        double r358740 = sqrt(r358733);
        double r358741 = r358739 * r358740;
        double r358742 = r358738 / r358741;
        double r358743 = r358737 - r358742;
        return r358743;
}
↓
double f(double x, double y) {
        double r358744 = 1.0;
        double r358745 = 0.1111111111111111;
        double r358746 = x;
        double r358747 = r358745 / r358746;
        double r358748 = r358744 - r358747;
        double r358749 = y;
        double r358750 = 3.0;
        double r358751 = r358749 / r358750;
        double r358752 = sqrt(r358746);
        double r358753 = r358751 / r358752;
        double r358754 = r358748 - r358753;
        return r358754;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 +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)))))