Average Error: 0.2 → 0.3
Time: 8.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r409023 = 1.0;
        double r409024 = x;
        double r409025 = 9.0;
        double r409026 = r409024 * r409025;
        double r409027 = r409023 / r409026;
        double r409028 = r409023 - r409027;
        double r409029 = y;
        double r409030 = 3.0;
        double r409031 = sqrt(r409024);
        double r409032 = r409030 * r409031;
        double r409033 = r409029 / r409032;
        double r409034 = r409028 - r409033;
        return r409034;
}
↓
double f(double x, double y) {
        double r409035 = 1.0;
        double r409036 = 0.1111111111111111;
        double r409037 = x;
        double r409038 = r409036 / r409037;
        double r409039 = r409035 - r409038;
        double r409040 = y;
        double r409041 = 3.0;
        double r409042 = sqrt(r409037);
        double r409043 = r409041 * r409042;
        double r409044 = r409040 / r409043;
        double r409045 = r409039 - r409044;
        return r409045;
}

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

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.3

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111049432054187491303309798}{x}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

  3. Final simplification0.3

    \[\leadsto \left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Reproduce

herbie shell --seed 2020001 +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)))))