Average Error: 0.2 → 0.2
Time: 12.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r361194 = 1.0;
        double r361195 = x;
        double r361196 = 9.0;
        double r361197 = r361195 * r361196;
        double r361198 = r361194 / r361197;
        double r361199 = r361194 - r361198;
        double r361200 = y;
        double r361201 = 3.0;
        double r361202 = sqrt(r361195);
        double r361203 = r361201 * r361202;
        double r361204 = r361200 / r361203;
        double r361205 = r361199 - r361204;
        return r361205;
}
↓
double f(double x, double y) {
        double r361206 = 1.0;
        double r361207 = x;
        double r361208 = 9.0;
        double r361209 = r361207 * r361208;
        double r361210 = r361206 / r361209;
        double r361211 = r361206 - r361210;
        double r361212 = y;
        double r361213 = 3.0;
        double r361214 = r361212 / r361213;
        double r361215 = sqrt(r361207);
        double r361216 = r361214 / r361215;
        double r361217 = r361211 - r361216;
        return r361217;
}

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
Target0.2
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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020002 +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)))))