Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r569252 = 1.0;
        double r569253 = x;
        double r569254 = 9.0;
        double r569255 = r569253 * r569254;
        double r569256 = r569252 / r569255;
        double r569257 = r569252 - r569256;
        double r569258 = y;
        double r569259 = 3.0;
        double r569260 = sqrt(r569253);
        double r569261 = r569259 * r569260;
        double r569262 = r569258 / r569261;
        double r569263 = r569257 - r569262;
        return r569263;
}
↓
double f(double x, double y) {
        double r569264 = 1.0;
        double r569265 = x;
        double r569266 = r569264 / r569265;
        double r569267 = 9.0;
        double r569268 = r569266 / r569267;
        double r569269 = r569264 - r569268;
        double r569270 = y;
        double r569271 = 3.0;
        double r569272 = sqrt(r569265);
        double r569273 = r569271 * r569272;
        double r569274 = r569270 / r569273;
        double r569275 = r569269 - r569274;
        return r569275;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +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)))))