Average Error: 0.2 → 0.3
Time: 9.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r300380 = 1.0;
        double r300381 = x;
        double r300382 = 9.0;
        double r300383 = r300381 * r300382;
        double r300384 = r300380 / r300383;
        double r300385 = r300380 - r300384;
        double r300386 = y;
        double r300387 = 3.0;
        double r300388 = sqrt(r300381);
        double r300389 = r300387 * r300388;
        double r300390 = r300386 / r300389;
        double r300391 = r300385 - r300390;
        return r300391;
}
↓
double f(double x, double y) {
        double r300392 = 1.0;
        double r300393 = x;
        double r300394 = r300392 / r300393;
        double r300395 = 9.0;
        double r300396 = r300394 / r300395;
        double r300397 = r300392 - r300396;
        double r300398 = 1.0;
        double r300399 = 3.0;
        double r300400 = r300398 / r300399;
        double r300401 = y;
        double r300402 = sqrt(r300393);
        double r300403 = r300401 / r300402;
        double r300404 = r300400 * r300403;
        double r300405 = r300397 - r300404;
        return r300405;
}

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

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. 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. Using strategy rm

  5. Applied *-un-lft-identity0.2

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

  6. Applied times-frac0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 +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)))))