Average Error: 0.2 → 0.2
Time: 12.8s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}
double f(double x, double y) {
        double r19733213 = 1.0;
        double r19733214 = x;
        double r19733215 = 9.0;
        double r19733216 = r19733214 * r19733215;
        double r19733217 = r19733213 / r19733216;
        double r19733218 = r19733213 - r19733217;
        double r19733219 = y;
        double r19733220 = 3.0;
        double r19733221 = sqrt(r19733214);
        double r19733222 = r19733220 * r19733221;
        double r19733223 = r19733219 / r19733222;
        double r19733224 = r19733218 - r19733223;
        return r19733224;
}
↓
double f(double x, double y) {
        double r19733225 = 1.0;
        double r19733226 = x;
        double r19733227 = r19733225 / r19733226;
        double r19733228 = 9.0;
        double r19733229 = r19733227 / r19733228;
        double r19733230 = r19733225 - r19733229;
        double r19733231 = y;
        double r19733232 = 3.0;
        double r19733233 = r19733231 / r19733232;
        double r19733234 = sqrt(r19733226);
        double r19733235 = r19733233 / r19733234;
        double r19733236 = r19733230 - r19733235;
        return r19733236;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \color{blue}{\frac{\frac{y}{3.0}}{\sqrt{x}}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

  6. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))