Average Error: 0.2 → 0.2
Time: 19.8s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{0.1111111111111111}{x}\right) - \frac{y}{\sqrt{x} \cdot 3.0}\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{0.1111111111111111}{x}\right) - \frac{y}{\sqrt{x} \cdot 3.0}
double f(double x, double y) {
        double r6548426 = 1.0;
        double r6548427 = x;
        double r6548428 = 9.0;
        double r6548429 = r6548427 * r6548428;
        double r6548430 = r6548426 / r6548429;
        double r6548431 = r6548426 - r6548430;
        double r6548432 = y;
        double r6548433 = 3.0;
        double r6548434 = sqrt(r6548427);
        double r6548435 = r6548433 * r6548434;
        double r6548436 = r6548432 / r6548435;
        double r6548437 = r6548431 - r6548436;
        return r6548437;
}
↓
double f(double x, double y) {
        double r6548438 = 1.0;
        double r6548439 = 0.1111111111111111;
        double r6548440 = x;
        double r6548441 = r6548439 / r6548440;
        double r6548442 = r6548438 - r6548441;
        double r6548443 = y;
        double r6548444 = sqrt(r6548440);
        double r6548445 = 3.0;
        double r6548446 = r6548444 * r6548445;
        double r6548447 = r6548443 / r6548446;
        double r6548448 = r6548442 - r6548447;
        return r6548448;
}

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

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. Taylor expanded around 0 0.2

    \[\leadsto \left(1.0 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

  3. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{0.1111111111111111}{x}\right) - \frac{y}{\sqrt{x} \cdot 3.0}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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)))))