Average Error: 0.2 → 0.2
Time: 3.8s
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 r411411 = 1.0;
        double r411412 = x;
        double r411413 = 9.0;
        double r411414 = r411412 * r411413;
        double r411415 = r411411 / r411414;
        double r411416 = r411411 - r411415;
        double r411417 = y;
        double r411418 = 3.0;
        double r411419 = sqrt(r411412);
        double r411420 = r411418 * r411419;
        double r411421 = r411417 / r411420;
        double r411422 = r411416 - r411421;
        return r411422;
}
↓
double f(double x, double y) {
        double r411423 = 1.0;
        double r411424 = x;
        double r411425 = r411423 / r411424;
        double r411426 = 9.0;
        double r411427 = r411425 / r411426;
        double r411428 = r411423 - r411427;
        double r411429 = y;
        double r411430 = 3.0;
        double r411431 = sqrt(r411424);
        double r411432 = r411430 * r411431;
        double r411433 = r411429 / r411432;
        double r411434 = r411428 - r411433;
        return r411434;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 2019353 
(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)))))