Average Error: 0.2 → 0.2
Time: 27.2s
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 r15325436 = 1.0;
        double r15325437 = x;
        double r15325438 = 9.0;
        double r15325439 = r15325437 * r15325438;
        double r15325440 = r15325436 / r15325439;
        double r15325441 = r15325436 - r15325440;
        double r15325442 = y;
        double r15325443 = 3.0;
        double r15325444 = sqrt(r15325437);
        double r15325445 = r15325443 * r15325444;
        double r15325446 = r15325442 / r15325445;
        double r15325447 = r15325441 - r15325446;
        return r15325447;
}
↓
double f(double x, double y) {
        double r15325448 = 1.0;
        double r15325449 = x;
        double r15325450 = r15325448 / r15325449;
        double r15325451 = 9.0;
        double r15325452 = r15325450 / r15325451;
        double r15325453 = r15325448 - r15325452;
        double r15325454 = y;
        double r15325455 = 3.0;
        double r15325456 = sqrt(r15325449);
        double r15325457 = r15325455 * r15325456;
        double r15325458 = r15325454 / r15325457;
        double r15325459 = r15325453 - r15325458;
        return r15325459;
}

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 2019169 
(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)))))