Average Error: 0.2 → 0.2
Time: 16.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\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 r1130980 = 1.0;
        double r1130981 = x;
        double r1130982 = 9.0;
        double r1130983 = r1130981 * r1130982;
        double r1130984 = r1130980 / r1130983;
        double r1130985 = r1130980 - r1130984;
        double r1130986 = y;
        double r1130987 = 3.0;
        double r1130988 = sqrt(r1130981);
        double r1130989 = r1130987 * r1130988;
        double r1130990 = r1130986 / r1130989;
        double r1130991 = r1130985 - r1130990;
        return r1130991;
}
↓
double f(double x, double y) {
        double r1130992 = 1.0;
        double r1130993 = x;
        double r1130994 = r1130992 / r1130993;
        double r1130995 = 9.0;
        double r1130996 = r1130994 / r1130995;
        double r1130997 = r1130992 - r1130996;
        double r1130998 = y;
        double r1130999 = 3.0;
        double r1131000 = sqrt(r1130993);
        double r1131001 = r1130999 * r1131000;
        double r1131002 = r1130998 / r1131001;
        double r1131003 = r1130997 - r1131002;
        return r1131003;
}

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. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019198 
(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)))))