Average Error: 0.2 → 0.2
Time: 14.3s
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 r14221033 = 1.0;
        double r14221034 = x;
        double r14221035 = 9.0;
        double r14221036 = r14221034 * r14221035;
        double r14221037 = r14221033 / r14221036;
        double r14221038 = r14221033 - r14221037;
        double r14221039 = y;
        double r14221040 = 3.0;
        double r14221041 = sqrt(r14221034);
        double r14221042 = r14221040 * r14221041;
        double r14221043 = r14221039 / r14221042;
        double r14221044 = r14221038 - r14221043;
        return r14221044;
}
↓
double f(double x, double y) {
        double r14221045 = 1.0;
        double r14221046 = x;
        double r14221047 = r14221045 / r14221046;
        double r14221048 = 9.0;
        double r14221049 = r14221047 / r14221048;
        double r14221050 = r14221045 - r14221049;
        double r14221051 = y;
        double r14221052 = 3.0;
        double r14221053 = r14221051 / r14221052;
        double r14221054 = sqrt(r14221046);
        double r14221055 = r14221053 / r14221054;
        double r14221056 = r14221050 - r14221055;
        return r14221056;
}

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

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 +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)))))