Average Error: 0.2 → 0.2
Time: 18.8s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]
\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 r15193115 = 1.0;
        double r15193116 = x;
        double r15193117 = 9.0;
        double r15193118 = r15193116 * r15193117;
        double r15193119 = r15193115 / r15193118;
        double r15193120 = r15193115 - r15193119;
        double r15193121 = y;
        double r15193122 = 3.0;
        double r15193123 = sqrt(r15193116);
        double r15193124 = r15193122 * r15193123;
        double r15193125 = r15193121 / r15193124;
        double r15193126 = r15193120 - r15193125;
        return r15193126;
}
↓
double f(double x, double y) {
        double r15193127 = 1.0;
        double r15193128 = x;
        double r15193129 = r15193127 / r15193128;
        double r15193130 = 9.0;
        double r15193131 = r15193129 / r15193130;
        double r15193132 = r15193127 - r15193131;
        double r15193133 = y;
        double r15193134 = 3.0;
        double r15193135 = r15193133 / r15193134;
        double r15193136 = sqrt(r15193128);
        double r15193137 = r15193135 / r15193136;
        double r15193138 = r15193132 - r15193137;
        return r15193138;
}

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)))))