Average Error: 0.2 → 0.2
Time: 31.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{9 \cdot x}\right) - \frac{1}{\sqrt{x}} \cdot \frac{y}{3}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{9 \cdot x}\right) - \frac{1}{\sqrt{x}} \cdot \frac{y}{3}
double f(double x, double y) {
        double r15454237 = 1.0;
        double r15454238 = x;
        double r15454239 = 9.0;
        double r15454240 = r15454238 * r15454239;
        double r15454241 = r15454237 / r15454240;
        double r15454242 = r15454237 - r15454241;
        double r15454243 = y;
        double r15454244 = 3.0;
        double r15454245 = sqrt(r15454238);
        double r15454246 = r15454244 * r15454245;
        double r15454247 = r15454243 / r15454246;
        double r15454248 = r15454242 - r15454247;
        return r15454248;
}
↓
double f(double x, double y) {
        double r15454249 = 1.0;
        double r15454250 = 9.0;
        double r15454251 = x;
        double r15454252 = r15454250 * r15454251;
        double r15454253 = r15454249 / r15454252;
        double r15454254 = r15454249 - r15454253;
        double r15454255 = 1.0;
        double r15454256 = sqrt(r15454251);
        double r15454257 = r15454255 / r15454256;
        double r15454258 = y;
        double r15454259 = 3.0;
        double r15454260 = r15454258 / r15454259;
        double r15454261 = r15454257 * r15454260;
        double r15454262 = r15454254 - r15454261;
        return r15454262;
}

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

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +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)))))