Average Error: 0.2 → 0.3
Time: 3.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r506218 = 1.0;
        double r506219 = x;
        double r506220 = 9.0;
        double r506221 = r506219 * r506220;
        double r506222 = r506218 / r506221;
        double r506223 = r506218 - r506222;
        double r506224 = y;
        double r506225 = 3.0;
        double r506226 = sqrt(r506219);
        double r506227 = r506225 * r506226;
        double r506228 = r506224 / r506227;
        double r506229 = r506223 - r506228;
        return r506229;
}
↓
double f(double x, double y) {
        double r506230 = 1.0;
        double r506231 = 0.1111111111111111;
        double r506232 = x;
        double r506233 = r506231 / r506232;
        double r506234 = r506230 - r506233;
        double r506235 = y;
        double r506236 = 1.0;
        double r506237 = 3.0;
        double r506238 = sqrt(r506232);
        double r506239 = r506237 * r506238;
        double r506240 = r506236 / r506239;
        double r506241 = r506235 * r506240;
        double r506242 = r506234 - r506241;
        return r506242;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.2
Target0.2
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

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 div-inv0.2

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

  4. Taylor expanded around 0 0.3

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]

  5. Final simplification0.3

    \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))