Average Error: 0.2 → 0.2
Time: 3.0s
Precision: binary64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{\frac{1}{x}}{\sqrt{9}}}{\sqrt{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{\frac{1}{x}}{\sqrt{9}}}{\sqrt{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}
double code(double x, double y) {
	return ((double) (((double) (1.0 - ((double) (1.0 / ((double) (x * 9.0)))))) - ((double) (y / ((double) (3.0 * ((double) sqrt(x))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 - ((double) (((double) (((double) (1.0 / x)) / ((double) sqrt(9.0)))) / ((double) sqrt(9.0)))))) - ((double) (y / ((double) (3.0 * ((double) sqrt(x))))))));
}

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

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

  5. Applied add-sqr-sqrt0.2

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

  6. Applied associate-/r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020171 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :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)))))