Average Error: 0.2 → 0.2
Time: 4.6s
Precision: binary64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{-1}{\sqrt{x} \cdot \frac{-3}{y}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{-1}{\sqrt{x} \cdot \frac{-3}{y}}
(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))
↓
(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ -1.0 (* (sqrt x) (/ -3.0 y)))))
double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}
↓
double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (-1.0 / (sqrt(x) * (-3.0 / y)));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

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 clear-num_binary64_116710.2

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

  4. Simplified0.2

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

  6. Applied frac-2neg_binary64_116830.2

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

  7. Simplified0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020356 
(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)))))