Average Error: 0.4 → 0.4
Time: 3.8s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\sqrt{3 \cdot \left(3 \cdot x\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\sqrt{3 \cdot \left(3 \cdot x\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (* 3.0 (* 3.0 x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
double code(double x, double y) {
	return ((double) (((double) (3.0 * ((double) sqrt(x)))) * ((double) (((double) (y + (1.0 / ((double) (x * 9.0))))) - 1.0))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (3.0 * ((double) (3.0 * x)))))) * ((double) (((double) (y + (1.0 / ((double) (x * 9.0))))) - 1.0))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary640.7

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

  5. Applied sqrt-unprod_binary640.5

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020210 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))