Average Error: 25.3 → 25.3
Time: 3.1s
Precision: binary64
\[\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}\]
↓
\[\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}\]
\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}
↓
\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}
double code(double t, double x, double l) {
	return ((double) (((double) (t * ((double) sqrt(((double) (x - 1.0)))))) / ((double) (((double) (l * l)) + ((double) (((double) (((double) (x + 1.0)) * t)) * t))))));
}
↓
double code(double t, double x, double l) {
	return ((double) (((double) (t * ((double) sqrt(((double) (x - 1.0)))))) / ((double) (((double) (l * l)) + ((double) (((double) (((double) (x + 1.0)) * t)) * t))))));
}

Error

Bits error versus t

Bits error versus x

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.3

    \[\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}\]

  2. Final simplification25.3

    \[\leadsto \frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (t x l)
  :name "(/ (* t (sqrt (- x 1))) (+ (* l l) (* (* (+ x 1) t) t)))"
  :precision binary64
  (/ (* t (sqrt (- x 1.0))) (+ (* l l) (* (* (+ x 1.0) t) t))))