Average Error: 31.2 → 31.2
Time: 3.2s
Precision: binary64
\[\frac{t \cdot \sqrt{x - 1}}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}}\]
↓
\[\frac{t \cdot \sqrt{x - 1}}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}}\]
\frac{t \cdot \sqrt{x - 1}}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}}
↓
\frac{t \cdot \sqrt{x - 1}}{\sqrt{\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) sqrt(((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) sqrt(((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 31.2

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

  2. Final simplification31.2

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

Reproduce

herbie shell --seed 2020153 
(FPCore (t x l)
  :name "(/ (* t (sqrt (- x 1))) (sqrt (+ (* l l) (* (* (+ x 1) t) t))))"
  :precision binary64
  (/ (* t (sqrt (- x 1.0))) (sqrt (+ (* l l) (* (* (+ x 1.0) t) t)))))