Average Error: 42.9 → 9.0
Time: 7.1s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double l, double t) {
	return ((double) (((double) (((double) sqrt(2.0)) * t)) / ((double) sqrt(((double) (((double) (((double) (((double) (x + 1.0)) / ((double) (x - 1.0)))) * ((double) (((double) (l * l)) + ((double) (2.0 * ((double) (t * t)))))))) - ((double) (l * l))))))));
}

↓
double code(double x, double l, double t) {
	double VAR;
	if ((t <= -2.6108511127275833e+52)) {
		VAR = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) (((double) (2.0 * ((double) (((double) (t / ((double) (x * ((double) (x * ((double) (2.0 * ((double) sqrt(2.0)))))))))) - ((double) (t / ((double) (((double) sqrt(2.0)) * x)))))))) - ((double) (t * ((double) sqrt(2.0))))))));
	} else {
		double VAR_1;
		if ((t <= 7.625086325191854e+80)) {
			VAR_1 = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) sqrt(((double) (((double) (4.0 * ((double) (t / ((double) (x / t)))))) + ((double) (2.0 * ((double) (((double) (t * t)) + ((double) (l / ((double) (x / l))))))))))))));
		} else {
			VAR_1 = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) (((double) (t * ((double) sqrt(2.0)))) + ((double) (((double) (2.0 * ((double) (t / ((double) (((double) sqrt(2.0)) * x)))))) + ((double) (((double) (t / ((double) (x * x)))) * ((double) (((double) (2.0 / ((double) sqrt(2.0)))) - ((double) (2.0 / ((double) (2.0 * ((double) sqrt(2.0))))))))))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus l
Bits error versus t
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 3 regimes
  2. if  t  < -2.6108511127275833e52
    1. Initial program 44.8
      \[\]
    2. Taylor expanded around inf 43.3
      \[\leadsto \]
    3. Simplified40.7
      \[\leadsto \]
    4. Taylor expanded around -inf 3.7
      \[\leadsto \]
    5. Simplified3.7
      \[\leadsto \]
    if -2.6108511127275833e52 <  t  < 7.6250863251918539e80
    1. Initial program 40.6
      \[\]
    2. Taylor expanded around inf 17.6
      \[\leadsto \]
    3. Simplified13.4
      \[\leadsto \]
    if 7.6250863251918539e80 <  t 
    1. Initial program 46.6
      \[\]
    2. Taylor expanded around inf 3.8
      \[\leadsto \]
    3. Simplified3.8
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification9.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x l t)
  :name "Toniolo and Linder, Equation (7)"
  :precision binary64
  (/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))))