Average Error: 43.4 → 9.2
Time: 8.4s
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 <= -3.0293523645168547e+106)) {
		VAR = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) (((double) (t / ((double) (((double) sqrt(2.0)) * ((double) (x * x)))))) - ((double) (((double) (t * ((double) sqrt(2.0)))) + ((double) (((double) sqrt(2.0)) * ((double) (t / x))))))))));
	} else {
		double VAR_1;
		if ((t <= 9.838482525780048e+101)) {
			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) sqrt(((double) (((double) (t * t)) + ((double) (l * ((double) (l / x)))))))) * ((double) sqrt(((double) (((double) (t * t)) + ((double) (l * ((double) (l / x))))))))))))))))));
		} else {
			VAR_1 = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) (((double) (t * ((double) sqrt(2.0)))) + ((double) (((double) (((double) sqrt(2.0)) * ((double) (t / x)))) - ((double) (t / ((double) (((double) sqrt(2.0)) * ((double) (x * x))))))))))));
		}
		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  < -3.0293523645168547e106
    1. Initial program 51.7
      \[\]
    2. Taylor expanded around inf 51.9
      \[\leadsto \]
    3. Simplified50.5
      \[\leadsto \]
    4. Taylor expanded around -inf 3.3
      \[\leadsto \]
    5. Simplified3.3
      \[\leadsto \]
    if -3.0293523645168547e106 <  t  < 9.83848252578004774e101
    1. Initial program 38.5
      \[\]
    2. Taylor expanded around inf 17.8
      \[\leadsto \]
    3. Simplified13.3
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-sqr-sqrt13.3
      \[\leadsto \]
    6. Simplified13.3
      \[\leadsto \]
    7. Simplified13.3
      \[\leadsto \]
    if 9.83848252578004774e101 <  t 
    1. Initial program 50.1
      \[\]
    2. Taylor expanded around inf 50.1
      \[\leadsto \]
    3. Simplified48.4
      \[\leadsto \]
    4. Taylor expanded around inf 2.6
      \[\leadsto \]
    5. Simplified2.6
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification9.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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)))))