Average Error: 42.8 → 9.3
Time: 7.6s
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 <= -3.2170273163093555e+100)) {
		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 <= -1.7771056583212281e-162)) {
			VAR_1 = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) sqrt(((double) (((double) (4.0 * ((double) (t * ((double) (t / x)))))) + ((double) (2.0 * ((double) (((double) (t * t)) + ((double) (l * ((double) (l / x))))))))))))));
		} else {
			double VAR_2;
			if ((t <= -7.795682222360029e-229)) {
				VAR_2 = ((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_3;
				if ((t <= 1.0593625536365536e-228)) {
					VAR_3 = ((double) (((double) (((double) sqrt(((double) sqrt(2.0)))) * ((double) (t * ((double) sqrt(((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 {
					double VAR_4;
					if (((t <= 3.1695088296437016e-156) || !(t <= 1.6275844446328344e+66))) {
						VAR_4 = ((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))))))))))))))));
					} else {
						VAR_4 = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) sqrt(((double) (((double) (4.0 * ((double) (t * ((double) (t / x)))))) + ((double) (2.0 * ((double) (((double) (t * t)) + ((double) (l * ((double) (l / x))))))))))))));
					}
					VAR_3 = VAR_4;
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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 4 regimes
  2. if  t  < -3.2170273163093555e100 or -1.7771056583212281e-162 <  t  < -7.79568222236002922e-229
    1. Initial program 52.0
      \[\]
    2. Taylor expanded around inf 48.1
      \[\leadsto \]
    3. Simplified46.1
      \[\leadsto \]
    4. Taylor expanded around -inf 7.8
      \[\leadsto \]
    5. Simplified7.8
      \[\leadsto \]
    if -3.2170273163093555e100 <  t  < -1.7771056583212281e-162 or 3.1695088296437016e-156 <  t  < 1.6275844446328344e66
    1. Initial program 27.5
      \[\]
    2. Taylor expanded around inf 9.8
      \[\leadsto \]
    3. Simplified5.1
      \[\leadsto \]
    4. Taylor expanded around 0 9.8
      \[\leadsto \]
    5. Simplified5.1
      \[\leadsto \]
    if -7.79568222236002922e-229 <  t  < 1.0593625536365536e-228
    1. Initial program 63.1
      \[\]
    2. Taylor expanded around inf 31.5
      \[\leadsto \]
    3. Simplified31.1
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-sqr-sqrt31.1
      \[\leadsto \]
    6. Applied sqrt-prod31.2
      \[\leadsto \]
    7. Applied associate-*l*31.2
      \[\leadsto \]
    8. Simplified31.2
      \[\leadsto \]
    if 1.0593625536365536e-228 <  t  < 3.1695088296437016e-156 or 1.6275844446328344e66 <  t 
    1. Initial program 49.0
      \[\]
    2. Taylor expanded around inf 8.6
      \[\leadsto \]
    3. Simplified8.6
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification9.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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)))))