Average Error: 42.7 → 9.8
Time: 10.6s
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 <= -1.9106906643099877e+104)) {
		VAR = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) (((double) (((double) (t / ((double) (x * x)))) * ((double) (((double) (2.0 / ((double) (2.0 * ((double) sqrt(2.0)))))) - ((double) (2.0 / ((double) sqrt(2.0)))))))) - ((double) (((double) (t * ((double) sqrt(2.0)))) + ((double) (2.0 * ((double) (t / ((double) (((double) sqrt(2.0)) * x))))))))))));
	} else {
		double VAR_1;
		if ((t <= -6.734784418776994e-167)) {
			VAR_1 = ((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_2;
			if ((t <= -3.3122382461118694e-302)) {
				VAR_2 = ((double) (((double) (t * ((double) sqrt(2.0)))) / ((double) (((double) (((double) (t / ((double) (x * x)))) * ((double) (((double) (2.0 / ((double) (2.0 * ((double) sqrt(2.0)))))) - ((double) (2.0 / ((double) sqrt(2.0)))))))) - ((double) (((double) (t * ((double) sqrt(2.0)))) + ((double) (2.0 * ((double) (t / ((double) (((double) sqrt(2.0)) * x))))))))))));
			} else {
				double VAR_3;
				if ((t <= 1.5420897965086547e+40)) {
					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 {
					VAR_3 = ((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_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 3 regimes
  2. if  t  < -1.91069066430998772e104 or -6.73478441877699396e-167 <  t  < -3.31223824611186937e-302
    1. Initial program 53.8
      \[\]
    2. Taylor expanded around -inf 12.6
      \[\leadsto \]
    3. Simplified12.6
      \[\leadsto \]
    if -1.91069066430998772e104 <  t  < -6.73478441877699396e-167 or -3.31223824611186937e-302 <  t  < 1.5420897965086547e40
    1. Initial program 34.9
      \[\]
    2. Taylor expanded around inf 14.3
      \[\leadsto \]
    3. Simplified10.6
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-sqr-sqrt10.6
      \[\leadsto \]
    6. Applied sqrt-prod10.8
      \[\leadsto \]
    7. Applied associate-*l*10.7
      \[\leadsto \]
    8. Simplified10.7
      \[\leadsto \]
    if 1.5420897965086547e40 <  t 
    1. Initial program 44.5
      \[\]
    2. Taylor expanded around inf 42.4
      \[\leadsto \]
    3. Simplified39.5
      \[\leadsto \]
    4. Taylor expanded around inf 5.1
      \[\leadsto \]
    5. Simplified5.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification9.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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)))))