Average Error: 43.3 → 9.7
Time: 12.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double l, double t) {
	return (sqrt(2.0) * t) / sqrt((((x + 1.0) / (x - 1.0)) * ((l * l) + (2.0 * (t * t)))) - (l * l));
}

↓
double code(double x, double l, double t) {
	double tmp;
	if (t <= -8.77596588101209e+129) {
		tmp = (t * sqrt(2.0)) / ((2.0 * (t / (2.0 * (x * (sqrt(2.0) * x))))) - ((t * sqrt(2.0)) + ((t / sqrt(2.0)) * ((2.0 / x) + (2.0 / (x * x))))));
	} else if ((t <= 3.4253329703721362e-276) || (!(t <= 1.951729093596874e-167) && (t <= 2.2489208127391157e+26))) {
		tmp = (t * sqrt(2.0)) / sqrt((4.0 * ((t * t) / x)) + (2.0 * ((t * t) + ((l / (cbrt(x) * cbrt(x))) * (l / cbrt(x))))));
	} else {
		tmp = (t * sqrt(2.0)) / ((t * sqrt(2.0)) + (((t / (x * x)) * ((2.0 / sqrt(2.0)) - (2.0 / (2.0 * sqrt(2.0))))) + (2.0 * (t / (sqrt(2.0) * x)))));
	}
	return tmp;
}

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  < -8.7759658810120904e129
    1. Initial program 56.2
      \[\]
    2. Taylor expanded around -inf 2.7
      \[\leadsto \]
    3. Simplified2.7
      \[\leadsto \]
    if -8.7759658810120904e129 <  t  < 3.42533297037213622e-276 or 1.95172909359687396e-167 <  t  < 2.24892081273911571e26
    1. Initial program 35.8
      \[\]
    2. Taylor expanded around inf 15.3
      \[\leadsto \]
    3. Simplified15.3
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-cube-cbrt15.3
      \[\leadsto \]
    6. Applied times-frac11.0
      \[\leadsto \]
    if 3.42533297037213622e-276 <  t  < 1.95172909359687396e-167 or 2.24892081273911571e26 <  t 
    1. Initial program 47.1
      \[\]
    2. Taylor expanded around inf 11.7
      \[\leadsto \]
    3. Simplified11.7
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification9.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020338 
(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)))))