Average Error: 32.7 → 17.8
Time: 18.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double t, double l, double k) {
	return ((double) (2.0 / ((double) (((double) (((double) (((double) (((double) pow(t, 3.0)) / ((double) (l * l)))) * ((double) sin(k)))) * ((double) tan(k)))) * ((double) (((double) (1.0 + ((double) pow(((double) (k / t)), 2.0)))) + 1.0))))));
}

↓
double code(double t, double l, double k) {
	double VAR;
	if ((t <= -4.278232628469712e+22)) {
		VAR = ((double) (2.0 / ((double) (((double) (((double) (((double) (((double) (((double) pow(((double) cbrt(t)), 3.0)) / ((double) (((double) cbrt(l)) * ((double) cbrt(l)))))) * ((double) (((double) pow(((double) cbrt(t)), 3.0)) / ((double) cbrt(l)))))) * ((double) (((double) (((double) cbrt(((double) (((double) pow(((double) cbrt(t)), 3.0)) / l)))) * ((double) cbrt(((double) (((double) pow(((double) cbrt(t)), 3.0)) / l)))))) * ((double) (((double) cbrt(((double) (((double) pow(((double) cbrt(t)), 3.0)) / l)))) * ((double) sin(k)))))))) * ((double) tan(k)))) * ((double) (1.0 + ((double) (1.0 + ((double) pow(((double) (k / t)), 2.0))))))))));
	} else {
		double VAR_1;
		if ((t <= 9.759191564357316e-84)) {
			VAR_1 = ((double) (2.0 / ((double) (((double) (((double) (((double) pow(((double) cbrt(t)), 3.0)) / ((double) (((double) cbrt(l)) * ((double) cbrt(l)))))) * ((double) (((double) pow(((double) cbrt(t)), 3.0)) / ((double) cbrt(l)))))) * ((double) (((double) (((double) pow(((double) cbrt(t)), 3.0)) / l)) * ((double) (((double) sin(k)) * ((double) (((double) tan(k)) * ((double) (1.0 + ((double) (1.0 + ((double) pow(((double) (k / t)), 2.0))))))))))))))));
		} else {
			VAR_1 = ((double) (2.0 / ((double) (((double) (1.0 + ((double) (1.0 + ((double) pow(((double) (k / t)), 2.0)))))) * ((double) (((double) tan(k)) * ((double) (((double) (((double) pow(t, ((double) (3.0 / 2.0)))) / l)) * ((double) (((double) sin(k)) * ((double) (((double) pow(t, ((double) (3.0 / 2.0)))) / l))))))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus t
Bits error versus l
Bits error versus k
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 3 regimes
  2. if  t  < -4.2782326284697117e22
    1. Initial program 23.2
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt23.3
      \[\leadsto \]
    4. Applied unpow-prod-down23.3
      \[\leadsto \]
    5. Applied times-frac16.1
      \[\leadsto \]
    6. Applied associate-*l*14.2
      \[\leadsto \]
    7. Using strategy rm
    8. Applied add-cube-cbrt14.2
      \[\leadsto \]
    9. Applied unpow-prod-down14.2
      \[\leadsto \]
    10. Applied times-frac8.1
      \[\leadsto \]
    11. Using strategy rm
    12. Applied add-cube-cbrt8.1
      \[\leadsto \]
    13. Applied associate-*l*8.1
      \[\leadsto \]
    14. Simplified8.1
      \[\leadsto \]
    if -4.2782326284697117e22 <  t  < 9.75919156435731628e-84
    1. Initial program 51.9
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt52.0
      \[\leadsto \]
    4. Applied unpow-prod-down52.0
      \[\leadsto \]
    5. Applied times-frac44.1
      \[\leadsto \]
    6. Applied associate-*l*42.8
      \[\leadsto \]
    7. Using strategy rm
    8. Applied add-cube-cbrt42.8
      \[\leadsto \]
    9. Applied unpow-prod-down42.8
      \[\leadsto \]
    10. Applied times-frac36.6
      \[\leadsto \]
    11. Using strategy rm
    12. Applied associate-*l*35.8
      \[\leadsto \]
    13. Simplified35.8
      \[\leadsto \]
    14. Using strategy rm
    15. Applied associate-*l*32.2
      \[\leadsto \]
    16. Simplified34.0
      \[\leadsto \]
    if 9.75919156435731628e-84 <  t 
    1. Initial program 23.1
      \[\]
    2. Using strategy rm
    3. Applied sqr-pow23.1
      \[\leadsto \]
    4. Applied times-frac14.4
      \[\leadsto \]
    5. Applied associate-*l*11.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification17.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  :precision binary64
  (/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))