Average Error: 32.7 → 17.7
Time: 21.6s
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 <= -3.3013132694615146e-252)) {
		VAR = ((double) (l * ((double) (((double) (1.0 / ((double) pow(((double) (((double) cbrt(t)) * ((double) cbrt(t)))), ((double) (3.0 / 2.0)))))) * ((double) (((double) (l / ((double) pow(((double) (((double) cbrt(t)) * ((double) cbrt(t)))), ((double) (3.0 / 2.0)))))) * ((double) (2.0 / ((double) (((double) sin(k)) * ((double) (((double) tan(k)) * ((double) (((double) (1.0 + ((double) (1.0 + ((double) pow(((double) (k / t)), 2.0)))))) * ((double) pow(((double) cbrt(t)), 3.0))))))))))))))));
	} else {
		double VAR_1;
		if ((t <= 2.2844510146699535e-95)) {
			VAR_1 = ((double) (l * ((double) (l * ((double) (2.0 / ((double) (((double) pow(((double) (((double) cbrt(t)) * ((double) cbrt(t)))), ((double) (3.0 / 2.0)))) * ((double) (((double) sin(k)) * ((double) (((double) (2.0 * ((double) (((double) pow(((double) (1.0 / ((double) pow(((double) (((double) pow(1.0, 2.0)) * ((double) (1.0 / ((double) pow(t, 2.0)))))), 1.0)))), 1.0)) * ((double) (((double) sin(k)) / ((double) cos(k)))))))) + ((double) (((double) sin(k)) * ((double) (((double) (k * k)) / ((double) cos(k))))))))))))))))));
		} else {
			VAR_1 = ((double) (l * ((double) (((double) (1.0 / ((double) pow(((double) (((double) cbrt(t)) * ((double) cbrt(t)))), ((double) (3.0 / 2.0)))))) * ((double) (l * ((double) (2.0 / ((double) (((double) (((double) tan(k)) * ((double) (((double) (1.0 + ((double) (1.0 + ((double) pow(((double) (k / t)), 2.0)))))) * ((double) pow(((double) cbrt(t)), 3.0)))))) * ((double) (((double) pow(((double) (((double) cbrt(t)) * ((double) cbrt(t)))), ((double) (3.0 / 2.0)))) * ((double) sin(k))))))))))))));
		}
		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  < -3.3013132694615146e-252
    1. Initial program 30.8
      \[\]
    2. Simplified31.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt31.6
      \[\leadsto \]
    5. Applied unpow-prod-down31.6
      \[\leadsto \]
    6. Applied associate-*l*29.0
      \[\leadsto \]
    7. Simplified26.3
      \[\leadsto \]
    8. Using strategy rm
    9. Applied sqr-pow26.3
      \[\leadsto \]
    10. Applied associate-*l*22.2
      \[\leadsto \]
    11. Simplified20.6
      \[\leadsto \]
    12. Using strategy rm
    13. Applied *-un-lft-identity20.6
      \[\leadsto \]
    14. Applied times-frac20.4
      \[\leadsto \]
    15. Applied associate-*l*18.3
      \[\leadsto \]
    16. Simplified18.8
      \[\leadsto \]
    17. Using strategy rm
    18. Applied *-un-lft-identity18.8
      \[\leadsto \]
    19. Applied times-frac19.0
      \[\leadsto \]
    20. Applied associate-*r*17.9
      \[\leadsto \]
    21. Simplified17.9
      \[\leadsto \]
    if -3.3013132694615146e-252 <  t  < 2.2844510146699535e-95
    1. Initial program 62.7
      \[\]
    2. Simplified62.6
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt62.6
      \[\leadsto \]
    5. Applied unpow-prod-down62.6
      \[\leadsto \]
    6. Applied associate-*l*56.4
      \[\leadsto \]
    7. Simplified56.4
      \[\leadsto \]
    8. Using strategy rm
    9. Applied sqr-pow56.4
      \[\leadsto \]
    10. Applied associate-*l*40.1
      \[\leadsto \]
    11. Simplified40.1
      \[\leadsto \]
    12. Taylor expanded around inf 32.4
      \[\leadsto \]
    13. Simplified28.3
      \[\leadsto \]
    if 2.2844510146699535e-95 <  t 
    1. Initial program 23.5
      \[\]
    2. Simplified24.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt24.9
      \[\leadsto \]
    5. Applied unpow-prod-down24.9
      \[\leadsto \]
    6. Applied associate-*l*24.1
      \[\leadsto \]
    7. Simplified20.3
      \[\leadsto \]
    8. Using strategy rm
    9. Applied sqr-pow20.3
      \[\leadsto \]
    10. Applied associate-*l*18.8
      \[\leadsto \]
    11. Simplified16.8
      \[\leadsto \]
    12. Using strategy rm
    13. Applied *-un-lft-identity16.8
      \[\leadsto \]
    14. Applied times-frac16.7
      \[\leadsto \]
    15. Applied associate-*l*14.4
      \[\leadsto \]
    16. Simplified15.3
      \[\leadsto \]
    17. Using strategy rm
    18. Applied associate-*r*13.4
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification17.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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))))