Average Error: 24.9 → 7.2
Time: 7.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (x * y)) * z)) / ((double) sqrt(((double) (((double) (z * z)) - ((double) (t * a))))))));
}

↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((z <= -3.38525079024628e+116)) {
		VAR = ((double) (y * ((double) (x / ((double) (((double) (((double) (0.5 * ((double) (((double) (a / z)) * t)))) - z)) / z))))));
	} else {
		double VAR_1;
		if ((z <= 1.2268572723557027e-234)) {
			VAR_1 = ((double) (y * ((double) (z * ((double) (x / ((double) sqrt(((double) (((double) (z * z)) - ((double) (a * t))))))))))));
		} else {
			double VAR_2;
			if (((z <= 1.3233303272720813e-182) || !(z <= 1.584046164603484e+132))) {
				VAR_2 = ((double) (y * ((double) (x / ((double) (((double) (z + ((double) (((double) (((double) (a / z)) * t)) * -0.5)))) / z))))));
			} else {
				VAR_2 = ((double) (y * ((double) (x / ((double) (((double) sqrt(((double) (((double) (z * z)) - ((double) (a * t)))))) / z))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original24.9
Target7.8
Herbie7.2
\[\]
Derivation
  1. Split input into 4 regimes
  2. if  z  < -3.3852507902462798e116
    1. Initial program 46.3
      \[\]
    2. Simplified44.0
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt44.2
      \[\leadsto \]
    5. Applied associate-*l*44.2
      \[\leadsto \]
    6. Simplified44.2
      \[\leadsto \]
    7. Using strategy rm
    8. Applied pow144.2
      \[\leadsto \]
    9. Applied pow144.2
      \[\leadsto \]
    10. Applied pow-prod-down44.2
      \[\leadsto \]
    11. Applied pow144.2
      \[\leadsto \]
    12. Applied pow-prod-down44.2
      \[\leadsto \]
    13. Applied pow144.2
      \[\leadsto \]
    14. Applied pow144.2
      \[\leadsto \]
    15. Applied pow-prod-down44.2
      \[\leadsto \]
    16. Applied pow-prod-down44.2
      \[\leadsto \]
    17. Simplified44.0
      \[\leadsto \]
    18. Taylor expanded around -inf 6.0
      \[\leadsto \]
    19. Simplified1.6
      \[\leadsto \]
    if -3.3852507902462798e116 <  z  < 1.22685727235570267e-234
    1. Initial program 12.2
      \[\]
    2. Simplified10.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt11.3
      \[\leadsto \]
    5. Applied associate-*l*11.3
      \[\leadsto \]
    6. Simplified10.8
      \[\leadsto \]
    7. Using strategy rm
    8. Applied pow110.8
      \[\leadsto \]
    9. Applied pow110.8
      \[\leadsto \]
    10. Applied pow-prod-down10.8
      \[\leadsto \]
    11. Applied pow110.8
      \[\leadsto \]
    12. Applied pow-prod-down10.8
      \[\leadsto \]
    13. Applied pow110.8
      \[\leadsto \]
    14. Applied pow110.8
      \[\leadsto \]
    15. Applied pow-prod-down10.8
      \[\leadsto \]
    16. Applied pow-prod-down10.8
      \[\leadsto \]
    17. Simplified10.7
      \[\leadsto \]
    18. Using strategy rm
    19. Applied *-un-lft-identity10.7
      \[\leadsto \]
    20. Applied *-un-lft-identity10.7
      \[\leadsto \]
    21. Applied sqrt-prod10.7
      \[\leadsto \]
    22. Applied times-frac10.7
      \[\leadsto \]
    23. Applied *-un-lft-identity10.7
      \[\leadsto \]
    24. Applied times-frac10.7
      \[\leadsto \]
    25. Simplified10.7
      \[\leadsto \]
    26. Simplified12.0
      \[\leadsto \]
    if 1.22685727235570267e-234 <  z  < 1.32333032727208128e-182 or 1.58404616460348404e132 <  z 
    1. Initial program 44.7
      \[\]
    2. Simplified43.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt43.9
      \[\leadsto \]
    5. Applied associate-*l*43.9
      \[\leadsto \]
    6. Simplified43.7
      \[\leadsto \]
    7. Using strategy rm
    8. Applied pow143.7
      \[\leadsto \]
    9. Applied pow143.7
      \[\leadsto \]
    10. Applied pow-prod-down43.7
      \[\leadsto \]
    11. Applied pow143.7
      \[\leadsto \]
    12. Applied pow-prod-down43.7
      \[\leadsto \]
    13. Applied pow143.7
      \[\leadsto \]
    14. Applied pow143.7
      \[\leadsto \]
    15. Applied pow-prod-down43.7
      \[\leadsto \]
    16. Applied pow-prod-down43.7
      \[\leadsto \]
    17. Simplified43.7
      \[\leadsto \]
    18. Taylor expanded around inf 10.3
      \[\leadsto \]
    19. Simplified6.6
      \[\leadsto \]
    if 1.32333032727208128e-182 <  z  < 1.58404616460348404e132
    1. Initial program 9.0
      \[\]
    2. Simplified5.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt6.6
      \[\leadsto \]
    5. Applied associate-*l*6.6
      \[\leadsto \]
    6. Simplified5.6
      \[\leadsto \]
    7. Using strategy rm
    8. Applied pow15.6
      \[\leadsto \]
    9. Applied pow15.6
      \[\leadsto \]
    10. Applied pow-prod-down5.6
      \[\leadsto \]
    11. Applied pow15.6
      \[\leadsto \]
    12. Applied pow-prod-down5.6
      \[\leadsto \]
    13. Applied pow15.6
      \[\leadsto \]
    14. Applied pow15.6
      \[\leadsto \]
    15. Applied pow-prod-down5.6
      \[\leadsto \]
    16. Applied pow-prod-down5.6
      \[\leadsto \]
    17. Simplified5.6
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification7.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x y z t a)
  :name "Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z -3.1921305903852764e+46) (neg (* y x)) (if (< z 5.976268120920894e+90) (/ (* x z) (/ (sqrt (- (* z z) (* a t))) y)) (* y x)))

  (/ (* (* x y) z) (sqrt (- (* z z) (* t a)))))