Average Error: 29.1 → 0.0
Time: 21.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (1.0 + ((double) (0.1049934947 * ((double) (x * x)))))) + ((double) (0.0424060604 * ((double) (((double) (x * x)) * ((double) (x * x)))))))) + ((double) (0.0072644182 * ((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0005064034 * ((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0001789971 * ((double) (((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) / ((double) (((double) (((double) (((double) (((double) (((double) (1.0 + ((double) (0.7715471019 * ((double) (x * x)))))) + ((double) (0.2909738639 * ((double) (((double) (x * x)) * ((double) (x * x)))))))) + ((double) (0.0694555761 * ((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0140005442 * ((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0008327945 * ((double) (((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (((double) (2.0 * 0.0001789971)) * ((double) (((double) (((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))))) * x));
}

↓
double code(double x) {
	double VAR;
	if (((x <= -539.4903273549138) || !(x <= 580.0686259485195))) {
		VAR = ((double) (((double) (((double) (0.15298196345929327 / ((double) pow(x, 5.0)))) + ((double) (0.2514179000665375 / ((double) pow(x, 3.0)))))) + ((double) (0.5 / x))));
	} else {
		VAR = ((double) (x * ((double) (((double) (((double) cbrt(((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))))) * ((double) cbrt(((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))))))) * ((double) (((double) cbrt(((double) (((double) cbrt(((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))))) / ((double) (1.0 + ((double) (((double) (x * ((double) (x * 0.7715471019)))) + ((double) (((double) (((double) pow(x, 4.0)) * 0.2909738639)) + ((double) (((double) (((double) pow(x, 6.0)) * 0.0694555761)) + ((double) (((double) (((double) pow(x, 8.0)) * 0.0140005442)) + ((double) (((double) (((double) pow(x, 10.0)) * 0.0008327945)) + ((double) (0.0001789971 * ((double) (2.0 * ((double) pow(x, 12.0)))))))))))))))))))))) * ((double) (((double) cbrt(((double) (((double) cbrt(((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))))) / ((double) (1.0 + ((double) (((double) (x * ((double) (x * 0.7715471019)))) + ((double) (((double) (((double) pow(x, 4.0)) * 0.2909738639)) + ((double) (((double) (((double) pow(x, 6.0)) * 0.0694555761)) + ((double) (((double) (((double) pow(x, 8.0)) * 0.0140005442)) + ((double) (((double) (((double) pow(x, 10.0)) * 0.0008327945)) + ((double) (0.0001789971 * ((double) (2.0 * ((double) pow(x, 12.0)))))))))))))))))))))) * ((double) cbrt(((double) (((double) cbrt(((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))))) / ((double) (1.0 + ((double) (((double) (x * ((double) (x * 0.7715471019)))) + ((double) (((double) (((double) pow(x, 4.0)) * 0.2909738639)) + ((double) (((double) (((double) pow(x, 6.0)) * 0.0694555761)) + ((double) (((double) (((double) pow(x, 8.0)) * 0.0140005442)) + ((double) (((double) (((double) pow(x, 10.0)) * 0.0008327945)) + ((double) (0.0001789971 * ((double) (2.0 * ((double) pow(x, 12.0))))))))))))))))))))))))))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  x  < -539.490327354913802 or 580.068625948519525 <  x 
    1. Initial program 59.3
      \[\]
    2. Simplified59.3
      \[\leadsto \]
    3. Taylor expanded around inf 0.0
      \[\leadsto \]
    4. Simplified0.0
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-+r+0.0
      \[\leadsto \]
    7. Simplified0.0
      \[\leadsto \]
    if -539.490327354913802 <  x  < 580.068625948519525
    1. Initial program 0.0
      \[\]
    2. Simplified0.0
      \[\leadsto \]
    3. Using strategy rm
    4. Applied *-un-lft-identity0.0
      \[\leadsto \]
    5. Applied add-cube-cbrt0.0
      \[\leadsto \]
    6. Applied times-frac0.0
      \[\leadsto \]
    7. Simplified0.0
      \[\leadsto \]
    8. Simplified0.0
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cube-cbrt0.1
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))