Average Error: 31.8 → 18.0
Time: 7.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double re, double im, double base) {
	return ((double) (((double) (((double) (((double) log(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))) * ((double) log(base)))) + ((double) (((double) atan2(im, re)) * 0.0)))) / ((double) (((double) (((double) log(base)) * ((double) log(base)))) + ((double) (0.0 * 0.0))))));
}

↓
double code(double re, double im, double base) {
	double VAR;
	if ((re <= -1.4211315624829081e+97)) {
		VAR = ((double) (((double) (((double) log(1.0)) - ((double) log(((double) (-1.0 / re)))))) / ((double) log(base))));
	} else {
		double VAR_1;
		if ((re <= -6.096374756574851e-218)) {
			VAR_1 = ((double) (((double) (((double) (((double) log(base)) * ((double) log(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))))) + ((double) (((double) atan2(im, re)) * 0.0)))) / ((double) (((double) (((double) (((double) log(base)) * ((double) log(((double) cbrt(base)))))) + ((double) (2.0 * ((double) (((double) log(base)) * ((double) log(((double) cbrt(base)))))))))) + ((double) (0.0 * 0.0))))));
		} else {
			double VAR_2;
			if ((re <= 1.2704163453201343e-272)) {
				VAR_2 = ((double) (((double) (((double) (((double) atan2(im, re)) * 0.0)) + ((double) (((double) log(base)) * ((double) log(im)))))) / ((double) (((double) (0.0 * 0.0)) + ((double) (((double) log(base)) * ((double) log(base))))))));
			} else {
				double VAR_3;
				if ((re <= 1.0123921509355413e+72)) {
					VAR_3 = ((double) (((double) (((double) (((double) log(base)) * ((double) log(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))))) + ((double) (((double) atan2(im, re)) * 0.0)))) / ((double) (((double) (((double) (((double) log(base)) * ((double) log(((double) cbrt(base)))))) + ((double) (2.0 * ((double) (((double) log(base)) * ((double) log(((double) cbrt(base)))))))))) + ((double) (0.0 * 0.0))))));
				} else {
					VAR_3 = ((double) (((double) log(re)) / ((double) log(base))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus re
Bits error versus im
Bits error versus base
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 4 regimes
  2. if  re  < -1.42113156248290814e97
    1. Initial program 50.2
      \[\]
    2. Taylor expanded around -inf 64.0
      \[\leadsto \]
    3. Simplified9.2
      \[\leadsto \]
    if -1.42113156248290814e97 <  re  < -6.09637475657485064e-218 or 1.2704163453201343e-272 <  re  < 1.0123921509355413e72
    1. Initial program 20.6
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt20.6
      \[\leadsto \]
    4. Applied log-prod20.6
      \[\leadsto \]
    5. Applied distribute-lft-in20.6
      \[\leadsto \]
    6. Simplified20.6
      \[\leadsto \]
    if -6.09637475657485064e-218 <  re  < 1.2704163453201343e-272
    1. Initial program 32.4
      \[\]
    2. Taylor expanded around 0 33.9
      \[\leadsto \]
    if 1.0123921509355413e72 <  re 
    1. Initial program 47.3
      \[\]
    2. Taylor expanded around inf 9.8
      \[\leadsto \]
    3. Simplified9.8
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification18.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (re im base)
  :name "math.log/2 on complex, real part"
  :precision binary64
  (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0))))