Average Error: 32.1 → 17.7
Time: 7.4s
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 <= -1.4091069253333409e+150)) {
		VAR = ((double) (1.0 / ((double) (((double) log(base)) / ((double) (((double) log(1.0)) - ((double) log(((double) (-1.0 / re))))))))));
	} else {
		double VAR_1;
		if ((re <= 1.1665438965232749e+122)) {
			VAR_1 = ((double) (1.0 / ((double) (((double) (((double) pow(((double) log(base)), 2.0)) + ((double) (0.0 * 0.0)))) / ((double) (((double) (((double) log(base)) * ((double) log(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))))) + ((double) (0.0 * ((double) atan2(im, re))))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (0.0 * ((double) atan2(im, re)))) + ((double) (((double) log(base)) * ((double) log(re)))))) / ((double) (((double) (0.0 * 0.0)) + ((double) (((double) log(base)) * ((double) log(base))))))));
		}
		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 3 regimes
  2. if  re  < -1.4091069253333409e150
    1. Initial program 62.7
      \[\]
    2. Using strategy rm
    3. Applied clear-num62.7
      \[\leadsto \]
    4. Simplified62.7
      \[\leadsto \]
    5. Taylor expanded around -inf 64.0
      \[\leadsto \]
    6. Simplified7.9
      \[\leadsto \]
    if -1.4091069253333409e150 <  re  < 1.1665438965232749e122
    1. Initial program 21.5
      \[\]
    2. Using strategy rm
    3. Applied clear-num21.5
      \[\leadsto \]
    4. Simplified21.5
      \[\leadsto \]
    if 1.1665438965232749e122 <  re 
    1. Initial program 57.2
      \[\]
    2. Taylor expanded around inf 7.4
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification17.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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))))