Average Error: 31.6 → 17.1
Time: 6.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double re, double im) {
	return ((double) (((double) log(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))) / ((double) log(10.0))));
}

↓
double code(double re, double im) {
	double VAR;
	if ((re <= -3.366208022369999e+135)) {
		VAR = ((double) (((double) (0.5 / ((double) sqrt(((double) log(10.0)))))) * ((double) (((double) (((double) log(1.0)) - ((double) (2.0 * ((double) log(((double) (-1.0 / re)))))))) * ((double) sqrt(((double) (1.0 / ((double) log(10.0))))))))));
	} else {
		double VAR_1;
		if ((re <= 2.9135650880734893e+125)) {
			VAR_1 = ((double) (((double) (0.5 / ((double) sqrt(((double) log(10.0)))))) * ((double) log(((double) pow(((double) (((double) (re * re)) + ((double) (im * im)))), ((double) (1.0 / ((double) sqrt(((double) log(10.0))))))))))));
		} else {
			VAR_1 = ((double) (((double) (0.5 / ((double) sqrt(((double) log(10.0)))))) * ((double) (((double) (((double) log(1.0)) - ((double) (((double) log(re)) * -2.0)))) / ((double) sqrt(((double) log(10.0))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus re
Bits error versus im
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 3 regimes
  2. if  re  < -3.3662080223699987e135
    1. Initial program 59.0
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt59.0
      \[\leadsto \]
    4. Applied pow1/259.0
      \[\leadsto \]
    5. Applied log-pow59.0
      \[\leadsto \]
    6. Applied times-frac59.0
      \[\leadsto \]
    7. Taylor expanded around -inf 7.4
      \[\leadsto \]
    if -3.3662080223699987e135 <  re  < 2.91356508807348929e125
    1. Initial program 21.1
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt21.1
      \[\leadsto \]
    4. Applied pow1/221.1
      \[\leadsto \]
    5. Applied log-pow21.1
      \[\leadsto \]
    6. Applied times-frac21.1
      \[\leadsto \]
    7. Using strategy rm
    8. Applied add-log-exp21.1
      \[\leadsto \]
    9. Simplified20.9
      \[\leadsto \]
    if 2.91356508807348929e125 <  re 
    1. Initial program 55.8
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt55.8
      \[\leadsto \]
    4. Applied pow1/255.8
      \[\leadsto \]
    5. Applied log-pow55.8
      \[\leadsto \]
    6. Applied times-frac55.8
      \[\leadsto \]
    7. Taylor expanded around inf 8.2
      \[\leadsto \]
    8. Simplified8.2
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification17.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  :precision binary64
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))