Average Error: 32.0 → 19.1
Time: 6.4s
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 <= -307633288.5871727)) {
		VAR = ((double) (((double) (0.5 / ((double) sqrt(((double) log(10.0)))))) * ((double) (((double) (((double) log(1.0)) + ((double) (((double) log(((double) (-1.0 / re)))) * -2.0)))) * ((double) sqrt(((double) (1.0 / ((double) log(10.0))))))))));
	} else {
		double VAR_1;
		if ((re <= -4.948094964353528e-208)) {
			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 {
			double VAR_2;
			if ((re <= -6.218827239863813e-276)) {
				VAR_2 = ((double) (((double) (0.5 / ((double) sqrt(((double) log(10.0)))))) * ((double) (((double) (((double) log(1.0)) + ((double) (((double) log(((double) (-1.0 / re)))) * -2.0)))) * ((double) sqrt(((double) (1.0 / ((double) log(10.0))))))))));
			} else {
				double VAR_3;
				if ((re <= 2.3077438582071508e+116)) {
					VAR_3 = ((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_3 = ((double) (((double) (0.5 / ((double) sqrt(((double) log(10.0)))))) * ((double) (((double) sqrt(((double) (1.0 / ((double) log(10.0)))))) * ((double) (((double) log(1.0)) + ((double) (2.0 * ((double) log(re))))))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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  < -307633288.587172687 or -4.948094964353528e-208 <  re  < -6.2188272398638127e-276
    1. Initial program 39.7
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt39.7
      \[\leadsto \]
    4. Applied pow1/239.7
      \[\leadsto \]
    5. Applied log-pow39.7
      \[\leadsto \]
    6. Applied times-frac39.7
      \[\leadsto \]
    7. Taylor expanded around -inf 20.5
      \[\leadsto \]
    8. Simplified20.5
      \[\leadsto \]
    if -307633288.587172687 <  re  < -4.948094964353528e-208 or -6.2188272398638127e-276 <  re  < 2.30774385820715081e116
    1. Initial program 21.4
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt21.4
      \[\leadsto \]
    4. Applied pow1/221.4
      \[\leadsto \]
    5. Applied log-pow21.4
      \[\leadsto \]
    6. Applied times-frac21.4
      \[\leadsto \]
    7. Using strategy rm
    8. Applied add-log-exp21.4
      \[\leadsto \]
    9. Simplified21.2
      \[\leadsto \]
    if 2.30774385820715081e116 <  re 
    1. Initial program 53.6
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt53.6
      \[\leadsto \]
    4. Applied pow1/253.6
      \[\leadsto \]
    5. Applied log-pow53.6
      \[\leadsto \]
    6. Applied times-frac53.6
      \[\leadsto \]
    7. Taylor expanded around inf 9.2
      \[\leadsto \]
    8. Simplified9.2
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification19.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  :precision binary64
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))