math.log10 on complex, real part

Percentage Accurate: 52.4% → 99.5%

Time: 8.6s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))

C

double code(double re, double im) {
	return log(sqrt(((re * re) + (im * im)))) / log(10.0);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = log(sqrt(((re * re) + (im * im)))) / log(10.0d0)
end function

Java

public static double code(double re, double im) {
	return Math.log(Math.sqrt(((re * re) + (im * im)))) / Math.log(10.0);
}

Python

def code(re, im):
	return math.log(math.sqrt(((re * re) + (im * im)))) / math.log(10.0)

Julia

function code(re, im)
	return Float64(log(sqrt(Float64(Float64(re * re) + Float64(im * im)))) / log(10.0))
end

MATLAB

function tmp = code(re, im)
	tmp = log(sqrt(((re * re) + (im * im)))) / log(10.0);
end

Wolfram

code[re_, im_] := N[(N[Log[N[Sqrt[N[(N[(re * re), $MachinePrecision] + N[(im * im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision]

Initial Program: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))

C

double code(double re, double im) {
	return log(sqrt(((re * re) + (im * im)))) / log(10.0);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = log(sqrt(((re * re) + (im * im)))) / log(10.0d0)
end function

Java

public static double code(double re, double im) {
	return Math.log(Math.sqrt(((re * re) + (im * im)))) / Math.log(10.0);
}

Python

def code(re, im):
	return math.log(math.sqrt(((re * re) + (im * im)))) / math.log(10.0)

Julia

function code(re, im)
	return Float64(log(sqrt(Float64(Float64(re * re) + Float64(im * im)))) / log(10.0))
end

MATLAB

function tmp = code(re, im)
	tmp = log(sqrt(((re * re) + (im * im)))) / log(10.0);
end

Wolfram

code[re_, im_] := N[(N[Log[N[Sqrt[N[(N[(re * re), $MachinePrecision] + N[(im * im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \log \left(\mathsf{hypot}\left(re, im\right)\right) \cdot \sqrt[3]{{\log 10}^{-3}} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (log (hypot re im)) (cbrt (pow (log 10.0) -3.0))))

C

double code(double re, double im) {
	return log(hypot(re, im)) * cbrt(pow(log(10.0), -3.0));
}

Java

public static double code(double re, double im) {
	return Math.log(Math.hypot(re, im)) * Math.cbrt(Math.pow(Math.log(10.0), -3.0));
}

Julia

function code(re, im)
	return Float64(log(hypot(re, im)) * cbrt((log(10.0) ^ -3.0)))
end

Wolfram

code[re_, im_] := N[(N[Log[N[Sqrt[re ^ 2 + im ^ 2], $MachinePrecision]], $MachinePrecision] * N[Power[N[Power[N[Log[10.0], $MachinePrecision], -3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 51.8%

   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]
2. Step-by-step derivation

   1. hypot-def 99.1%

      \[\leadsto \frac{\log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}}{\log 10} \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}} \]
4. Step-by-step derivation

   1. add-exp-log 73.4%

      \[\leadsto \color{blue}{e^{\log \left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right)}} \]

5. Applied egg-rr 73.4%

   \[\leadsto \color{blue}{e^{\log \left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right)}} \]
6. Step-by-step derivation

   1. rem-cbrt-cube 73.3%

      \[\leadsto e^{\log \left(\frac{\color{blue}{\sqrt[3]{{\log \left(\mathsf{hypot}\left(re, im\right)\right)}^{3}}}}{\log 10}\right)} \]

   2. rem-cbrt-cube 73.1%

      \[\leadsto e^{\log \left(\frac{\sqrt[3]{{\log \left(\mathsf{hypot}\left(re, im\right)\right)}^{3}}}{\color{blue}{\sqrt[3]{{\log 10}^{3}}}}\right)} \]

   3. cbrt-div 73.3%

      \[\leadsto e^{\log \color{blue}{\left(\sqrt[3]{\frac{{\log \left(\mathsf{hypot}\left(re, im\right)\right)}^{3}}{{\log 10}^{3}}}\right)}} \]

   4. add-exp-log 98.9%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{{\log \left(\mathsf{hypot}\left(re, im\right)\right)}^{3}}{{\log 10}^{3}}}} \]

   5. div-inv 98.8%

      \[\leadsto \sqrt[3]{\color{blue}{{\log \left(\mathsf{hypot}\left(re, im\right)\right)}^{3} \cdot \frac{1}{{\log 10}^{3}}}} \]

   6. cbrt-prod 98.7%

      \[\leadsto \color{blue}{\sqrt[3]{{\log \left(\mathsf{hypot}\left(re, im\right)\right)}^{3}} \cdot \sqrt[3]{\frac{1}{{\log 10}^{3}}}} \]

   7. rem-cbrt-cube 98.5%

      \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)} \cdot \sqrt[3]{\frac{1}{{\log 10}^{3}}} \]

   8. pow-flip 99.6%

      \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right) \cdot \sqrt[3]{\color{blue}{{\log 10}^{\left(-3\right)}}} \]

   9. metadata-eval 99.6%

      \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right) \cdot \sqrt[3]{{\log 10}^{\color{blue}{-3}}} \]

7. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right) \cdot \sqrt[3]{{\log 10}^{-3}}} \]

8. Final simplification 99.6%

   \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right) \cdot \sqrt[3]{{\log 10}^{-3}} \]

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10} + -1\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (+ 1.0 (+ (/ (log (hypot re im)) (log 10.0)) -1.0)))

C

double code(double re, double im) {
	return 1.0 + ((log(hypot(re, im)) / log(10.0)) + -1.0);
}

Java

public static double code(double re, double im) {
	return 1.0 + ((Math.log(Math.hypot(re, im)) / Math.log(10.0)) + -1.0);
}

Python

def code(re, im):
	return 1.0 + ((math.log(math.hypot(re, im)) / math.log(10.0)) + -1.0)

Julia

function code(re, im)
	return Float64(1.0 + Float64(Float64(log(hypot(re, im)) / log(10.0)) + -1.0))
end

MATLAB

function tmp = code(re, im)
	tmp = 1.0 + ((log(hypot(re, im)) / log(10.0)) + -1.0);
end

Wolfram

code[re_, im_] := N[(1.0 + N[(N[(N[Log[N[Sqrt[re ^ 2 + im ^ 2], $MachinePrecision]], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 51.8%

   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]
2. Step-by-step derivation

   1. hypot-def 99.1%

      \[\leadsto \frac{\log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}}{\log 10} \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}} \]
4. Step-by-step derivation

   1. expm1-log1p-u 73.7%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right)\right)} \]

   2. expm1-udef 73.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right)} - 1} \]

   3. log1p-udef 73.7%

      \[\leadsto e^{\color{blue}{\log \left(1 + \frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right)}} - 1 \]

   4. add-exp-log 99.0%

      \[\leadsto \color{blue}{\left(1 + \frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right)} - 1 \]

5. Applied egg-rr 99.0%

   \[\leadsto \color{blue}{\left(1 + \frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}\right) - 1} \]
6. Step-by-step derivation

   1. associate--l+ 99.1%

      \[\leadsto \color{blue}{1 + \left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10} - 1\right)} \]

7. Simplified 99.1%

   \[\leadsto \color{blue}{1 + \left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10} - 1\right)} \]

8. Final simplification 99.1%

   \[\leadsto 1 + \left(\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10} + -1\right) \]

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10} \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (/ (log (hypot re im)) (log 10.0)))

C

double code(double re, double im) {
	return log(hypot(re, im)) / log(10.0);
}

Java

public static double code(double re, double im) {
	return Math.log(Math.hypot(re, im)) / Math.log(10.0);
}

Python

def code(re, im):
	return math.log(math.hypot(re, im)) / math.log(10.0)

Julia

function code(re, im)
	return Float64(log(hypot(re, im)) / log(10.0))
end

MATLAB

function tmp = code(re, im)
	tmp = log(hypot(re, im)) / log(10.0);
end

Wolfram

code[re_, im_] := N[(N[Log[N[Sqrt[re ^ 2 + im ^ 2], $MachinePrecision]], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 51.8%

   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]
2. Step-by-step derivation

   1. hypot-def 99.1%

      \[\leadsto \frac{\log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}}{\log 10} \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}} \]

4. Final simplification 99.1%

   \[\leadsto \frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10} \]

Alternative 4: 27.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \frac{\log im}{\log 10} \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (/ (log im) (log 10.0)))

C

double code(double re, double im) {
	return log(im) / log(10.0);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = log(im) / log(10.0d0)
end function

Java

public static double code(double re, double im) {
	return Math.log(im) / Math.log(10.0);
}

Python

def code(re, im):
	return math.log(im) / math.log(10.0)

Julia

function code(re, im)
	return Float64(log(im) / log(10.0))
end

MATLAB

function tmp = code(re, im)
	tmp = log(im) / log(10.0);
end

Wolfram

code[re_, im_] := N[(N[Log[im], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 51.8%

   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]
2. Step-by-step derivation

   1. hypot-def 99.1%

      \[\leadsto \frac{\log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}}{\log 10} \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}} \]

4. Taylor expanded in re around 0 30.4%

   \[\leadsto \color{blue}{\frac{\log im}{\log 10}} \]

5. Final simplification 30.4%

   \[\leadsto \frac{\log im}{\log 10} \]

Alternative 5: 3.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \left(re \cdot \frac{re}{\log 10}\right) \cdot 0.5 \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (* (* re (/ re (log 10.0))) 0.5))

C

double code(double re, double im) {
	return (re * (re / log(10.0))) * 0.5;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (re * (re / log(10.0d0))) * 0.5d0
end function

Java

public static double code(double re, double im) {
	return (re * (re / Math.log(10.0))) * 0.5;
}

Python

def code(re, im):
	return (re * (re / math.log(10.0))) * 0.5

Julia

function code(re, im)
	return Float64(Float64(re * Float64(re / log(10.0))) * 0.5)
end

MATLAB

function tmp = code(re, im)
	tmp = (re * (re / log(10.0))) * 0.5;
end

Wolfram

code[re_, im_] := N[(N[(re * N[(re / N[Log[10.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]

Derivation

1. Initial program 51.8%

   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]
2. Step-by-step derivation

   1. hypot-def 99.1%

      \[\leadsto \frac{\log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}}{\log 10} \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}} \]

4. Taylor expanded in re around 0 26.0%

   \[\leadsto \color{blue}{\frac{\log im}{\log 10} + 0.5 \cdot \frac{{re}^{2}}{\log 10 \cdot {im}^{2}}} \]
5. Step-by-step derivation

   1. unpow2 26.0%

      \[\leadsto \frac{\log im}{\log 10} + 0.5 \cdot \frac{\color{blue}{re \cdot re}}{\log 10 \cdot {im}^{2}} \]

   2. unpow2 26.0%

      \[\leadsto \frac{\log im}{\log 10} + 0.5 \cdot \frac{re \cdot re}{\log 10 \cdot \color{blue}{\left(im \cdot im\right)}} \]

6. Simplified 26.0%

   \[\leadsto \color{blue}{\frac{\log im}{\log 10} + 0.5 \cdot \frac{re \cdot re}{\log 10 \cdot \left(im \cdot im\right)}} \]

7. Taylor expanded in im around 0 2.7%

   \[\leadsto \color{blue}{0.5 \cdot \frac{{re}^{2}}{\log 10 \cdot {im}^{2}}} \]
8. Step-by-step derivation

   1. *-commutative 2.7%

      \[\leadsto \color{blue}{\frac{{re}^{2}}{\log 10 \cdot {im}^{2}} \cdot 0.5} \]

   2. unpow2 2.7%

      \[\leadsto \frac{\color{blue}{re \cdot re}}{\log 10 \cdot {im}^{2}} \cdot 0.5 \]

   3. *-commutative 2.7%

      \[\leadsto \frac{re \cdot re}{\color{blue}{{im}^{2} \cdot \log 10}} \cdot 0.5 \]

   4. unpow2 2.7%

      \[\leadsto \frac{re \cdot re}{\color{blue}{\left(im \cdot im\right)} \cdot \log 10} \cdot 0.5 \]

   5. associate-*r* 2.7%

      \[\leadsto \frac{re \cdot re}{\color{blue}{im \cdot \left(im \cdot \log 10\right)}} \cdot 0.5 \]

9. Simplified 2.7%

   \[\leadsto \color{blue}{\frac{re \cdot re}{im \cdot \left(im \cdot \log 10\right)} \cdot 0.5} \]
10. Step-by-step derivation

    1. associate-/l* 3.0%

       \[\leadsto \color{blue}{\frac{re}{\frac{im \cdot \left(im \cdot \log 10\right)}{re}}} \cdot 0.5 \]

    2. div-inv 3.0%

       \[\leadsto \color{blue}{\left(re \cdot \frac{1}{\frac{im \cdot \left(im \cdot \log 10\right)}{re}}\right)} \cdot 0.5 \]

    3. associate-/l* 3.4%

       \[\leadsto \left(re \cdot \frac{1}{\color{blue}{\frac{im}{\frac{re}{im \cdot \log 10}}}}\right) \cdot 0.5 \]

    4. associate-/r* 3.4%

       \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\color{blue}{\frac{\frac{re}{im}}{\log 10}}}}\right) \cdot 0.5 \]

    5. div-inv 3.4%

       \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{\color{blue}{re \cdot \frac{1}{im}}}{\log 10}}}\right) \cdot 0.5 \]

    6. add-exp-log 1.7%

       \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot \color{blue}{e^{\log \left(\frac{1}{im}\right)}}}{\log 10}}}\right) \cdot 0.5 \]

    7. neg-log 1.7%

       \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot e^{\color{blue}{-\log im}}}{\log 10}}}\right) \cdot 0.5 \]

    8. add-sqr-sqrt 0.6%

       \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot e^{\color{blue}{\sqrt{-\log im} \cdot \sqrt{-\log im}}}}{\log 10}}}\right) \cdot 0.5 \]

    9. sqrt-unprod 1.8%

       \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot e^{\color{blue}{\sqrt{\left(-\log im\right) \cdot \left(-\log im\right)}}}}{\log 10}}}\right) \cdot 0.5 \]

    10. sqr-neg 1.8%

        \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot e^{\sqrt{\color{blue}{\log im \cdot \log im}}}}{\log 10}}}\right) \cdot 0.5 \]

    11. sqrt-unprod 1.2%

        \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot e^{\color{blue}{\sqrt{\log im} \cdot \sqrt{\log im}}}}{\log 10}}}\right) \cdot 0.5 \]

    12. add-sqr-sqrt 2.1%

        \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot e^{\color{blue}{\log im}}}{\log 10}}}\right) \cdot 0.5 \]

    13. add-exp-log 3.9%

        \[\leadsto \left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot \color{blue}{im}}{\log 10}}}\right) \cdot 0.5 \]

11. Applied egg-rr 3.9%

    \[\leadsto \color{blue}{\left(re \cdot \frac{1}{\frac{im}{\frac{re \cdot im}{\log 10}}}\right)} \cdot 0.5 \]
12. Step-by-step derivation

    1. associate-*r/ 3.9%

       \[\leadsto \color{blue}{\frac{re \cdot 1}{\frac{im}{\frac{re \cdot im}{\log 10}}}} \cdot 0.5 \]

    2. *-rgt-identity 3.9%

       \[\leadsto \frac{\color{blue}{re}}{\frac{im}{\frac{re \cdot im}{\log 10}}} \cdot 0.5 \]

    3. associate-/r/ 3.8%

       \[\leadsto \color{blue}{\left(\frac{re}{im} \cdot \frac{re \cdot im}{\log 10}\right)} \cdot 0.5 \]

    4. times-frac 3.8%

       \[\leadsto \color{blue}{\frac{re \cdot \left(re \cdot im\right)}{im \cdot \log 10}} \cdot 0.5 \]

    5. associate-*l* 3.8%

       \[\leadsto \frac{\color{blue}{\left(re \cdot re\right) \cdot im}}{im \cdot \log 10} \cdot 0.5 \]

    6. *-commutative 3.8%

       \[\leadsto \frac{\color{blue}{im \cdot \left(re \cdot re\right)}}{im \cdot \log 10} \cdot 0.5 \]

    7. *-commutative 3.8%

       \[\leadsto \frac{im \cdot \left(re \cdot re\right)}{\color{blue}{\log 10 \cdot im}} \cdot 0.5 \]

    8. associate-*r/ 3.7%

       \[\leadsto \color{blue}{\left(im \cdot \frac{re \cdot re}{\log 10 \cdot im}\right)} \cdot 0.5 \]

    9. times-frac 3.7%

       \[\leadsto \left(im \cdot \color{blue}{\left(\frac{re}{\log 10} \cdot \frac{re}{im}\right)}\right) \cdot 0.5 \]

13. Simplified 3.7%

    \[\leadsto \color{blue}{\left(im \cdot \left(\frac{re}{\log 10} \cdot \frac{re}{im}\right)\right)} \cdot 0.5 \]

14. Taylor expanded in im around 0 3.9%

    \[\leadsto \color{blue}{\frac{{re}^{2}}{\log 10}} \cdot 0.5 \]
15. Step-by-step derivation

    1. unpow2 3.9%

       \[\leadsto \frac{\color{blue}{re \cdot re}}{\log 10} \cdot 0.5 \]

    2. associate-*r/ 3.9%

       \[\leadsto \color{blue}{\left(re \cdot \frac{re}{\log 10}\right)} \cdot 0.5 \]

16. Simplified 3.9%

    \[\leadsto \color{blue}{\left(re \cdot \frac{re}{\log 10}\right)} \cdot 0.5 \]

17. Final simplification 3.9%

    \[\leadsto \left(re \cdot \frac{re}{\log 10}\right) \cdot 0.5 \]

Reproduce

herbie shell --seed 2023200 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  :precision binary64
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))