Average Error: 30.6 → 17.5
Time: 31.6s
Precision: 64
Internal Precision: 128
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.1401983261996084 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\left(\sqrt{\frac{1}{\log 10}} \cdot \log \left(\frac{-1}{re}\right)\right) \cdot -2\right)\\ \mathbf{elif}\;re \le -4.41087148146037 \cdot 10^{-297}:\\ \;\;\;\;\frac{\left(\log \left(re \cdot re + im \cdot im\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le 4.374664428585637 \cdot 10^{-243}:\\ \;\;\;\;\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\frac{2 \cdot \log im}{\sqrt{\log 10}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\\ \mathbf{elif}\;re \le 5.6224680550833235 \cdot 10^{+107}:\\ \;\;\;\;\frac{\log \left(\sqrt[3]{re \cdot re + im \cdot im} \cdot \left(\sqrt[3]{re \cdot re + im \cdot im} \cdot \sqrt[3]{re \cdot re + im \cdot im}\right)\right)}{\sqrt{\log 10}} \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log re \cdot 2}{\sqrt{\log 10}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \end{array}\]

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 5 regimes

  2. if re < -1.1401983261996084e+55

    1. Initial program 43.1

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

    2. Initial simplification43.1

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt43.1

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

    5. Applied pow1/243.1

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    6. Applied log-pow43.1

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    7. Applied times-frac43.1

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]

    8. Taylor expanded around -inf 10.6

      \[\leadsto \frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \color{blue}{\left(-2 \cdot \left(\log \left(\frac{-1}{re}\right) \cdot \sqrt{\frac{1}{\log 10}}\right)\right)}\]

    if -1.1401983261996084e+55 < re < -4.41087148146037e-297

    1. Initial program 21.1

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

    2. Initial simplification21.1

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt21.1

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

    5. Applied pow1/221.1

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    6. Applied log-pow21.1

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    7. Applied times-frac21.1

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]
    8. Using strategy rm

    9. Applied add-sqr-sqrt21.2

      \[\leadsto \color{blue}{\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\]

    10. Applied associate-*l*21.1

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\right)}\]
    11. Using strategy rm

    12. Applied associate-*r/21.1

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]

    13. Applied associate-*r/21.1

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \log \left(re \cdot re + im \cdot im\right)\right)}{\sqrt{\log 10}}}\]

    if -4.41087148146037e-297 < re < 4.374664428585637e-243

    1. Initial program 29.7

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

    2. Initial simplification29.7

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt29.7

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

    5. Applied pow1/229.7

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    6. Applied log-pow29.7

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    7. Applied times-frac29.6

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]
    8. Using strategy rm

    9. Applied add-sqr-sqrt29.7

      \[\leadsto \color{blue}{\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\]

    10. Applied associate-*l*29.6

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\right)}\]

    11. Taylor expanded around 0 34.7

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\color{blue}{2 \cdot \log im}}{\sqrt{\log 10}}\right)\]

    if 4.374664428585637e-243 < re < 5.6224680550833235e+107

    1. Initial program 19.9

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

    2. Initial simplification19.9

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt19.9

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

    5. Applied pow1/219.9

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    6. Applied log-pow19.9

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    7. Applied times-frac19.9

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt19.9

      \[\leadsto \frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \color{blue}{\left(\left(\sqrt[3]{re \cdot re + im \cdot im} \cdot \sqrt[3]{re \cdot re + im \cdot im}\right) \cdot \sqrt[3]{re \cdot re + im \cdot im}\right)}}{\sqrt{\log 10}}\]

    if 5.6224680550833235e+107 < re

    1. Initial program 51.3

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

    2. Initial simplification51.3

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt51.3

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

    5. Applied pow1/251.3

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    6. Applied log-pow51.3

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

    7. Applied times-frac51.3

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]
    8. Using strategy rm

    9. Applied add-sqr-sqrt51.3

      \[\leadsto \color{blue}{\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\]

    10. Applied associate-*l*51.3

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\right)}\]

    11. Taylor expanded around inf 8.2

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\color{blue}{-2 \cdot \log \left(\frac{1}{re}\right)}}{\sqrt{\log 10}}\right)\]

    12. Simplified8.2

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\color{blue}{\log re \cdot 2}}{\sqrt{\log 10}}\right)\]
  3. Recombined 5 regimes into one program.

  4. Final simplification17.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.1401983261996084 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\left(\sqrt{\frac{1}{\log 10}} \cdot \log \left(\frac{-1}{re}\right)\right) \cdot -2\right)\\ \mathbf{elif}\;re \le -4.41087148146037 \cdot 10^{-297}:\\ \;\;\;\;\frac{\left(\log \left(re \cdot re + im \cdot im\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le 4.374664428585637 \cdot 10^{-243}:\\ \;\;\;\;\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\frac{2 \cdot \log im}{\sqrt{\log 10}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\\ \mathbf{elif}\;re \le 5.6224680550833235 \cdot 10^{+107}:\\ \;\;\;\;\frac{\log \left(\sqrt[3]{re \cdot re + im \cdot im} \cdot \left(\sqrt[3]{re \cdot re + im \cdot im} \cdot \sqrt[3]{re \cdot re + im \cdot im}\right)\right)}{\sqrt{\log 10}} \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log re \cdot 2}{\sqrt{\log 10}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))

Details

Time bar (total: 26.5s)Debug log

start77.0ms

Algorithm
intervals

setup45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize40.0ms

Local error

Found 3 expressions with local error:

30.9b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
3 → 62
Calls

3 calls. Slowest were:

16.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
6.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(+ (* re re) (* im im))

series272.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

191.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
54.0ms
(sqrt (+ (* re re) (* im im)))
26.0ms
(+ (* re re) (* im im))

simplify1.0s

Counts
55 → 71
Calls

55 calls. Slowest were:

143.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
131.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
116.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.1b

localize22.0ms

Local error

Found 4 expressions with local error:

32.1b
(log (+ (* re re) (* im im)))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 121
Calls

4 calls. Slowest were:

7.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
6.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
2.0ms
(+ (* re re) (* im im))

series446.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

191.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
180.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
49.0ms
(log (+ (* re re) (* im im)))
25.0ms
(+ (* re re) (* im im))

simplify2.6s

Counts
118 → 133
Calls

118 calls. Slowest were:

575.0ms
(* (* (* (/ 1/2 (sqrt (log 10))) (/ 1/2 (sqrt (log 10)))) (/ 1/2 (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
172.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))
167.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

localize8.0ms

Local error

Found 4 expressions with local error:

32.1b
(log (+ (* re re) (* im im)))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 144
Calls

4 calls. Slowest were:

16.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
7.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
7.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

548.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
251.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
193.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
54.0ms
(log (+ (* re re) (* im im)))

simplify4.8s

Counts
146 → 156
Calls

146 calls. Slowest were:

563.0ms
(* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))))
387.0ms
(* -2 (/ (* (log (/ -1 re)) (pow (sqrt 1/2) 2)) (log 10)))
314.0ms
(* 2 (/ (* (log im) (pow (sqrt 1/2) 2)) (log 10)))

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize17.0ms

Local error

Found 4 expressions with local error:

32.1b
(log (+ (* re re) (* im im)))
0.5b
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (sqrt (log 10)))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Counts
4 → 112
Calls

4 calls. Slowest were:

29.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (sqrt (log 10)))
25.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))
13.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))

series927.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

381.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))
274.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))
224.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (sqrt (log 10)))
48.0ms
(log (+ (* re re) (* im im)))

simplify5.9s

Counts
95 → 124
Calls

95 calls. Slowest were:

744.0ms
(* 2 (* (* (log im) (pow (sqrt 1/2) 2)) (sqrt (/ 1 (log 10)))))
578.0ms
(* -2 (* (sqrt (/ 1 (log 10))) (* (log (/ 1 re)) (pow (sqrt 1/2) 2))))
377.0ms
(* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im))))))

prune1.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.9b

regimes1.2s

Accuracy

55.8% (10.3b remaining)

Error of 17.5b against oracle of 7.1b and baseline of 30.5b

bsearch400.0ms