Average Error: 30.9 → 25.6
Time: 36.2s
Precision: 64
Internal Precision: 128
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
↓
\[\begin{array}{l} \mathbf{if}\;im \le -6.5154143042887985 \cdot 10^{-195}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\\ \mathbf{elif}\;im \le -4.419307702247496 \cdot 10^{-287}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\left(\log re \cdot 2\right) \cdot \sqrt{\frac{1}{\log 10}}\right)\\ \mathbf{elif}\;im \le 5.085782676534846 \cdot 10^{-253}:\\ \;\;\;\;\left(\left(\sqrt{\frac{1}{\log 10}} \cdot \log \left(\frac{-1}{re}\right)\right) \cdot -2\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\\ \mathbf{elif}\;im \le 1.5629530404064845 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\left(\log re \cdot 2\right) \cdot \sqrt{\frac{1}{\log 10}}\right)\\ \mathbf{elif}\;im \le 2.4769712697335444 \cdot 10^{+139}:\\ \;\;\;\;\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\log \left(im \cdot im + re \cdot re\right) \cdot \frac{1}{\sqrt{\log 10}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right)\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\\ \end{array}\]

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 im < -6.5154143042887985e-195

    1. Initial program 31.1

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

    2. Initial simplification31.1

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

    4. Applied add-sqr-sqrt31.1

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

    5. Applied pow1/231.1

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

    6. Applied log-pow31.1

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

    7. Applied times-frac31.1

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

    9. Applied add-sqr-sqrt31.1

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

    10. Applied associate-*l*31.0

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

    12. Applied *-commutative31.0

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

    14. Applied associate-*r/31.0

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

    15. Applied associate-*l/31.0

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

    16. Simplified31.1

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

    if -6.5154143042887985e-195 < im < -4.419307702247496e-287 or 5.085782676534846e-253 < im < 1.5629530404064845e-115

    1. Initial program 27.1

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

    2. Initial simplification27.1

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

    4. Applied add-sqr-sqrt27.1

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

    5. Applied pow1/227.1

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

    6. Applied log-pow27.1

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

    7. Applied times-frac27.1

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

    8. Taylor expanded around inf 36.1

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

    9. Simplified36.1

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

    if -4.419307702247496e-287 < im < 5.085782676534846e-253

    1. Initial program 30.8

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

    2. Initial simplification30.8

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

    4. Applied add-sqr-sqrt30.8

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

    5. Applied pow1/230.8

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

    6. Applied log-pow30.8

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

    7. Applied times-frac30.8

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

    8. Taylor expanded around -inf 32.7

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

    if 1.5629530404064845e-115 < im < 2.4769712697335444e+139

    1. Initial program 16.3

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

    2. Initial simplification16.3

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

    4. Applied add-sqr-sqrt16.3

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

    5. Applied pow1/216.3

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

    6. Applied log-pow16.3

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

    7. Applied times-frac16.3

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

    9. Applied add-sqr-sqrt16.3

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

    10. Applied associate-*l*16.2

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

    12. Applied *-commutative16.2

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

    14. Applied div-inv16.3

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

    if 2.4769712697335444e+139 < im

    1. Initial program 57.1

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

    2. Initial simplification57.1

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

    4. Applied add-sqr-sqrt57.1

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

    5. Applied pow1/257.1

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

    6. Applied log-pow57.1

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

    7. Applied times-frac57.1

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

    8. Taylor expanded around 0 6.2

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

  4. Final simplification25.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;im \le -6.5154143042887985 \cdot 10^{-195}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\\ \mathbf{elif}\;im \le -4.419307702247496 \cdot 10^{-287}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\left(\log re \cdot 2\right) \cdot \sqrt{\frac{1}{\log 10}}\right)\\ \mathbf{elif}\;im \le 5.085782676534846 \cdot 10^{-253}:\\ \;\;\;\;\left(\left(\sqrt{\frac{1}{\log 10}} \cdot \log \left(\frac{-1}{re}\right)\right) \cdot -2\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\\ \mathbf{elif}\;im \le 1.5629530404064845 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\left(\log re \cdot 2\right) \cdot \sqrt{\frac{1}{\log 10}}\right)\\ \mathbf{elif}\;im \le 2.4769712697335444 \cdot 10^{+139}:\\ \;\;\;\;\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\log \left(im \cdot im + re \cdot re\right) \cdot \frac{1}{\sqrt{\log 10}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right)\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))

Details

Time bar (total: 31.4s)Debug log

start81.0ms

Algorithm
intervals

setup29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize25.0ms

Local error

Found 3 expressions with local error:

29.8b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
3 → 62
Calls

3 calls. Slowest were:

16.0ms
(+ (* re re) (* im im))
8.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
3.0ms
(sqrt (+ (* re re) (* im im)))

series243.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

171.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
46.0ms
(sqrt (+ (* re re) (* im im)))
26.0ms
(+ (* re re) (* im im))

simplify964.0ms

Counts
55 → 71
Calls

55 calls. Slowest were:

153.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
147.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
147.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))

prune992.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.4b

localize13.0ms

Local error

Found 4 expressions with local error:

31.0b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.2b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
4 → 121
Calls

4 calls. Slowest were:

12.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
7.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
4.0ms
(+ (* re re) (* im im))

series379.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

179.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
126.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
58.0ms
(log (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify2.3s

Counts
118 → 133
Calls

118 calls. Slowest were:

435.0ms
(* (* (* (/ 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)))))
173.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))
158.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

31.0b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Counts
4 → 144
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)))))
15.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
14.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

579.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
222.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
205.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
69.0ms
(log (+ (* re re) (* im im)))

simplify7.3s

Counts
146 → 156
Calls

146 calls. Slowest were:

2.7s
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
586.0ms
(* (* (* (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))))))
427.0ms
(* 2 (/ (* (log im) (pow (sqrt 1/2) 2)) (log 10)))

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.2b

localize4.0ms

Local error

Found 4 expressions with local error:

31.0b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.4b
(* (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)))) (sqrt (/ 1/2 (sqrt (log 10)))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
4 → 144
Calls

4 calls. Slowest were:

15.0ms
(* (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (sqrt (/ 1/2 (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))))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

656.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
192.0ms
(* (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10)))))
187.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
41.0ms
(log (+ (* re re) (* im im)))

simplify8.1s

Counts
147 → 156
Calls

147 calls. Slowest were:

2.5s
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
1.0s
(* (* (* (* (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))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))))
763.0ms
(* (* (* (* (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))))) (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))))

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.2b

regimes1.1s

Accuracy

22.5% (18.3b remaining)

Error of 25.6b against oracle of 7.3b and baseline of 30.9b

bsearch550.0ms