Average Error: 31.2 → 17.0
Time: 18.9s
Precision: 64
Internal Precision: 128
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -6.584480180407772 \cdot 10^{+139}:\\ \;\;\;\;\left(\left(\log \left(\frac{-1}{re}\right) \cdot -2\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le -3.563193184801198 \cdot 10^{-257}:\\ \;\;\;\;\frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\frac{\frac{\frac{1}{8}}{\sqrt{\log 10}}}{\log 10} \cdot {\left(\log \left(im \cdot im + re \cdot re\right)\right)}^{3}}\\ \mathbf{elif}\;re \le 8.074029395986411 \cdot 10^{-300}:\\ \;\;\;\;\left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le 5.5117051751623776 \cdot 10^{+144}:\\ \;\;\;\;\left(\log \left(\sqrt[3]{im \cdot im + re \cdot re} \cdot \sqrt[3]{im \cdot im + re \cdot re}\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}} + \log \left(\sqrt[3]{im \cdot im + re \cdot re}\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\log 10}} \cdot \left(\sqrt{\frac{1}{\log 10}} \cdot \log re\right)\\ \end{array}\]

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 < -6.584480180407772e+139

    1. Initial program 58.6

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

    3. Applied add-sqr-sqrt58.6

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

    4. Applied pow1/258.6

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

    5. Applied log-pow58.6

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

    6. Applied times-frac58.6

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

    8. Applied div-inv58.6

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

    9. Applied associate-*r*58.6

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

    10. Taylor expanded around -inf 7.1

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

    11. Simplified7.1

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

    if -6.584480180407772e+139 < re < -3.563193184801198e-257

    1. Initial program 19.3

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

    3. Applied add-sqr-sqrt19.3

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

    4. Applied pow1/219.3

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

    5. Applied log-pow19.4

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

    6. Applied times-frac19.3

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

    8. Applied div-inv19.2

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

    9. Applied associate-*r*19.2

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

    11. Applied add-cbrt-cube19.4

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

    12. Applied add-cbrt-cube19.4

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

    13. Applied cbrt-unprod19.3

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

    14. Simplified19.3

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\log \left(im \cdot im + re \cdot re\right)\right)}^{3} \cdot \frac{\frac{\frac{1}{8}}{\sqrt{\log 10}}}{\log 10}}} \cdot \frac{1}{\sqrt{\log 10}}\]

    if -3.563193184801198e-257 < re < 8.074029395986411e-300

    1. Initial program 32.5

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

    3. Applied add-sqr-sqrt32.5

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

    4. Applied pow1/232.5

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

    5. Applied log-pow32.5

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

    6. Applied times-frac32.5

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

    8. Applied div-inv32.4

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

    9. Applied associate-*r*32.4

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

    10. Taylor expanded around 0 31.4

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

    if 8.074029395986411e-300 < re < 5.5117051751623776e+144

    1. Initial program 20.7

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

    3. Applied add-sqr-sqrt20.7

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

    4. Applied pow1/220.7

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

    5. Applied log-pow20.7

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

    6. Applied times-frac20.7

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

    8. Applied div-inv20.6

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

    9. Applied associate-*r*20.6

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

    11. Applied add-cube-cbrt20.6

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

    12. Applied log-prod20.6

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

    13. Applied distribute-lft-in20.6

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

    if 5.5117051751623776e+144 < re

    1. Initial program 59.6

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

    3. Applied add-sqr-sqrt59.6

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

    4. Applied pow1/259.6

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

    5. Applied log-pow59.6

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

    6. Applied times-frac59.6

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

    8. Applied div-inv59.6

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

    9. Applied associate-*r*59.6

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

    10. Taylor expanded around inf 6.7

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

    11. Simplified6.7

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

  4. Final simplification17.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -6.584480180407772 \cdot 10^{+139}:\\ \;\;\;\;\left(\left(\log \left(\frac{-1}{re}\right) \cdot -2\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le -3.563193184801198 \cdot 10^{-257}:\\ \;\;\;\;\frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\frac{\frac{\frac{1}{8}}{\sqrt{\log 10}}}{\log 10} \cdot {\left(\log \left(im \cdot im + re \cdot re\right)\right)}^{3}}\\ \mathbf{elif}\;re \le 8.074029395986411 \cdot 10^{-300}:\\ \;\;\;\;\left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le 5.5117051751623776 \cdot 10^{+144}:\\ \;\;\;\;\left(\log \left(\sqrt[3]{im \cdot im + re \cdot re} \cdot \sqrt[3]{im \cdot im + re \cdot re}\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}} + \log \left(\sqrt[3]{im \cdot im + re \cdot re}\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\log 10}} \cdot \left(\sqrt{\frac{1}{\log 10}} \cdot \log re\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))

Details

Time bar (total: 17.3s)Debug log

sample42.0ms

Algorithm
intervals
Results
30.0ms256×body80valid

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize38.0ms

Local error

Found 3 expressions with local error:

31.0b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
15×times-frac
15×add-sqr-sqrt
14×add-cube-cbrt
14×*-un-lft-identity
8×log-pow
7×pow1
5×add-log-exp
5×associate-/l*
5×add-exp-log
5×pow1/2
5×add-cbrt-cube
4×sqrt-div
3×flip-+
3×sqrt-prod
3×flip3-+
3×associate-/r*
2×div-sub
2×log-div
1×div-inv
1×div-exp
1×frac-2neg
1×sum-log
1×clear-num
1×rem-sqrt-square
1×+-commutative
1×cbrt-undiv
Counts
3 → 62
Calls
3 calls:
Slowest
30.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
4.0ms
(+ (* re re) (* im im))
4.0ms
(sqrt (+ (* re re) (* im im)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
167.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
33.0ms
(sqrt (+ (* re re) (* im im)))
24.0ms
(+ (* re re) (* im im))

simplify942.0ms

Counts
55 → 71
Calls
55 calls:
Slowest
144.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
128.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
114.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
79.0ms
(* -1 (/ (log (/ -1 re)) (log 10)))
77.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))

prune801.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize30.0ms

Local error

Found 4 expressions with local error:

32.1b
(log (+ (* re re) (* im im)))
0.5b
(/ (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))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
38×add-cube-cbrt
38×*-un-lft-identity
38×add-sqr-sqrt
28×associate-*r*
27×sqrt-prod
20×pow1
14×log-pow
12×add-exp-log
11×add-cbrt-cube
6×add-log-exp
6×associate-/r*
4×associate-/l*
4×associate-*l*
4×log-div
3×div-inv
3×flip-+
3×flip3-+
3×log-prod
2×cbrt-unprod
2×prod-exp
2×div-exp
2×div-sub
2×cbrt-undiv
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×rem-log-exp
1×frac-2neg
1×sum-log
1×clear-num
1×+-commutative
1×frac-times
Counts
4 → 121
Calls
4 calls:
Slowest
14.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
12.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
4.0ms
(+ (* re re) (* im im))
3.0ms
(log (+ (* re re) (* im im)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
148.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
61.0ms
(log (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify2.2s

Counts
118 → 133
Calls
118 calls:
Slowest
439.0ms
(* (* (* (/ 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)))))
145.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))
131.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
110.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
102.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (- (log (log (+ (* re re) (* im im)))) (log (sqrt (log 10)))))

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.6b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
13×pow1
11×add-cbrt-cube
10×add-cube-cbrt
10×*-un-lft-identity
10×add-sqr-sqrt
9×log-prod
8×associate-*r*
7×prod-exp
6×add-log-exp
5×associate-*l*
4×cbrt-unprod
4×associate-*l/
4×pow-prod-down
3×distribute-lft-in
3×distribute-rgt-in
2×div-inv
2×flip-+
2×*-commutative
2×log-pow
2×flip3-+
2×rec-exp
2×log-div
1×un-div-inv
1×associate-*r/
1×rem-log-exp
1×sum-log
1×+-commutative
1×frac-times
Counts
4 → 76
Calls
4 calls:
Slowest
11.0ms
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))
5.0ms
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
2.0ms
(+ (* re re) (* im im))
2.0ms
(log (+ (* re re) (* im im)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
148.0ms
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))
40.0ms
(log (+ (* re re) (* im im)))
18.0ms
(+ (* re re) (* im im))

simplify3.0s

Counts
53 → 88
Calls
53 calls:
Slowest
631.0ms
(* (* (* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))) (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))) (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))))
288.0ms
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))
247.0ms
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))
213.0ms
(+ (+ (log (/ 1/2 (sqrt (log 10)))) (log (log (+ (* re re) (* im im))))) (- (log (sqrt (log 10)))))
195.0ms
(+ (+ (log (/ 1/2 (sqrt (log 10)))) (log (log (+ (* re re) (* im im))))) (log (/ 1 (sqrt (log 10)))))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize46.0ms

Local error

Found 4 expressions with local error:

31.9b
(cbrt (+ (* re re) (* im im)))
31.9b
(cbrt (+ (* re re) (* im im)))
31.9b
(cbrt (+ (* re re) (* im im)))
13.8b
(log (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
10×pow1
9×flip-+
9×flip3-+
9×cbrt-prod
8×log-div
7×add-cube-cbrt
7×log-pow
7×add-exp-log
7×pow1/3
7×*-un-lft-identity
7×add-sqr-sqrt
4×add-log-exp
4×add-cbrt-cube
4×frac-times
2×pow-prod-up
2×associate-*r/
2×associate-*l/
2×pow-prod-down
2×rem-log-exp
1×prod-exp
1×pow-plus
1×log-prod
1×pow2
Counts
4 → 64
Calls
4 calls:
Slowest
8.0ms
(log (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(cbrt (+ (* re re) (* im im)))
107.0ms
(cbrt (+ (* re re) (* im im)))
93.0ms
(cbrt (+ (* re re) (* im im)))
92.0ms
(log (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))

simplify1.7s

Counts
41 → 76
Calls
41 calls:
Slowest
186.0ms
(log (* (cbrt (+ (pow (* re re) 3) (pow (* im im) 3))) (cbrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))))
173.0ms
(log (* (cbrt (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (cbrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))))
154.0ms
(cbrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
152.0ms
(log (* (cbrt (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (cbrt (+ (pow (* re re) 3) (pow (* im im) 3)))))
142.0ms
(cbrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.6b

regimes1.0s

Accuracy

59.1% (9.7b remaining)

Error of 17.0b against oracle of 7.3b and baseline of 31.1b

bsearch343.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.5s8000×body80valid