Details

Time bar (total: 5.2s)

analyze5.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 99.996948%

sample27.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.1b

Counts
2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
33.4b
(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
4×add-exp-log sqrt-div associate-/r* add-cbrt-cube
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
7.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms
(sqrt (+ (* re re) (* im im)))

series34.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
14.0ms
(sqrt (+ (* re re) (* im im)))

simplify119.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (111.0ms)

IterNodesCost
0224668
1555635
21317630
33981628
45001627

prune150.0ms

Filtered
45 candidates to 69 candidates (-53.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New561369
Fresh000
Picked101
Done000
Total571370

Merged error: 7.5b

Counts
70 → 13

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.6b
(/ (log 10.0) (log (+ (* re re) (* im im))))
34.7b
(log (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
71×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
46×pow1
43×log-pow
24×associate-/r*
11×add-exp-log
10×add-cbrt-cube
7×associate-/l*
6×div-inv
4×cbrt-undiv div-exp
3×log-prod add-log-exp
2×log-div frac-2neg clear-num
1×flip3-+ rem-log-exp associate-/r/ flip-+
Counts
3 → 148
Calls
3 calls:
7.0ms
(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
4.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
3.0ms
(log (+ (* re re) (* im im)))

series61.0ms

Counts
3 → 9
Calls
3 calls:
22.0ms
(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
30.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
10.0ms
(log (+ (* re re) (* im im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04551849
117531758
250011747

prune237.0ms

Filtered
101 candidates to 157 candidates (-55.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1489157
Fresh9312
Picked101
Done000
Total15812170

Merged error: 7.4b

Counts
170 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
0.5b
(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
0.5b
(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
34.7b
(log (+ (* re re) (* im im)))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
896×times-frac
537×add-sqr-sqrt
521×sqrt-prod
389×add-cube-cbrt *-un-lft-identity
197×associate-*r*
169×pow1
163×log-pow
46×associate-*l*
36×associate-/r*
35×unswap-sqr
33×add-exp-log
32×add-cbrt-cube
17×div-inv
13×cbrt-undiv div-exp associate-/l*
6×prod-exp cbrt-unprod
4×add-log-exp
3×log-prod
2×log-div frac-2neg clear-num associate-/r/
1×frac-times flip3-+ associate-*r/ rem-log-exp pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 612
Calls
4 calls:
138.0ms
(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
12.0ms
(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
5.0ms
(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
4.0ms
(log (+ (* re re) (* im im)))

series101.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
32.0ms
(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
31.0ms
(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
10.0ms
(log (+ (* re re) (* im im)))

simplify118.0ms

Algorithm
egg-herbie
Counts
624 → 624
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0143810601
150019984

prune1.1s

Filtered
248 candidates to 624 candidates (-151.6%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New6177624
Fresh2911
Picked011
Done000
Total61917636

Merged error: 7.3b

Counts
636 → 17

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2))
0.5b
(/ (sqrt 1/2) (/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2)))
0.6b
(/ (log 10.0) (log (+ (* re re) (* im im))))
34.7b
(log (+ (* re re) (* im im)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
2504×times-frac
1035×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
858×sqrt-prod
407×pow1
403×log-pow
134×associate-/r*
59×div-inv
30×associate-/l*
21×add-exp-log
20×add-cbrt-cube
10×cbrt-undiv div-exp
4×add-log-exp
3×log-prod frac-2neg clear-num
2×log-div
1×flip3-+ rem-log-exp associate-/r/ flip-+ associate-/l/
Counts
4 → 1102
Calls
4 calls:
9.0ms
(/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2))
32.0ms
(/ (sqrt 1/2) (/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2)))
4.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
4.0ms
(log (+ (* re re) (* im im)))

series103.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2))
28.0ms
(/ (sqrt 1/2) (/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2)))
32.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
10.0ms
(log (+ (* re re) (* im im)))

simplify248.0ms

Algorithm
egg-herbie
Counts
1114 → 1114
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0206122558
1500121727

prune1.5s

Filtered
382 candidates to 1114 candidates (-191.6%)
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New111041114
Fresh31215
Picked011
Done011
Total1113181131

Merged error: 7.2b

Counts
1131 → 18

regimes886.0ms

bsearch2.0ms

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