Details

Time bar (total: 21.1s)

sample154.0ms

Algorithm
intervals
Results
69.0ms256×body80valid
58.0ms249×body80nan

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done2408
82408
71116
6232
578
453
339
224
122
018

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0b
(sqrt (+ (* re re) (* im im)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r* sqrt-div
3×flip3-+ sqrt-prod flip-+ insert-posit16
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp div-inv
Counts
3 → 77
Calls
3 calls:
13.0ms
(+ (* re re) (* im im))
31.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

series201.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ (* re re) (* im im))
121.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts
86 → 86
Iterations
IterNodes
done2007
32007
2686
1269
0133

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(/ 1 (log base))
0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
28.0b
(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×times-frac
24×*-un-lft-identity
23×add-cube-cbrt
17×pow1 add-exp-log
16×associate-*r*
11×add-cbrt-cube
10×log-pow
6×associate-*l* add-log-exp
4×associate-/r* div-exp prod-exp insert-posit16
3×sqrt-prod associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-pow1 flip3-+ pow1/2 sqrt-div 1-exp cbrt-unprod flip-+ div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 107
Calls
4 calls:
7.0ms
(+ (* re re) (* im im))
5.0ms
(/ 1 (log base))
15.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
6.0ms
(sqrt (+ (* re re) (* im im)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* re re) (* im im))
203.0ms
(/ 1 (log base))
114.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
46.0ms
(sqrt (+ (* re re) (* im im)))

simplify982.0ms

Counts
119 → 119
Iterations
IterNodes
done2011
32011
2981
1355
0152

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
0.5b
(* (log base) (log base))
28.0b
(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×pow1 add-cube-cbrt
12×log-prod
10×add-cbrt-cube associate-*l* add-exp-log log-pow
9×times-frac
8×associate-*r*
6×distribute-rgt-in distribute-lft-in swap-sqr
4×insert-posit16 add-log-exp
3×associate-/r* flip3-+ sqrt-prod flip-+ associate-/l*
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod unswap-sqr associate-/l/
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg pow-plus div-exp pow-sqr pow-prod-up div-inv
Counts
4 → 114
Calls
4 calls:
12.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
32.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
7.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
143.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
173.0ms
(* (log base) (log base))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify858.0ms

Counts
126 → 126
Iterations
IterNodes
done2003
32003
21087
1492
0204

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (fabs (log base)))
0.4b
(/ (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (fabs (log base))) (sqrt (+ (* (log base) (log base)) (* 0 0))))
0.5b
(* (log base) (log base))
28.0b
(sqrt (+ (* re re) (* im im)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
46×add-sqr-sqrt
45×*-un-lft-identity
43×add-cube-cbrt
27×sqrt-prod
20×add-cbrt-cube add-exp-log
18×pow1
9×associate-/r* div-inv
8×associate-/l*
7×cbrt-undiv div-exp
6×log-prod swap-sqr log-pow
4×sqrt-div associate-*r* associate-*l* insert-posit16 add-log-exp
3×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod
2×clear-num frac-2neg flip3-+ associate-/r/ flip-+
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr associate-/l/
Counts
4 → 150
Calls
4 calls:
13.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (fabs (log base)))
35.0ms
(/ (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (fabs (log base))) (sqrt (+ (* (log base) (log base)) (* 0 0))))
8.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (fabs (log base)))
103.0ms
(/ (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (fabs (log base))) (sqrt (+ (* (log base) (log base)) (* 0 0))))
272.0ms
(* (log base) (log base))
50.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
162 → 162
Iterations
IterNodes
done2002
32002
21861
1653
0264

prune2.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.1b

regimes660.0ms

Accuracy

58.9% (9.7b remaining)

Error of 16.6b against oracle of 6.9b and baseline of 30.5b

bsearch575.0ms

Steps
ItersRangePoint
11
8.336365768052704e+53
8.956910311863033e+85
7.455578618187527e+81
9
5.972186919243248e-200
1.96569304420625e-191
6.649021261519885e-193
6
2.372021361203639e-235
2.558373950144983e-234
3.581675146123889e-235
9
-5.659786164417142e+71
-5.416718010051998e+66
-1.6633647338752457e+69

simplify918.0ms

Iterations
IterNodes
done2001
1552001
1541993
1531981
1521969
1511957
1501945
1491933
1481921
1471909
1461897
1451885
1441873
1431861
1421849
1411837
1401825
1391813
1381801
1371789
1361777
1351765
1341753
1331741
1321729
1311717
1301705
1291693
1281681
1271669
1261657
1251645
1241633
1231621
1221609
1211597
1201585
1191573
1181561
1171549
1161537
1151525
1141513
1131501
1121489
1111477
1101465
1091453
1081441
1071429
1061417
1051405
1041393
1031381
1021369
1011357
1001345
991333
981321
971309
961297
951285
941273
931261
921249
911237
901225
891213
881201
871189
861177
851165
841153
831141
821129
811117
801105
791093
781081
771069
761057
751045
741033
731021
721009
71997
70985
69973
68961
67949
66937
65925
64913
63901
62889
61877
60865
59853
58841
57829
56817
55805
54793
53781
52769
51757
50745
49733
48721
47709
46697
45685
44673
43661
42649
41637
40625
39613
38601
37589
36577
35565
34553
33541
32529
31517
30505
29493
28481
27469
26457
25445
24433
23421
22409
21397
20385
19373
18361
17349
16337
15325
14313
13301
12285
11265
10219
9199
8155
7126
6105
595
486
380
270
166
054

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.4s8156×body80nan
1.7s8000×body80valid