Details

Time bar (total: 15.3s)

analyze1.2s

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
0%100%0%5
0%100%0%6
0%100%0%7
0%100%0%8
0%100%0%9
0%100%0%10
0%100%0%11
0%100%0%12
0%100%0%13
0.1%99.9%0%14

sample221.0ms

Algorithm
intervals
Results
124.0ms56×body2560valid
60.0ms94×body1280valid
19.0ms55×body640valid
6.0ms30×body320valid
2.0ms13×body160valid
1.0ms8×body80valid

simplify211.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
099114
199114

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.1b
(-.f64 x (tan.f64 x))
1.1b
(-.f64 x (sin.f64 x))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
25×times-frac_binary64
15×add-cube-cbrt_binary64
14×difference-of-squares_binary64 distribute-lft-out--_binary64
7×add-log-exp_binary64
5×associate-/r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
4×flip3--_binary64 flip--_binary64
3×pow1_binary64 insert-posit16
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 associate-/r/_binary64
1×cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
3 → 81
Calls
3 calls:
10.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms
(-.f64 x (tan.f64 x))
207.0ms
(-.f64 x (sin.f64 x))

series671.0ms

Counts
3 → 9
Calls
3 calls:
285.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
202.0ms
(-.f64 x (tan.f64 x))
184.0ms
(-.f64 x (sin.f64 x))
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0249195
1249195
01215
11215
0249195
1249195
01215
11215
0303
1303
0382435
1382435
01715
11715
0382435
1382435
01715
11715
0303
1303
06591279
16591279
0229956
1229956
06591279
16591279
0229956
1229956
08155
18155

simplify107.0ms

Counts
90 → 90
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
056361631

prune55.0ms

Filtered
64 candidates to 90 candidates (-40.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New88290
Fresh000
Picked011
Done000
Total88391

Merged error: 32.4b

Counts
91 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
1.1b
(-.f64 x (sin.f64 x))
3.9b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
15.9b
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
465×add-sqr-sqrt_binary64
292×*-un-lft-identity_binary64
251×times-frac_binary64
244×difference-of-squares_binary64
144×unpow-prod-down_binary64 cube-prod_binary64
131×associate-*l*_binary64
112×distribute-lft-out--_binary64
96×sqr-pow_binary64
68×add-cube-cbrt_binary64
25×associate-/r*_binary64
12×difference-cubes_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64
6×pow1_binary64
5×flip3--_binary64 associate-/l*_binary64 flip--_binary64
4×associate-/r/_binary64 insert-posit16
3×associate-*r*_binary64
2×flip3-+_binary64 associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-*r/_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64 frac-times_binary64
1×pow-prod-down_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 378
Calls
4 calls:
14.0ms
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
5.0ms
(-.f64 x (sin.f64 x))
24.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
53.0ms
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
309.0ms
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
172.0ms
(-.f64 x (sin.f64 x))
400.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
479.0ms
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
014842131
114842131
03811659
13811659
014842131
114842131
03811659
13811659
06041
16041
011031586
111031586
02221038
12221038
011031586
111031586
02221038
12221038
08155
18155
0249195
1249195
01215
11215
0249195
1249195
01215
11215
0303
1303
08261203
18261203
0108259
1108259
08261203
18261203
0108259
1108259
013
113

simplify193.0ms

Counts
390 → 390
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
0511814354

prune318.0ms

Filtered
201 candidates to 390 candidates (-94.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3891390
Fresh011
Picked101
Done011
Total3903393

Merged error: 32.4b

Counts
393 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3))))
1.0b
(-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))
1.1b
(-.f64 x (sin.f64 x))
23.6b
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
50×times-frac_binary64
31×associate-*l*_binary64
27×pow-prod-down_binary64 add-cube-cbrt_binary64
24×difference-of-squares_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
16×frac-times_binary64
12×difference-cubes_binary64 flip3-+_binary64 associate-*r/_binary64 distribute-lft-out--_binary64 flip-+_binary64
9×pow1_binary64
8×add-log-exp_binary64
6×cbrt-unprod_binary64 prod-exp_binary64
5×associate-/r*_binary64 flip3--_binary64 associate-/l*_binary64 flip--_binary64 associate-*l/_binary64
4×distribute-lft-in_binary64 associate-/r/_binary64 distribute-rgt-in_binary64 insert-posit16
3×cbrt-undiv_binary64 div-exp_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 div-inv_binary64
1×associate-*r*_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 153
Calls
4 calls:
21.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3))))
13.0ms
(-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))
5.0ms
(-.f64 x (sin.f64 x))
43.0ms
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))

series1.6s

Counts
4 → 12
Calls
4 calls:
474.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3))))
369.0ms
(-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))
173.0ms
(-.f64 x (sin.f64 x))
625.0ms
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
017082428
117082428
06132007
16132007
017082428
117082428
06132007
16132007
05138
15138
0249195
1249195
01215
11215
0249195
1249195
01215
11215
0303
1303
09661718
19661718
0215984
1215984
09661718
19661718
0215984
1215984
013
113
012431960
112431960
02991504
12991504
012431960
112431960
02991504
12991504
06041
16041

simplify183.0ms

Counts
165 → 165
Iterations

Useful iterations: 0 (115.0ms)

IterNodesCost
049836804
149836804

prune273.0ms

Filtered
126 candidates to 165 candidates (-31.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1641165
Fresh011
Picked101
Done011
Total1653168

Merged error: 32.4b

Counts
168 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(-.f64 x (sin.f64 x))
1.1b
(-.f64 x (sin.f64 x))
1.1b
(-.f64 x (sin.f64 x))
23.6b
(*.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log_binary64
28×add-cbrt-cube_binary64
18×cbrt-unprod_binary64 prod-exp_binary64
16×frac-times_binary64
12×flip3-+_binary64 *-un-lft-identity_binary64 associate-*r/_binary64 add-sqr-sqrt_binary64 flip-+_binary64
11×associate-*l*_binary64
10×add-log-exp_binary64
9×pow1_binary64
6×cbrt-undiv_binary64 add-cube-cbrt_binary64 div-exp_binary64
5×pow-prod-down_binary64 times-frac_binary64 associate-*l/_binary64
4×flip3--_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 difference-of-squares_binary64 insert-posit16 flip--_binary64
3×sub-neg_binary64 diff-log_binary64 distribute-lft-out--_binary64
2×associate-/r/_binary64
1×difference-cubes_binary64 associate-*r*_binary64 div-inv_binary64 *-commutative_binary64
Counts
4 → 102
Calls
4 calls:
5.0ms
(-.f64 x (sin.f64 x))
5.0ms
(-.f64 x (sin.f64 x))
5.0ms
(-.f64 x (sin.f64 x))
53.0ms
(*.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))

series1.3s

Counts
4 → 12
Calls
4 calls:
180.0ms
(-.f64 x (sin.f64 x))
178.0ms
(-.f64 x (sin.f64 x))
179.0ms
(-.f64 x (sin.f64 x))
793.0ms
(*.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 x) 3)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))) (+.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
018442714
118442714
051582136
018442714
118442714
051582136
06354175
0249195
1249195
01215
11215
0249195
1249195
01215
11215
0303
1303
0249195
1249195
01215
11215
0249195
1249195
01215
11215
0303
1303
0249195
1249195
01215
11215
0249195
1249195
01215
11215
0303
1303

simplify168.0ms

Counts
114 → 114
Iterations

Useful iterations: 0 (115.0ms)

IterNodesCost
050074388

prune182.0ms

Filtered
81 candidates to 114 candidates (-40.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh011
Picked011
Done011
Total1143117

Merged error: 32.4b

Counts
117 → 3

regimes39.0ms

Accuracy

87% (0.1b remaining)

Error of 30.6b against oracle of 30.5b and baseline of 31.5b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02934
12934

end0.0ms

sample6.6s

Algorithm
intervals
Results
4.0s1578×body2560valid
1.7s2793×body1280valid
497.0ms1880×body640valid
165.0ms902×body320valid
67.0ms488×body160valid
33.0ms359×body80valid

Profiling

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