Details

Time bar (total: 7.3s)

analyze781.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.2%0.1%6
21.9%78%0.1%7
23.4%76.5%0.1%8
24.2%75.7%0.1%9
24.6%75.3%0.1%10
24.8%75.1%0.1%11
24.9%75%0.1%12
24.9%75%0.1%13
25%75%0.1%14

sample82.0ms

Algorithm
intervals
Results
37.0ms100×body1280valid
17.0ms20×body2560valid
13.0ms62×body640valid
4.0ms30×body320valid
2.0ms36×body80valid
1.0ms8×body160valid

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0537411

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.3b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.8b
(tan.f64 (+.f64 x eps))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
6×frac-sub_binary64 consolidate-tan_binary64 tan-quot_binary64
4×*-un-lft-identity_binary64 add-log-exp_binary64 add-sqr-sqrt_binary64
3×tan-sum_binary64
2×pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 insert-posit16
1×sub-neg_binary64 flip3--_binary64 diff-log_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 flip--_binary64
Counts
2 → 31
Calls
2 calls:
13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms
(tan.f64 (+.f64 x eps))

series305.0ms

Counts
2 → 6
Calls
2 calls:
160.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
145.0ms
(tan.f64 (+.f64 x eps))
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
06632556
16632556
0459
1459
06632556
16632556
0459
1459
013
113
010132619
110132619
0789
1789
010132619
110132619
0789
1789
013
113

simplify99.0ms

Counts
37 → 37
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
05587613

prune40.0ms

Filtered
26 candidates to 37 candidates (-42.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New221537
Fresh000
Picked011
Done000
Total221638

Merged error: 36.9b

Counts
38 → 16

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
3.8b
(cos.f64 (+.f64 x eps))
4.0b
(sin.f64 (+.f64 x eps))
9.4b
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
10×times-frac_binary64
6×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×pow1_binary64 insert-posit16
3×associate-/r*_binary64 associate-/l*_binary64
2×difference-of-squares_binary64 frac-sub_binary64
1×sub-neg_binary64 flip3--_binary64 diff-log_binary64 cbrt-undiv_binary64 sin-sum_binary64 clear-num_binary64 frac-2neg_binary64 cos-sum_binary64 distribute-lft-out--_binary64 div-inv_binary64 div-exp_binary64 quot-tan_binary64 flip--_binary64 consolidate-tan_binary64 tan-quot_binary64
Counts
4 → 64
Calls
4 calls:
9.0ms
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
8.0ms
(cos.f64 (+.f64 x eps))
5.0ms
(sin.f64 (+.f64 x eps))
13.0ms
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))

series596.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
143.0ms
(cos.f64 (+.f64 x eps))
141.0ms
(sin.f64 (+.f64 x eps))
165.0ms
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
010112727
110112727
01059
11059
010112727
110112727
01059
11059
013
113
06552556
16552556
0419
1419
06552556
16552556
0419
1419
013
113
06532556
16532556
0439
1439
06532556
16532556
0439
1439
013
113
06592664
16592664
0729
1729
06592664
16592664
0729
1729
013
113

simplify112.0ms

Counts
76 → 76
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
050401345

prune84.0ms

Filtered
57 candidates to 76 candidates (-33.3%)
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New591776
Fresh7714
Picked101
Done011
Total672592

Merged error: 36.4b

Counts
92 → 25

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.2b
(/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 (+.f64 x eps)))
3.8b
(cos.f64 (+.f64 x eps))
7.2b
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 (+.f64 x eps))) (tan.f64 x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
10×times-frac_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
6×add-log-exp_binary64 pow1_binary64
4×insert-posit16
3×associate-/l/_binary64 associate-/r*_binary64 associate-*r*_binary64 associate-*l*_binary64 consolidate-/-/-b_binary64_1 associate-/l*_binary64
2×flip3-+_binary64 consolidate-+-/-l_binary64 difference-of-squares_binary64 sin-cos-mult_binary64 flip-+_binary64 frac-sub_binary64
1×pow-prod-down_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 unswap-sqr_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 cos-sum_binary64 distribute-lft-out--_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64 consolidate-tan_binary64 tan-quot_binary64 *-commutative_binary64
Counts
4 → 79
Calls
4 calls:
6.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
13.0ms
(/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 (+.f64 x eps)))
5.0ms
(cos.f64 (+.f64 x eps))
15.0ms
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 (+.f64 x eps))) (tan.f64 x))

series595.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
160.0ms
(/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 (+.f64 x eps)))
145.0ms
(cos.f64 (+.f64 x eps))
182.0ms
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
011502871
111502871
01629
11629
011502871
111502871
01629
11629
013
113
06532556
16532556
0439
1439
06532556
16532556
0439
1439
013
113
06762808
16762808
01319
11319
06762808
16762808
01319
11319
013
113
0672574
1672574
0799
1799
0672574
1672574
0799
1799
013
113

simplify101.0ms

Counts
91 → 91
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
050732332

prune102.0ms

Filtered
66 candidates to 91 candidates (-37.9%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New86591
Fresh91423
Picked101
Done011
Total9620116

Merged error: 22.3b

Counts
116 → 20

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.2b
(*.f64 (sin.f64 x) (sin.f64 eps))
0.2b
(/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
7.1b
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (tan.f64 x))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64 times-frac_binary64
8×pow1_binary64
6×add-log-exp_binary64 associate-*r*_binary64 associate-*l*_binary64
5×sin-mult_binary64
4×cos-mult_binary64 consolidate-/-/-b_binary64 associate-/r/_binary64 insert-posit16 frac-sub_binary64
3×associate-/l/_binary64 associate-/r*_binary64 flip3--_binary64 consolidate-/-/-b_binary64_1 associate-/l*_binary64 flip--_binary64
2×pow-prod-down_binary64 flip3-+_binary64 cbrt-unprod_binary64 consolidate-+-/-l_binary64 unswap-sqr_binary64 prod-exp_binary64 difference-of-squares_binary64 sin-cos-mult_binary64 sub-div_binary64 flip-+_binary64 *-commutative_binary64
1×sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 distribute-lft-out--_binary64 div-inv_binary64 div-exp_binary64 consolidate-tan_binary64 tan-quot_binary64
Counts
4 → 98
Calls
4 calls:
6.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
6.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))
17.0ms
(/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
21.0ms
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (tan.f64 x))

series1.1s

Counts
4 → 12
Calls
4 calls:
106.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
108.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))
551.0ms
(/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
308.0ms
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (tan.f64 x))
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
054163015
02759
12759
054163015
02759
12759
013
113
056472952
02299
12299
056472952
02299
12299
013
113
0672574
1672574
0769
1769
0672574
1672574
0769
1769
013
113
0672574
1672574
0799
1799
0672574
1672574
0799
1799
013
113

simplify124.0ms

Counts
110 → 110
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
049783647
149783647

prune117.0ms

Filtered
80 candidates to 110 candidates (-37.5%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New9614110
Fresh9918
Picked101
Done101
Total10723130

Merged error: 22.1b

Counts
130 → 23

regimes133.0ms

Accuracy

0% (0.6b remaining)

Error of 21.5b against oracle of 21.0b and baseline of 21.5b

bsearch0.0ms

simplify20.0ms

Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
038273
138273

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3429×body1280valid
503.0ms588×body2560valid
385.0ms1790×body640valid
103.0ms743×body320valid
47.0ms1105×body80valid
33.0ms345×body160valid

Profiling

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