Details

Time bar (total: 16.6s)

analyze1.3s

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
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
25%74.9%0.1%8
54.6%45.2%0.1%9
56.2%43.7%0.1%10
62.4%37.4%0.1%11
65.9%33.9%0.1%12
66.3%33.5%0.1%13
69%30.8%0.1%14

sample215.0ms

Algorithm
intervals
Results
150.0ms135×body1280valid
36.0ms54×body640valid
11.0ms24×body320valid
4.0ms34×body80valid
2.0ms9×body160valid

simplify165.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (150.0ms)

IterNodesCost
0517126

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.6b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b
(pow.f64 (sin.f64 kx) 2)
0.3b
(pow.f64 (sin.f64 ky) 2)
4.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity_binary64
34×add-sqr-sqrt_binary64
30×associate-*l*_binary64
26×times-frac_binary64
25×add-cube-cbrt_binary64
21×sqrt-prod_binary64
14×unpow-prod-down_binary64
11×add-exp-log_binary64
9×pow1_binary64 add-cbrt-cube_binary64
8×distribute-lft-out_binary64
6×pow-unpow_binary64
4×add-log-exp_binary64 insert-posit16 sqrt-div_binary64
3×associate-*r*_binary64 unswap-sqr_binary64
2×pow-to-exp_binary64 flip3-+_binary64 cbrt-unprod_binary64 unpow2_binary64 pow-pow_binary64 sqr-pow_binary64 associate-/r/_binary64 prod-exp_binary64 flip-+_binary64 pow-exp_binary64
1×pow-prod-down_binary64 pow1/2_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 div-inv_binary64 div-exp_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 107
Calls
4 calls:
21.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
3.0ms
(pow.f64 (sin.f64 kx) 2)
3.0ms
(pow.f64 (sin.f64 ky) 2)
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
312.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
229.0ms
(pow.f64 (sin.f64 kx) 2)
231.0ms
(pow.f64 (sin.f64 ky) 2)
299.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0519744
1519744
01945
11945
0519744
1519744
01945
11945
01689
11689
0447804
1447804
0129
1129
0447804
1447804
0129
1129
013
113
0447804
1447804
0129
1129
0447804
1447804
0129
1129
013
113
06751383
16751383
050459
150459
06751383
16751383
050459
150459
03064
13064

simplify129.0ms

Counts
119 → 119
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
052652187

prune154.0ms

Filtered
78 candidates to 119 candidates (-52.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10712119
Fresh000
Picked101
Done000
Total10812120

Merged error: 4.1b

Counts
120 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))
12.3b
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
12.3b
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
12.3b
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod_binary64
12×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64 add-cube-cbrt_binary64
9×unpow-prod-down_binary64
5×pow1_binary64
4×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 insert-posit16
3×unpow2_binary64 pow1/3_binary64 sqr-pow_binary64 sqrt-prod_binary64
2×sqrt-div_binary64
1×flip3-+_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64
Counts
4 → 67
Calls
4 calls:
6.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))
3.0ms
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
3.0ms
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
3.0ms
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

series2.6s

Counts
4 → 12
Calls
4 calls:
471.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))
725.0ms
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
726.0ms
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
726.0ms
(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
Iterations

Useful iterations: 0 (109.0ms)

IterNodesCost
0561648
1561648
049301630
149301630
0561648
1561648
049301630
149301630
0491960
1491960
0561648
1561648
049301630
149301630
0561648
1561648
049301630
149301630
0491960
1491960
0561648
1561648
049301630
149301630
0561648
1561648
049301630
149301630
0491960
1491960
05201985
15201985
049671609
149671609
05201985
15201985
049671609
149671609
0509264

simplify127.0ms

Counts
79 → 79
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
048831164
148831164

prune124.0ms

Filtered
64 candidates to 79 candidates (-23.4%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New79079
Fresh01111
Picked011
Done000
Total791291

Merged error: 4.1b

Counts
91 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (sin.f64 kx))
0.6b
(cbrt.f64 (sin.f64 kx))
0.8b
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.2b
(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64 add-cube-cbrt_binary64
9×cbrt-prod_binary64
6×pow1_binary64 unpow-prod-down_binary64
5×add-exp-log_binary64
4×add-log-exp_binary64 add-cbrt-cube_binary64 insert-posit16
3×pow-unpow_binary64 pow1/3_binary64 sqrt-prod_binary64
2×pow-pow_binary64 sqrt-div_binary64
1×pow-to-exp_binary64 flip3-+_binary64 pow1/2_binary64 sqr-pow_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64 pow-exp_binary64
Counts
4 → 62
Calls
4 calls:
2.0ms
(cbrt.f64 (sin.f64 kx))
2.0ms
(cbrt.f64 (sin.f64 kx))
4.0ms
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
15.0ms
(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
272.0ms
(cbrt.f64 (sin.f64 kx))
272.0ms
(cbrt.f64 (sin.f64 kx))
460.0ms
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
546.0ms
(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
Iterations

Useful iterations: 0 (142.0ms)

IterNodesCost
07061871
17061871
050191702
07061871
17061871
050191702
0490353
1490353
02791648
12791648
049411633
149411633
02791648
12791648
049411633
149411633
0500049
0481621
1481621
0461606
1461606
0481621
1481621
0461606
1461606
0489154
1489154
0481621
1481621
0461606
1461606
0481621
1481621
0461606
1461606
0489154
1489154

simplify144.0ms

Counts
74 → 74
Iterations

Useful iterations: 0 (117.0ms)

IterNodesCost
049361015
149361015

prune107.0ms

Filtered
63 candidates to 74 candidates (-17.5%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New72274
Fresh1910
Picked011
Done011
Total731386

Merged error: 4.0b

Counts
86 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.9b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
4.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod_binary64
87×*-un-lft-identity_binary64
66×times-frac_binary64
53×add-sqr-sqrt_binary64
51×add-cube-cbrt_binary64
45×add-exp-log_binary64
39×associate-*l*_binary64
27×add-cbrt-cube_binary64
20×prod-exp_binary64
18×distribute-lft-out_binary64 unpow-prod-down_binary64
12×sqrt-div_binary64
11×associate-/r*_binary64 pow1_binary64 div-exp_binary64
10×cbrt-unprod_binary64
6×cbrt-undiv_binary64
4×flip3-+_binary64 add-log-exp_binary64 associate-/r/_binary64 insert-posit16 flip-+_binary64
3×pow-prod-down_binary64 1-exp_binary64 associate-*r/_binary64 rec-exp_binary64 associate-/l*_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 div-inv_binary64
1×associate-*r*_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 170
Calls
4 calls:
17.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
43.0ms
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
428.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
572.0ms
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
292.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
289.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0519744
1519744
01945
11945
0519744
1519744
01945
11945
01689
11689
0519744
1519744
01945
11945
0519744
1519744
01945
11945
01689
11689
09342134
19342134
049171537
149171537
09342134
19342134
049171537
149171537
0546171
07331451
17331451
091610
191610
07331451
17331451
091610
191610
0233
1233

simplify190.0ms

Counts
182 → 182
Iterations

Useful iterations: 0 (129.0ms)

IterNodesCost
049225516
149225516

prune215.0ms

Filtered
105 candidates to 182 candidates (-73.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1811182
Fresh2810
Picked101
Done022
Total18411195

Merged error: 4.0b

Counts
195 → 11

regimes263.0ms

Accuracy

0% (0.9b remaining)

Error of 4.2b against oracle of 3.3b and baseline of 4.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02048
12048

end0.0ms

sample6.4s

Algorithm
intervals
Results
4.1s3675×body1280valid
1.4s2050×body640valid
340.0ms717×body320valid
159.0ms1260×body80valid
87.0ms298×body160valid

Profiling

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