Details

Time bar (total: 12.4s)

analyze6.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
75%25%0%5
87.5%12.5%0%6
93.7%6.2%0%7
96.8%3.1%0%8
98.4%1.6%0%9
99.2%0.8%0%10
99.6%0.4%0%11
99.8%0.2%0%12
99.9%0.1%0%13
99.9%0.1%0.1%14

sample25.0ms

Algorithm
intervals
Results
8.0ms59×body640valid
5.0ms140×body80valid
4.0ms21×body1280valid
3.0ms25×body320valid
1.0ms11×body160valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
019322
119322

prune3.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 10.7b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/.f64 1 (+.f64 x 1))
0.0b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b
(/.f64 1 (-.f64 x 1))
1.9b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity_binary64
58×add-sqr-sqrt_binary64
56×times-frac_binary64
25×add-cube-cbrt_binary64
18×distribute-lft-out--_binary64
17×distribute-lft-out_binary64
14×difference-of-squares_binary64
12×add-exp-log_binary64
11×associate-/r*_binary64 add-log-exp_binary64
8×add-cbrt-cube_binary64 div-inv_binary64
6×pow1_binary64 associate-/l*_binary64
4×difference-of-sqr-1_binary64 associate-/r/_binary64 div-exp_binary64 insert-posit16
3×flip3--_binary64 frac-add_binary64 flip--_binary64
2×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 1-exp_binary64 cbrt-undiv_binary64 clear-num_binary64 inv-pow_binary64 frac-2neg_binary64 rec-exp_binary64 pow-flip_binary64 flip-+_binary64 frac-sub_binary64 sum-log_binary64
1×associate-+l+_binary64 associate-+l-_binary64 +-commutative_binary64
Counts
4 → 139
Calls
4 calls:
7.0ms
(/.f64 1 (+.f64 x 1))
25.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms
(/.f64 1 (-.f64 x 1))
44.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series1.6s

Counts
4 → 12
Calls
4 calls:
346.0ms
(/.f64 1 (+.f64 x 1))
358.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
368.0ms
(/.f64 1 (-.f64 x 1))
494.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
06881016
16881016
071688
171688
06881016
16881016
071688
171688
0585947
0299435
1299435
079
179
0299435
1299435
079
179
0506342
0481765
1481765
089
189
0481765
1481765
089
189
0494736
1494736
0299435
1299435
069
169
0299435
1299435
069
169
0492111
1492111

simplify134.0ms

Counts
151 → 151
Iterations

Useful iterations: 0 (96.0ms)

IterNodesCost
055222538

prune144.0ms

Filtered
95 candidates to 151 candidates (-58.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New14110151
Fresh000
Picked101
Done000
Total14210152

Merged error: 10.5b

Counts
152 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt.f64 (-.f64 x 1))
0.2b
(cbrt.f64 (-.f64 x 1))
0.2b
(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
15.4b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity_binary64
54×cbrt-prod_binary64
50×add-sqr-sqrt_binary64
16×cbrt-div_binary64
14×swap-sqr_binary64 add-cube-cbrt_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
12×times-frac_binary64
11×pow1_binary64
10×associate-*r*_binary64 associate-*l*_binary64
9×add-log-exp_binary64 flip3--_binary64 distribute-lft-out_binary64 flip--_binary64
8×pow1/3_binary64 difference-of-sqr-1_binary64
6×add-exp-log_binary64
4×add-cbrt-cube_binary64 unswap-sqr_binary64 insert-posit16 frac-times_binary64
3×frac-add_binary64 div-inv_binary64
2×pow-prod-down_binary64 pow-prod-up_binary64 associate-*r/_binary64 pow-sqr_binary64 associate-*l/_binary64 sum-log_binary64
1×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 cbrt-unprod_binary64 associate-+l+_binary64 associate-+l-_binary64 pow-plus_binary64 prod-exp_binary64 +-commutative_binary64 flip-+_binary64 frac-sub_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 126
Calls
4 calls:
4.0ms
(cbrt.f64 (-.f64 x 1))
4.0ms
(cbrt.f64 (-.f64 x 1))
15.0ms
(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
125.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))

series2.0s

Counts
4 → 12
Calls
4 calls:
224.0ms
(cbrt.f64 (-.f64 x 1))
220.0ms
(cbrt.f64 (-.f64 x 1))
1.0s
(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
508.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))
Iterations

Useful iterations: 0 (135.0ms)

IterNodesCost
09711997
19711997
01321886
11321886
09711997
19711997
01321886
11321886
0477529
1477529
01181718
11181718
068331692
01181718
11181718
068331692
0488183
1488183
0471627
1471627
0541614
1541614
0471627
1471627
0541614
1541614
0485456
1485456
0471627
1471627
0541614
1541614
0471627
1471627
0541614
1541614
0485456
1485456

simplify143.0ms

Counts
138 → 138
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
053002538

prune192.0ms

Filtered
96 candidates to 138 candidates (-43.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1344138
Fresh369
Picked101
Done000
Total13810148

Merged error: 10.5b

Counts
148 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (cbrt.f64 (-.f64 x 1)) 2)
7.3b
(/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
7.4b
(/.f64 (+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (*.f64 (cbrt.f64 (-.f64 x 1)) (*.f64 x (+.f64 1 x))))
18.4b
(+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
30×unpow-prod-down_binary64
27×add-exp-log_binary64 add-sqr-sqrt_binary64
24×*-un-lft-identity_binary64
21×cbrt-prod_binary64
18×cbrt-div_binary64 times-frac_binary64
16×associate-/r*_binary64 frac-add_binary64 add-cbrt-cube_binary64
15×flip3--_binary64 add-cube-cbrt_binary64 flip--_binary64
14×associate-*r/_binary64
12×associate-/l/_binary64 frac-times_binary64
9×div-exp_binary64
8×associate-/r/_binary64
6×flip3-+_binary64 add-log-exp_binary64 prod-exp_binary64 difference-of-squares_binary64 flip-+_binary64 associate-*l/_binary64
5×pow1_binary64 cbrt-undiv_binary64
4×cbrt-unprod_binary64 associate-/l*_binary64 insert-posit16
3×pow-to-exp_binary64 pow-unpow_binary64 unpow2_binary64 difference-of-sqr-1_binary64 sqr-pow_binary64 distribute-lft-out--_binary64 pow-exp_binary64
2×sub-neg_binary64 pow-pow_binary64 associate-+l+_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64
1×pow1/3_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 143
Calls
4 calls:
7.0ms
(pow.f64 (cbrt.f64 (-.f64 x 1)) 2)
15.0ms
(/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
37.0ms
(/.f64 (+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (*.f64 (cbrt.f64 (-.f64 x 1)) (*.f64 x (+.f64 1 x))))
23.0ms
(+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
363.0ms
(pow.f64 (cbrt.f64 (-.f64 x 1)) 2)
518.0ms
(/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
922.0ms
(/.f64 (+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (*.f64 (cbrt.f64 (-.f64 x 1)) (*.f64 x (+.f64 1 x))))
531.0ms
(+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (/.f64 (*.f64 x (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))
Iterations

Useful iterations: 0 (347.0ms)

IterNodesCost
09422007
19422007
050331887
09422007
19422007
050331887
07145
17145
012552217
112552217
055981963
012552217
112552217
055981963
049266
149266
07031773
17031773
050341690
07031773
17031773
050341690
0490915
1490915
02771654
12771654
055751641
02771654
12771654
055751641
0489365
1489365

simplify185.0ms

Counts
155 → 155
Iterations

Useful iterations: 0 (132.0ms)

IterNodesCost
049535518
149535518

prune363.0ms

Filtered
116 candidates to 155 candidates (-33.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1505155
Fresh189
Picked101
Done000
Total15213165

Merged error: 10.5b

Counts
165 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

7.3b
(/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
7.3b
(/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
10.1b
(/.f64 (+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))))) (*.f64 (cbrt.f64 (-.f64 x 1)) (*.f64 x (+.f64 1 x))))
22.0b
(+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
282×cbrt-div_binary64
140×frac-times_binary64
112×frac-add_binary64
110×associate-*l/_binary64
88×associate-*r/_binary64
87×flip3--_binary64 flip--_binary64
62×associate-/l/_binary64
40×unpow-prod-down_binary64
39×add-exp-log_binary64
34×add-sqr-sqrt_binary64
33×times-frac_binary64
31×associate-/r*_binary64
30×*-un-lft-identity_binary64
28×cbrt-prod_binary64
21×add-cbrt-cube_binary64
18×add-cube-cbrt_binary64
15×div-exp_binary64
9×prod-exp_binary64
8×associate-/r/_binary64 difference-of-squares_binary64
7×flip3-+_binary64 cbrt-undiv_binary64 flip-+_binary64
6×add-log-exp_binary64
5×cbrt-unprod_binary64 associate-/l*_binary64
4×pow-to-exp_binary64 pow1_binary64 unpow2_binary64 difference-of-sqr-1_binary64 sqr-pow_binary64 distribute-lft-out--_binary64 insert-posit16 pow-exp_binary64
3×clear-num_binary64 frac-2neg_binary64 div-inv_binary64
2×sub-neg_binary64 associate-+l+_binary64
1×distribute-lft-in_binary64 distribute-rgt-in_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 264
Calls
4 calls:
16.0ms
(/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
15.0ms
(/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
35.0ms
(/.f64 (+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))))) (*.f64 (cbrt.f64 (-.f64 x 1)) (*.f64 x (+.f64 1 x))))
16.0ms
(+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
522.0ms
(/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
517.0ms
(/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))
856.0ms
(/.f64 (+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))))) (*.f64 (cbrt.f64 (-.f64 x 1)) (*.f64 x (+.f64 1 x))))
480.0ms
(+.f64 (*.f64 (cbrt.f64 (-.f64 x 1)) (-.f64 x (*.f64 (+.f64 1 x) 2))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))) (cbrt.f64 (/.f64 (*.f64 x (+.f64 x 1)) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)))))
Iterations

Useful iterations: 0 (279.0ms)

IterNodesCost
06462535
16462535
053061851
06462535
16462535
053061851
02245
12245
010542745
110542745
055391969
010542745
110542745
055391969
050396
07031773
17031773
050341690
07031773
17031773
050341690
0490915
1490915
07031773
17031773
050341690
07031773
17031773
050341690
0490915
1490915

simplify238.0ms

Counts
276 → 276
Iterations

Useful iterations: 0 (109.0ms)

IterNodesCost
0496415849
1496415849

prune1.2s

Filtered
193 candidates to 276 candidates (-43.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New2688276
Fresh4812
Picked101
Done000
Total27316289

Merged error: 10.5b

Counts
289 → 16

regimes116.0ms

Accuracy

95.4% (0.8b remaining)

Error of 10.0b against oracle of 9.2b and baseline of 25.5b

bsearch104.0ms

Steps
ItersRangePoint
9
1.1959733022539398e+133
4.647542358488778e+141
1.691942371348407e+134
10
-2.4679444857839995e+155
-3.986541999333381e+145
-1.3430294122385343e+154

simplify10.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0157216
1157216

end0.0ms

sample726.0ms

Algorithm
intervals
Results
243.0ms1816×body640valid
158.0ms4212×body80valid
98.0ms571×body1280valid
95.0ms931×body320valid
32.0ms470×body160valid

Profiling

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