Details

analyze39.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

sample40.0ms

Algorithm

intervals

Results

13.0ms	42×	body	2048	valid
10.0ms	72×	body	1024	valid
3.0ms	35×	body	512	valid
2.0ms	89×	body	128	valid
1.0ms	18×	body	256	valid
0.0ms	2×	body	128	invalid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4955	9
1	4955	9

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.1b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 25

Calls

2 calls:

2.0ms	(exp.f64 (*.f64 a x))
5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series73.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(exp.f64 (*.f64 a x))
50.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify82.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5076	374

prune27.0ms

Filtered

20 candidates to 31 candidates (-55.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	3	32

Merged error: 3.8b

Counts

32 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
4.4b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
4.6b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
11.5b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

7.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
11.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
9.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
178.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
77.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
87.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5330	1832

prune82.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.1b

Counts

89 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 1/6) a)
0.4b	(*.f64 x 1/6)
2.9b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
4.4b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
16×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`associate-r/_binary64` `associate-l*_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 97

Calls

4 calls:

6.0ms	(.f64 (.f64 x 1/6) a)
5.0ms	(*.f64 x 1/6)
16.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
15.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 (.f64 x 1/6) a)
23.0ms	(*.f64 x 1/6)
160.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
146.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

simplify44.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5436	1810

prune64.0ms

Filtered

57 candidates to 109 candidates (-91.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Merged error: 0.1b

Counts

113 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

4.4b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
18.8b	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))
18.8b	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))
18.8b	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-*r/_binary64`
6×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`
3×	`pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
1×	`associate-r_binary64` `*-commutative_binary64`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
6.0ms	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))
6.0ms	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))
5.0ms	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

148.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
457.0ms	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))
455.0ms	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))
467.0ms	(cbrt.f64 (.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5176	2394

prune149.0ms

Filtered

58 candidates to 72 candidates (-24.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	72	4	76

Merged error: 0.1b

Counts

76 → 4

regimes85.0ms

Accuracy

88.1% (2.8b remaining)

Error of 3.1b against oracle of 0.3b and baseline of 23.7b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	71
1	48	71

end0.0ms

sample1.1s

Algorithm

intervals

Results

466.0ms	1452×	body	2048	valid
267.0ms	1788×	body	1024	valid
99.0ms	1109×	body	512	valid
70.0ms	3011×	body	128	valid
35.0ms	640×	body	256	valid
3.0ms	135×	body	128	invalid

Details

analyze39.0ms

sample40.0ms

simplify63.0ms

prune1.0ms

localize4.0ms

rewrite8.0ms

series73.0ms

simplify82.0ms

prune27.0ms

localize12.0ms

rewrite43.0ms

series492.0ms

simplify43.0ms

prune82.0ms

localize12.0ms

rewrite52.0ms

series357.0ms

simplify44.0ms

prune64.0ms

localize17.0ms

rewrite40.0ms

series1.5s

simplify64.0ms

prune149.0ms

regimes85.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling