Details

analyze42.0ms

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

sample33.0ms

Algorithm

intervals

Results

16.0ms	86×	body	1280	valid
5.0ms	44×	body	640	valid
2.0ms	94×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	4×	body	80	invalid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4957	9
1	4957	9

prune4.0ms

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: 28.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.9b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite6.0ms

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))
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series42.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp.f64 (*.f64 a x))
28.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify114.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4961	374
1	4961	374

prune31.0ms

Filtered

20 candidates to 31 candidates (-55.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 3.7b

Counts

32 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.4b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.2b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
9.5b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite30.0ms

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:

5.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
6.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
49.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
97.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
42.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5332	1832

prune78.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 0.1b

Counts

93 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x 1/6)
0.5b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.7b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
7.2b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

4.0ms	(*.f64 x 1/6)
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
6.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
10.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 x 1/6)
33.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
84.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
76.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6117	1933

prune72.0ms

Filtered

65 candidates to 102 candidates (-56.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Merged error: 0.1b

Counts

108 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 1/6) a)
0.4b	(*.f64 x 1/6)
0.5b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
9.5b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64`
3×	`unpow-prod-down_binary64` `exp-prod_binary64` `*-commutative_binary64`
2×	`associate-*r/_binary64` `unpow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(.f64 (.f64 x 1/6) a)
4.0ms	(*.f64 x 1/6)
7.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
4.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (.f64 x 1/6) a)
11.0ms	(*.f64 x 1/6)
39.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
60.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

simplify111.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4930	1374
1	4930	1374

prune65.0ms

Filtered

58 candidates to 91 candidates (-56.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	91	6	97

Merged error: 0.1b

Counts

97 → 6

regimes150.0ms

Accuracy

87.8% (2.9b remaining)

Error of 3.1b against oracle of 0.2b and baseline of 24.1b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	117
1	65	117

end0.0ms

sample968.0ms

Algorithm

intervals

Results

499.0ms	2782×	body	1280	valid
154.0ms	1286×	body	640	valid
71.0ms	2817×	body	80	valid
62.0ms	738×	body	320	valid
21.0ms	377×	body	160	valid
3.0ms	117×	body	80	invalid

Details

analyze42.0ms

sample33.0ms

simplify80.0ms

prune4.0ms

localize5.0ms

rewrite6.0ms

series42.0ms

simplify114.0ms

prune31.0ms

localize12.0ms

rewrite30.0ms

series277.0ms

simplify52.0ms

prune78.0ms

localize13.0ms

rewrite30.0ms

series204.0ms

simplify52.0ms

prune72.0ms

localize12.0ms

rewrite22.0ms

series124.0ms

simplify111.0ms

prune65.0ms

regimes150.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample968.0ms

Profiling