Details

analyze41.0ms

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

sample32.0ms

Algorithm

intervals

Results

14.0ms	82×	body	1280	valid
5.0ms	42×	body	640	valid
2.0ms	93×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	5×	body	80	invalid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4778	6
1	4778	6

prune3.0ms

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: 29.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.1b	(-.f64 (exp.f64 (*.f64 a x)) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

1 → 13

Calls

1 calls:

8.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1.0)

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4903	161
1	4903	161

prune32.0ms

Filtered

12 candidates to 16 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	4	17

Merged error: 4.6b

Counts

17 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
4.7b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.1b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.9b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite34.0ms

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:

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
14.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
26.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
13.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify30.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5186	1359

prune85.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 2.3b

Counts

90 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
4.2b	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
13.4b	(.f64 (.f64 a a) (*.f64 x x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1_binary64`
33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow-prod-down_binary64`
21×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64`
4×	`-un-lft-identity_binary64` `pow-prod-up_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `pow-plus_binary64` `add-sqr-sqrt_binary64`
2×	`associate-r_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 67

Calls

3 calls:

12.0ms	(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
5.0ms	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
9.0ms	(.f64 (.f64 a a) (*.f64 x x))

series30.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
12.0ms	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
8.0ms	(.f64 (.f64 a a) (*.f64 x x))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	572
1	4962	572

prune55.0ms

Filtered

40 candidates to 76 candidates (-90.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	77	4	81

Merged error: 0.1b

Counts

81 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 1/2 (pow.f64 (.f64 a x) 2))
0.3b	(pow.f64 (*.f64 a x) 2)
4.2b	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
6×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
4×	`pow-exp_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `unpow-prod-down_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 54

Calls

3 calls:

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

series28.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(.f64 1/2 (pow.f64 (.f64 a x) 2))
6.0ms	(pow.f64 (*.f64 a x) 2)
11.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

simplify28.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5115	523

prune43.0ms

Filtered

39 candidates to 63 candidates (-61.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	63	4	67

Merged error: 0.1b

Counts

67 → 4

regimes243.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 22.0b

bsearch12.0ms

Steps

Iters	Range		Point
9	-7.603404984815863e-05	-1.4312525623687216e-11	-5.984861235991215e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	25
1	29	25

end0.0ms

sample949.0ms

Algorithm

intervals

Results

480.0ms	2692×	body	1280	valid
153.0ms	1297×	body	640	valid
71.0ms	2853×	body	80	valid
63.0ms	773×	body	320	valid
21.0ms	385×	body	160	valid
4.0ms	146×	body	80	invalid

Details

analyze41.0ms

sample32.0ms

simplify67.0ms

prune3.0ms

localize4.0ms

rewrite8.0ms

series9.0ms

simplify53.0ms

prune32.0ms

localize12.0ms

rewrite34.0ms

series86.0ms

simplify30.0ms

prune85.0ms

localize8.0ms

rewrite29.0ms

series30.0ms

simplify62.0ms

prune55.0ms

localize7.0ms

rewrite18.0ms

series28.0ms

simplify28.0ms

prune43.0ms

regimes243.0ms

bsearch12.0ms

simplify2.0ms

end0.0ms

sample949.0ms

Profiling