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

sample37.0ms

Algorithm

intervals

Results

17.0ms	101×	body	1280	valid
4.0ms	11×	body	160	valid
4.0ms	33×	body	640	valid
2.0ms	27×	body	320	valid
2.0ms	84×	body	80	valid
0.0ms	6×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4934	6
1	4934	6

prune2.0ms

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: 28.8b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

3.7b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

4.0ms

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

series8.0ms

Counts

1 → 3

Calls

1 calls:

8.0ms

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

simplify50.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5023	180

prune22.0ms

Filtered

12 candidates to 18 candidates (-50.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	5	19

Merged error: 3.9b

Counts

19 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
3.8b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
8.0b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.7b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite33.0ms

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
12.0ms	(.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)))))
10.0ms	(+.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

prune65.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 2.4b

Counts

91 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

8.7b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
11.6b	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
11.6b	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
11.6b	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/3_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 50

Calls

4 calls:

8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
5.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
65.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
65.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
64.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4957	1559
1	4957	1559

prune132.0ms

Filtered

58 candidates to 62 candidates (-6.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	62	8	70

Merged error: 2.4b

Counts

70 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
11.6b	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))
11.6b	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))
11.6b	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
63.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))
63.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))
63.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4941	1784
1	4941	1784

prune194.0ms

Filtered

61 candidates to 64 candidates (-4.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	64	8	72

Merged error: 2.4b

Counts

72 → 8

regimes285.0ms

Accuracy

89.5% (2.5b remaining)

Error of 4.7b against oracle of 2.3b and baseline of 25.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	40
1	37	40

end0.0ms

sample965.0ms

Algorithm

intervals

Results

491.0ms	2728×	body	1280	valid
157.0ms	1305×	body	640	valid
70.0ms	795×	body	320	valid
70.0ms	2790×	body	80	valid
21.0ms	382×	body	160	valid
4.0ms	134×	body	80	invalid

Details

analyze42.0ms

sample37.0ms

simplify38.0ms

prune2.0ms

localize4.0ms

rewrite5.0ms

series8.0ms

simplify50.0ms

prune22.0ms

localize13.0ms

rewrite33.0ms

series75.0ms

simplify30.0ms

prune65.0ms

localize19.0ms

rewrite20.0ms

series204.0ms

simplify40.0ms

prune132.0ms

localize32.0ms

rewrite14.0ms

series254.0ms

simplify68.0ms

prune194.0ms

regimes285.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample965.0ms

Profiling