Details

analyze58.0ms

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

sample51.0ms

Algorithm

intervals

Results

28.0ms	98×	body	1280	valid
5.0ms	36×	body	640	valid
3.0ms	91×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	1×	body	80	invalid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	3
7	5001	3

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: 28.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.0b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

2.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series11.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(exp (* a x))
7.0ms	(- (exp (* a x)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune60.0ms

Filtered

20 candidates to 30 candidates (-50.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	25	5	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	6	31

Merged error: 6.7b

Counts

31 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
0.0b	(exp (* a x))
0.0b	(exp (* a x))
3.1b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`sqrt-prod`
10×	`add-log-exp`
9×	`associate-r`
8×	`difference-of-squares`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`associate-l`
4×	`frac-times` `flip3--` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `exp-prod` `exp-to-pow` `distribute-lft-in` `associate-r/` `associate-l/` `rem-exp-log` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

15.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
2.0ms	(exp (* a x))
2.0ms	(exp (* a x))
6.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series39.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
7.0ms	(exp (* a x))
4.0ms	(exp (* a x))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	262	833
1	1208	723
2	5003	698

prune139.0ms

Filtered

55 candidates to 88 candidates (-60.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	86	8	94

Merged error: 6.7b

Counts

94 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(exp (* a x))
3.1b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-log-exp`
8×	`*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares`
3×	`exp-prod` `exp-to-pow` `rem-exp-log`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 48

Calls

4 calls:

2.0ms	(exp (* a x))
2.0ms	(exp (* a x))
2.0ms	(exp (* a x))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series20.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (* a x))
4.0ms	(exp (* a x))
4.0ms	(exp (* a x))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify154.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	117	298
1	328	274
2	945	273
3	3964	272
4	5002	272

prune105.0ms

Filtered

37 candidates to 60 candidates (-62.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Merged error: 6.7b

Counts

68 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))) (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))) (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))))
3.1b	(- (sqrt (exp (* a x))) (sqrt 1.0))
3.1b	(- (sqrt (exp (* a x))) (sqrt 1.0))
3.1b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

2188×	`frac-times`
1944×	`cbrt-div`
732×	`flip3--` `flip--`
729×	`flip3-+` `flip-+`
638×	`associate-*l/`
566×	`associate-*r/`
30×	`add-sqr-sqrt`
23×	`pow1`
18×	`sqrt-prod`
17×	`*-un-lft-identity`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`add-exp-log` `pow1/3` `pow-prod-up`
6×	`pow-plus` `distribute-lft-out--`
5×	`add-cube-cbrt` `pow-prod-down` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `diff-log` `prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2`
1×	`cbrt-prod` `associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 814

Calls

4 calls:

35.0ms	(* (* (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))) (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))) (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))))
6.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))
6.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))
6.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series53.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))) (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))) (cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify584.0ms

Algorithm

egg-herbie

Counts

826 → 826

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	2919	74184
1	4487	73248
2	5002	72964

prune2.8s

Filtered

250 candidates to 826 candidates (-230.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	823	3	826
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	826	8	834

Merged error: 6.6b

Counts

834 → 8

regimes446.0ms

Accuracy

91.8% (1.8b remaining)

Error of 10.2b against oracle of 8.4b and baseline of 29.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	52
1	57	52

end0.0ms

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

sample1.0s

Algorithm

intervals

Results

512.0ms	2673×	body	1280	valid
175.0ms	1354×	body	640	valid
76.0ms	2777×	body	80	valid
70.0ms	797×	body	320	valid
26.0ms	399×	body	160	valid
4.0ms	146×	body	80	invalid

Details

analyze58.0ms

sample51.0ms

simplify71.0ms

prune3.0ms

localize5.0ms

rewrite6.0ms

series11.0ms

simplify40.0ms

prune60.0ms

localize9.0ms

rewrite26.0ms

series39.0ms

simplify41.0ms

prune139.0ms

localize14.0ms

rewrite15.0ms

series20.0ms

simplify154.0ms

prune105.0ms

localize13.0ms

rewrite208.0ms

series53.0ms

simplify584.0ms

prune2.8s

regimes446.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze41.0ms

sample1.0s

Profiling