Details

analyze46.0ms (1.8%)

Algorithm

1×

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 (1.3%)

Algorithm

1×

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

simplify56.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4778	6
1	4778	6

prune10.0ms (0.4%)

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: 28.9b

Counts

2 → 2

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 13

Calls

1 calls:

4.0ms

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

series7.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

7.0ms

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

simplify45.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4903	161
1	4903	161

prune32.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	15	3	18

Merged error: 4.6b

Counts

18 → 3

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt` `add-cbrt-cube`
10×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp`
7×	`associate-r`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`associate-*r/`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `pow-exp` `sum-log`

Counts

4 → 74

Calls

4 calls:

8.0ms	(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
6.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))
6.0ms	(* x (* 1/6 (pow a 3)))
5.0ms	(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))

series63.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
21.0ms	(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
10.0ms	(* x (* 1/6 (pow a 3)))
8.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify29.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5281	1359

prune173.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	85	4	89

Merged error: 0.1b

Counts

89 → 4

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

3.5b	(* a (* (* a 1/2) (* x x)))
4.2b	(+ (* a x) (* a (* (* a 1/2) (* x x))))
6.9b	(* (* a 1/2) (* x x))

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`pow1` `add-exp-log` `add-cbrt-cube`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 61

Calls

3 calls:

11.0ms	(* a (* (* a 1/2) (* x x)))
7.0ms	(* (* a 1/2) (* x x))
4.0ms	(+ (* a x) (* a (* (* a 1/2) (* x x))))

series25.0ms (1%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ (* a x) (* a (* (* a 1/2) (* x x))))
7.0ms	(* a (* (* a 1/2) (* x x)))
7.0ms	(* (* a 1/2) (* x x))

simplify45.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4991	683
1	4991	683

prune106.0ms (4.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	70	4	74

Merged error: 0.1b

Counts

74 → 4

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

8.9b	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))
8.9b	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))
9.4b	(sqrt (* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))))))
9.4b	(sqrt (* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))))))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1`
8×	`add-log-exp`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-r/` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod`

Counts

4 → 48

Calls

4 calls:

6.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))
6.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))
4.0ms	(sqrt (* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))))))
4.0ms	(sqrt (* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))))))

series104.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))))))
42.0ms	(sqrt (* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))))))
8.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))
8.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify52.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4922	1096
1	4922	1096

prune366.0ms (14.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	60	4	64

Merged error: 0.1b

Counts

64 → 4

regimes244.0ms (9.7%)

Accuracy

Total 2.8b remaining (92.1%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	25
1	30	25

end0.0ms (0%)

sample959.0ms (38.1%)

Algorithm

1×

intervals

Results

486.0ms	2692×	body	1280	valid
153.0ms	1297×	body	640	valid
76.0ms	2853×	body	80	valid
64.0ms	773×	body	320	valid
21.0ms	385×	body	160	valid
4.0ms	146×	body	80	invalid

Details

analyze46.0ms (1.8%)

sample33.0ms (1.3%)

simplify56.0ms (2.2%)

prune10.0ms (0.4%)

localize5.0ms (0.2%)

rewrite4.0ms (0.2%)

series7.0ms (0.3%)

simplify45.0ms (1.8%)

prune32.0ms (1.3%)

localize12.0ms (0.5%)

rewrite27.0ms (1.1%)

series63.0ms (2.5%)

simplify29.0ms (1.1%)

prune173.0ms (6.9%)

localize8.0ms (0.3%)

rewrite25.0ms (1%)

series25.0ms (1%)

simplify45.0ms (1.8%)

prune106.0ms (4.2%)

localize16.0ms (0.6%)

rewrite21.0ms (0.8%)

series104.0ms (4.1%)

simplify52.0ms (2.1%)

prune366.0ms (14.6%)

regimes244.0ms (9.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample959.0ms (38.1%)

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