Details

analyze46.0ms (2.2%)

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

sample37.0ms (1.8%)

Algorithm

1×

intervals

Results

19.0ms	97×	body	1280	valid
5.0ms	41×	body	640	valid
2.0ms	25×	body	320	valid
2.0ms	78×	body	80	valid
1.0ms	15×	body	160	valid
0.0ms	6×	body	80	invalid

simplify65.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4778	6
1	4778	6

prune5.0ms (0.2%)

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: 29.1b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.3b	(- (exp (* a x)) 1.0)

rewrite6.0ms (0.3%)

Algorithm

1×	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 → 23

Calls

2 calls:

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

series13.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(- (exp (* a x)) 1.0)
6.0ms	(exp (* a x))

simplify66.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4915	224
1	4915	224

prune56.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	5	30

Merged error: 4.7b

Counts

30 → 5

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.7b	(* x (+ a (* x (+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3)))))))
6.4b	(* x (* 1/6 (pow a 3)))
6.4b	(* x (+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3)))))
10.6b	(+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3))))

rewrite27.0ms (1.3%)

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:

9.0ms	(* x (+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3)))))
6.0ms	(+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3))))
6.0ms	(* x (* 1/6 (pow a 3)))
5.0ms	(* x (+ a (* x (+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3)))))))

series62.0ms (3%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (+ a (* x (+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3)))))))
21.0ms	(* x (+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3)))))
10.0ms	(* x (* 1/6 (pow a 3)))
9.0ms	(+ (* 1/2 (* a a)) (* x (* 1/6 (pow a 3))))

simplify29.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5186	1359

prune158.0ms (7.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Merged error: 2.6b

Counts

91 → 5

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (* (* a a) (* x x)))
4.2b	(+ (* a x) (* 1/2 (* (* a a) (* x x))))
15.5b	(* (* a a) (* x x))

rewrite26.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`pow1`
33×	`add-exp-log` `add-cbrt-cube`
27×	`pow-prod-down`
21×	`prod-exp` `cbrt-unprod`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `pow-plus` `associate-l*` `pow-prod-up`
2×	`pow2` `associate-r` `pow-sqr` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

11.0ms	(* 1/2 (* (* a a) (* x x)))
8.0ms	(* (* a a) (* x x))
5.0ms	(+ (* a x) (* 1/2 (* (* a a) (* x x))))

series26.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ (* a x) (* 1/2 (* (* a a) (* x x))))
9.0ms	(* 1/2 (* (* a a) (* x x)))
6.0ms	(* (* a a) (* x x))

simplify58.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4963	570
1	4963	570

prune108.0ms (5.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	2	1	3
Picked	1	0	1
Done	1	0	1
Total	79	2	81

Merged error: 0.1b

Counts

81 → 2

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (pow (* a x) 2))
0.2b	(pow (* a x) 2)
4.2b	(+ (* a x) (* 1/2 (pow (* a x) 2)))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log`
10×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `prod-exp`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow-exp`
3×	`pow-unpow` `associate-l` `unpow2` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

3 → 54

Calls

3 calls:

5.0ms	(* 1/2 (pow (* a x) 2))
4.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
3.0ms	(pow (* a x) 2)

series22.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
7.0ms	(* 1/2 (pow (* a x) 2))
4.0ms	(pow (* a x) 2)

simplify26.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5115	523

prune88.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Merged error: 0.1b

Counts

65 → 2

regimes145.0ms (6.9%)

Accuracy

Total 0.2b remaining (61.3%)

Threshold costs 0.2b (61.3%)

bsearch13.0ms (0.6%)

Steps

Iters	Range		Point
10	-7.62739742382033	-1.1098068008089188e-11	-1.2065385524619287e-05

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	36
1	31	36

end0.0ms (0%)

sample963.0ms (46.1%)

Algorithm

1×

intervals

Results

490.0ms	2718×	body	1280	valid
153.0ms	1306×	body	640	valid
77.0ms	2865×	body	80	valid
56.0ms	708×	body	320	valid
22.0ms	403×	body	160	valid
6.0ms	131×	body	80	invalid

Details

analyze46.0ms (2.2%)

sample37.0ms (1.8%)

simplify65.0ms (3.1%)

prune5.0ms (0.2%)

localize5.0ms (0.2%)

rewrite6.0ms (0.3%)

series13.0ms (0.6%)

simplify66.0ms (3.1%)

prune56.0ms (2.7%)

localize12.0ms (0.6%)

rewrite27.0ms (1.3%)

series62.0ms (3%)

simplify29.0ms (1.4%)

prune158.0ms (7.6%)

localize7.0ms (0.4%)

rewrite26.0ms (1.3%)

series26.0ms (1.3%)

simplify58.0ms (2.8%)

prune108.0ms (5.2%)

localize6.0ms (0.3%)

rewrite14.0ms (0.6%)

series22.0ms (1.1%)

simplify26.0ms (1.2%)

prune88.0ms (4.2%)

regimes145.0ms (6.9%)

bsearch13.0ms (0.6%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample963.0ms (46.1%)

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