Details

analyze1.0s (23.1%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample43.0ms (1%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	80	valid
8.0ms	105×	body	80	invalid
3.0ms	73×	body	80	nan

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4961	13
1	4961	13

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 2.4b

Counts

2 → 1

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* a (pow k m))
2.4b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`prod-exp`
4×	`pow1` `unpow-prod-down` `div-exp` `sum-log`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms	(* a (pow k m))
3.0ms	(+ 1.0 (* 10.0 k))

series54.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.0ms	(* a (pow k m))
3.0ms	(+ 1.0 (* 10.0 k))
3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4953	920
1	4953	920

prune146.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Merged error: 2.4b

Counts

87 → 5

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* k (+ k 10.0)))
0.0b	(* k (+ k 10.0))
0.0b	(/ (+ 1.0 (* k (+ k 10.0))) (pow k m))
2.4b	(/ a (/ (+ 1.0 (* k (+ k 10.0))) (pow k m)))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac`
106×	`add-sqr-sqrt` `*-un-lft-identity`
104×	`add-cube-cbrt`
48×	`unpow-prod-down`
32×	`associate-/r*`
21×	`add-exp-log`
16×	`sqr-pow`
13×	`add-cbrt-cube`
10×	`div-exp`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `associate-r`
3×	`flip3-+` `associate-l` `flip-+`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+r+` `frac-2neg` `distribute-lft-in` `associate-*r/` `pow-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

10.0ms	(/ a (/ (+ 1.0 (* k (+ k 10.0))) (pow k m)))
6.0ms	(/ (+ 1.0 (* k (+ k 10.0))) (pow k m))
6.0ms	(* k (+ k 10.0))
3.0ms	(+ 1.0 (* k (+ k 10.0)))

series61.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ a (/ (+ 1.0 (* k (+ k 10.0))) (pow k m)))
17.0ms	(/ (+ 1.0 (* k (+ k 10.0))) (pow k m))
5.0ms	(* k (+ k 10.0))
3.0ms	(+ 1.0 (* k (+ k 10.0)))

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4951	4263
1	4951	4263

prune385.0ms (8.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	215	5	220

Merged error: 2.3b

Counts

220 → 5

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* k (+ k 10.0)))
0.0b	(* k (+ k 10.0))
2.4b	(/ a (* (+ 1.0 (* k (+ k 10.0))) (pow k (neg m))))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/`
7×	`add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+` `add-log-exp`
4×	`frac-times` `pow-neg` `associate-r/` `div-exp` `associate-r*` `prod-exp`
3×	`neg-sub0` `times-frac` `associate-l` `associate-/l*` `pow-sub`
2×	`cbrt-undiv` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*l/` `cbrt-unprod`
1×	`+-commutative` `pow-to-exp` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `sum-log` `un-div-inv` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

3 → 68

Calls

3 calls:

8.0ms	(/ a (* (+ 1.0 (* k (+ k 10.0))) (pow k (neg m))))
6.0ms	(* k (+ k 10.0))
4.0ms	(+ 1.0 (* k (+ k 10.0)))

series55.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ a (* (+ 1.0 (* k (+ k 10.0))) (pow k (neg m))))
5.0ms	(* k (+ k 10.0))
3.0ms	(+ 1.0 (* k (+ k 10.0)))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4925	876
1	4925	876

prune120.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Merged error: 2.3b

Counts

82 → 5

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ a (sqrt (+ 1.0 (* k (+ k 10.0)))))
0.1b	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
12.0b	(sqrt (+ 1.0 (* k (+ k 10.0))))
12.0b	(sqrt (+ 1.0 (* k (+ k 10.0))))

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`add-sqr-sqrt`
110×	`times-frac`
64×	`sqrt-prod`
61×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
30×	`add-exp-log`
24×	`unpow-prod-down` `associate-l`
21×	`unswap-sqr`
18×	`add-cbrt-cube`
12×	`sqr-pow`
11×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 188

Calls

4 calls:

34.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
5.0ms	(/ a (sqrt (+ 1.0 (* k (+ k 10.0)))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

series58.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
17.0ms	(/ a (sqrt (+ 1.0 (* k (+ k 10.0)))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4952	4399
1	4952	4399

prune552.0ms (12.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	200	5	205

Merged error: 2.3b

Counts

205 → 5

regimes163.0ms (3.7%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms (0%)

sample1.2s (27.2%)

Algorithm

1×

intervals

Results

521.0ms	8000×	body	80	valid
271.0ms	3200×	body	80	invalid
94.0ms	1992×	body	80	nan

Details

analyze1.0s (23.1%)

sample43.0ms (1%)

simplify109.0ms (2.4%)

prune9.0ms (0.2%)

localize11.0ms (0.3%)

rewrite28.0ms (0.6%)

series54.0ms (1.2%)

simplify64.0ms (1.4%)

prune146.0ms (3.3%)

localize10.0ms (0.2%)

rewrite35.0ms (0.8%)

series61.0ms (1.4%)

simplify69.0ms (1.6%)

prune385.0ms (8.6%)

localize11.0ms (0.2%)

rewrite19.0ms (0.4%)

series55.0ms (1.2%)

simplify60.0ms (1.3%)

prune120.0ms (2.7%)

localize13.0ms (0.3%)

rewrite54.0ms (1.2%)

series58.0ms (1.3%)

simplify84.0ms (1.9%)

prune552.0ms (12.4%)

regimes163.0ms (3.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.2s (27.2%)

Profiling