Details

analyze44.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

sample33.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5230	53

prune9.0ms (0.1%)

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: 56.0b

Counts

2 → 1

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.8b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
47.6b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite92.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

35.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
23.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))
13.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))

series390.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
56.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))
24.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4999	10097
1	4999	10097

prune622.0ms (8.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	8	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	8	213

Merged error: 35.7b

Counts

213 → 8

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0))) (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0))) (+ (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))) (/ (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0))) (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))))
35.9b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))
35.9b	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))

rewrite168.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-exp-log` `add-cbrt-cube`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 364

Calls

4 calls:

97.0ms	(* (/ (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0))) (+ (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))) (/ (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0))) (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))))
26.0ms	(/ (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0))) (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0)))
12.0ms	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))
10.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))

series479.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

384.0ms	(* (/ (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0))) (+ (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))) (/ (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0))) (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))))
52.0ms	(/ (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0))) (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0)))
27.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))
16.0ms	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5005	18793

prune1.8s (25%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	372	4	376
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	376	8	384

Merged error: 35.7b

Counts

384 → 8

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))) (sqrt (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))))
35.9b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))
35.9b	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))
35.9b	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod`
40×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
19×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
14×	`swap-sqr` `associate-/r/`
12×	`associate-r` `associate-l`
10×	`flip3-+` `flip-+`
9×	`associate-/r*`
8×	`sqrt-pow1` `pow1/2`
7×	`div-inv`
6×	`associate-/l/`
5×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-up` `associate-/l`
4×	`sqrt-div` `add-log-exp` `unswap-sqr`
3×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `cbrt-unprod`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-l/` `rem-square-sqrt` `-commutative`

Counts

4 → 151

Calls

4 calls:

28.0ms	(* (sqrt (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))) (sqrt (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))))
12.0ms	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))
12.0ms	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))
10.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))

series88.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))
26.0ms	(* (sqrt (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))) (sqrt (/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))))
19.0ms	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))
15.0ms	(/ (* i (+ i (+ alpha beta))) (+ (+ alpha beta) (* i 2.0)))

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5279	3266

prune564.0ms (7.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	163	8	171

Merged error: 35.7b

Counts

171 → 8

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/ i (sqrt (+ (+ alpha beta) (* i 2.0))))
0.5b	(* (/ i (sqrt (+ (+ alpha beta) (* i 2.0)))) (/ (+ i (+ alpha beta)) (sqrt (+ (+ alpha beta) (* i 2.0)))))
0.5b	(/ (+ i (+ alpha beta)) (sqrt (+ (+ alpha beta) (* i 2.0))))
35.9b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity`
117×	`times-frac`
106×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
60×	`sqrt-prod`
39×	`distribute-lft-out`
36×	`associate-r`
24×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r*`
11×	`associate-/l*`
10×	`associate-/r/`
9×	`unswap-sqr`
8×	`sqrt-div`
7×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
6×	`pow1`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 218

Calls

4 calls:

33.0ms	(* (/ i (sqrt (+ (+ alpha beta) (* i 2.0)))) (/ (+ i (+ alpha beta)) (sqrt (+ (+ alpha beta) (* i 2.0)))))
14.0ms	(/ (+ i (+ alpha beta)) (sqrt (+ (+ alpha beta) (* i 2.0))))
10.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))
8.0ms	(/ i (sqrt (+ (+ alpha beta) (* i 2.0))))

series116.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (/ i (sqrt (+ (+ alpha beta) (* i 2.0)))) (/ (+ i (+ alpha beta)) (sqrt (+ (+ alpha beta) (* i 2.0)))))
31.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ (+ alpha beta) (* i 2.0)))
28.0ms	(/ i (sqrt (+ (+ alpha beta) (* i 2.0))))
25.0ms	(/ (+ i (+ alpha beta)) (sqrt (+ (+ alpha beta) (* i 2.0))))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4965	5179
1	4965	5179

prune1.0s (14.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	231	7	238

Merged error: 2.7b

Counts

238 → 7

regimes234.0ms (3.2%)

Accuracy

Total 12.2b remaining (82.8%)

Threshold costs 0b (0%)

bsearch64.0ms (0.9%)

Steps

Iters	Range	Point
5	1.4214025905189597e+180	3.5038899697870747e+180	2.178716223398337e+180
8	4.425378108998965e+140	1.2196746002532731e+144	1.202295370415579e+144
9	1.5609937890440059e+111	5.040828458311111e+116	1.5824841192270528e+111

Iters

Range

Point

1.4214025905189597e+180

3.5038899697870747e+180

2.178716223398337e+180

4.425378108998965e+140

1.2196746002532731e+144

1.202295370415579e+144

1.5609937890440059e+111

5.040828458311111e+116

1.5824841192270528e+111

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	119
1	66	119

end0.0ms (0%)

sample950.0ms (13.2%)

Algorithm

1×

intervals

Results

607.0ms	8000×	body	80	valid
171.0ms	8000×	pre	80	true

Details

analyze44.0ms (0.6%)

sample33.0ms (0.5%)

simplify28.0ms (0.4%)

prune9.0ms (0.1%)

localize15.0ms (0.2%)

rewrite92.0ms (1.3%)

series390.0ms (5.4%)

simplify76.0ms (1%)

prune622.0ms (8.6%)

localize22.0ms (0.3%)

rewrite168.0ms (2.3%)

series479.0ms (6.6%)

simplify107.0ms (1.5%)

prune1.8s (25%)

localize23.0ms (0.3%)

rewrite67.0ms (0.9%)

series88.0ms (1.2%)

simplify40.0ms (0.6%)

prune564.0ms (7.8%)

localize22.0ms (0.3%)

rewrite74.0ms (1%)

series116.0ms (1.6%)

simplify64.0ms (0.9%)

prune1.0s (14.2%)

regimes234.0ms (3.2%)

bsearch64.0ms (0.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample950.0ms (13.2%)

Profiling