Details

analyze5.0ms (0.1%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

prune6.0ms (0.1%)

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: 27.9b

Counts

2 → 1

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
25.7b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

7.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series29.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(+ (* re re) (* im im))

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4916	1166
1	4916	1166

prune207.0ms (4.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	68	15	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	15	84

Merged error: 6.0b

Counts

84 → 15

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
26.7b	(log (+ (* re re) (* im im)))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`times-frac`
83×	`add-sqr-sqrt`
54×	`sqrt-prod`
53×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
19×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`div-sub`
1×	`+-commutative` `frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 164

Calls

4 calls:

22.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(+ (* re re) (* im im))
4.0ms	(log (+ (* re re) (* im im)))

series61.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
21.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
9.0ms	(log (+ (* re re) (* im im)))
5.0ms	(+ (* re re) (* im im))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4984	3029
1	4984	3029

prune505.0ms (10.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	180	11	191

Merged error: 5.8b

Counts

191 → 11

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
12.9b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
15.4b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`times-frac`
40×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
13×	`pow1`
12×	`add-exp-log` `unpow-prod-down`
9×	`add-cbrt-cube`
8×	`log-pow`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-log-exp`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-pow` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

13.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
7.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))
7.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
4.0ms	(+ (* re re) (* im im))

series121.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
36.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))
36.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
5.0ms	(+ (* re re) (* im im))

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4931	2232
1	4931	2232

prune413.0ms (8.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	138	13	151

Merged error: 5.8b

Counts

151 → 13

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
0.4b	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.6b	(/ (log 10.0) (log (+ (* re re) (* im im))))
26.7b	(log (+ (* re re) (* im im)))

rewrite100.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

532×	`times-frac`
318×	`add-sqr-sqrt`
238×	`*-un-lft-identity`
228×	`add-cube-cbrt`
152×	`sqrt-prod`
125×	`associate-r`
121×	`pow1`
115×	`log-pow`
42×	`add-exp-log`
32×	`add-cbrt-cube`
25×	`unswap-sqr`
24×	`associate-/r*`
22×	`associate-l`
19×	`div-exp`
17×	`div-inv`
13×	`cbrt-undiv`
10×	`associate-/l*`
9×	`prod-exp`
6×	`cbrt-unprod`
4×	`add-log-exp`
3×	`log-prod` `1-exp`
2×	`log-div` `frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 410

Calls

4 calls:

56.0ms	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
8.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))

series89.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
27.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
26.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify109.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4960	8322
1	4960	8322

prune1.5s (30.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	416	6	422
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	419	16	435

Merged error: 5.7b

Counts

435 → 16

regimes703.0ms (14.3%)

Accuracy

Total 10.6b remaining (58.6%)

Threshold costs 0b (0%)

bsearch69.0ms (1.4%)

Steps

Iters	Range		Point
7	5.593272397438366e+152	9.395708374779484e+153	5.659830230443159e+152
8	4.3085783133892625e-146	2.2271702186917563e-143	4.37904483532928e-146
7	-6.153499804866572e-304	-3.7969242946917145e-306	-3.0666539773149642e-304
8	-7.897480876259031e+121	-2.7073730689024295e+119	-2.092298405732528e+120

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	98
1	60	98

end0.0ms (0%)

sample628.0ms (12.8%)

Algorithm

1×

intervals

Results

481.0ms

8000×

body

valid

Details

analyze5.0ms (0.1%)

sample23.0ms (0.5%)

simplify3.0ms (0.1%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.4%)

series29.0ms (0.6%)

simplify50.0ms (1%)

prune207.0ms (4.2%)

localize14.0ms (0.3%)

rewrite44.0ms (0.9%)

series61.0ms (1.2%)

simplify75.0ms (1.5%)

prune505.0ms (10.3%)

localize19.0ms (0.4%)

rewrite36.0ms (0.7%)

series121.0ms (2.5%)

simplify48.0ms (1%)

prune413.0ms (8.4%)

localize14.0ms (0.3%)

rewrite100.0ms (2%)

series89.0ms (1.8%)

simplify109.0ms (2.2%)

prune1.5s (30.5%)

regimes703.0ms (14.3%)

bsearch69.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample628.0ms (12.8%)

Profiling