Details

analyze342.0ms (4.3%)

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
0%	99.9%	0.1%	3
12.5%	87.4%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

sample150.0ms (1.9%)

Algorithm

1×

intervals

Results

58.0ms	103×	body	1280	valid
27.0ms	84×	body	640	valid
18.0ms	49×	body	1280	invalid
9.0ms	36×	body	640	invalid
7.0ms	37×	body	320	valid
6.0ms	17×	body	320	invalid
5.0ms	82×	body	80	invalid
3.0ms	24×	body	160	valid
2.0ms	14×	body	160	invalid
1.0ms	8×	body	80	valid

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4868	11
1	4868	11

prune7.0ms (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: 44.1b

Counts

2 → 1

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (sin re)) (- (exp (neg im)) (exp im)))
6.9b	(- (exp (neg im)) (exp im))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`add-cube-cbrt` `sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-l` `*-commutative`

Counts

2 → 37

Calls

2 calls:

10.0ms	(* (* 0.5 (sin re)) (- (exp (neg im)) (exp im)))
6.0ms	(- (exp (neg im)) (exp im))

series20.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

15.0ms	(* (* 0.5 (sin re)) (- (exp (neg im)) (exp im)))
5.0ms	(- (exp (neg im)) (exp im))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5022	469

prune83.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	4	44

Merged error: 0.1b

Counts

44 → 4

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* im -2) (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))))
0.0b	(* 1/60 (pow im 5))
0.2b	(* (* 0.5 (sin re)) (+ (* im -2) (- (* (pow im 3) -1/3) (* 1/60 (pow im 5)))))
0.2b	(* (pow im 3) -1/3)

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`associate-l`
13×	`associate-r` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp` `add-log-exp`
8×	`unpow-prod-down`
7×	`unswap-sqr`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `sum-log` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `associate-+r-` `sub-neg` `associate-+r+` `distribute-lft-in` `diff-log` `unpow3`

Counts

4 → 92

Calls

4 calls:

10.0ms	(* (* 0.5 (sin re)) (+ (* im -2) (- (* (pow im 3) -1/3) (* 1/60 (pow im 5)))))
7.0ms	(+ (* im -2) (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))))
5.0ms	(* (pow im 3) -1/3)
5.0ms	(* 1/60 (pow im 5))

series47.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 0.5 (sin re)) (+ (* im -2) (- (* (pow im 3) -1/3) (* 1/60 (pow im 5)))))
6.0ms	(+ (* im -2) (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))))
4.0ms	(* 1/60 (pow im 5))
4.0ms	(* (pow im 3) -1/3)

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5018	1256

prune276.0ms (3.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	97	11	108

Merged error: 0.1b

Counts

108 → 11

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))) (cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))))
13.9b	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
13.9b	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
13.9b	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

11.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
10.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
9.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
8.0ms	(* (cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))) (cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))))

series335.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))) (cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))))
77.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
76.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
73.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4919	2673
1	4919	2673

prune596.0ms (7.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	78	17	95

Merged error: 0.0b

Counts

95 → 17

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* 0.5 (sin re)))
0.7b	(cbrt (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))
13.9b	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
13.9b	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-prod` `cbrt-div`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `associate-*r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`

Counts

4 → 44

Calls

4 calls:

9.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
9.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
7.0ms	(cbrt (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))
3.0ms	(cbrt (* 0.5 (sin re)))

series195.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
76.0ms	(cbrt (* (* 0.5 (sin re)) (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))))))
21.0ms	(cbrt (* 0.5 (sin re)))
21.0ms	(cbrt (+ (* im -2) (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5)))))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4984	1323
1	4984	1323

prune335.0ms (4.2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	3	11	14
Picked	1	0	1
Done	0	2	2
Total	56	17	73

Merged error: 0.0b

Counts

73 → 17

regimes541.0ms (6.8%)

Accuracy

Total 0.7b remaining (91.1%)

Threshold costs 0.7b (91.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	20
1	50	20

end0.0ms (0%)

sample4.5s (57.4%)

Algorithm

1×

intervals

Results

1.9s	3300×	body	1280	valid
816.0ms	2486×	body	640	valid
515.0ms	1455×	body	1280	invalid
303.0ms	1268×	body	640	invalid
282.0ms	1322×	body	320	valid
157.0ms	2393×	body	80	invalid
107.0ms	626×	body	320	invalid
85.0ms	635×	body	160	valid
36.0ms	290×	body	160	invalid
17.0ms	257×	body	80	valid

Details

analyze342.0ms (4.3%)

sample150.0ms (1.9%)

simplify56.0ms (0.7%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite17.0ms (0.2%)

series20.0ms (0.3%)

simplify40.0ms (0.5%)

prune83.0ms (1%)

localize15.0ms (0.2%)

rewrite31.0ms (0.4%)

series47.0ms (0.6%)

simplify42.0ms (0.5%)

prune276.0ms (3.5%)

localize21.0ms (0.3%)

rewrite41.0ms (0.5%)

series335.0ms (4.2%)

simplify76.0ms (1%)

prune596.0ms (7.5%)

localize25.0ms (0.3%)

rewrite29.0ms (0.4%)

series195.0ms (2.5%)

simplify44.0ms (0.6%)

prune335.0ms (4.2%)

regimes541.0ms (6.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample4.5s (57.4%)

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