Details

analyze350.0ms (8%)

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
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

sample84.0ms (1.9%)

Algorithm

1×

intervals

Results

20.0ms	40×	body	1280	valid
12.0ms	38×	body	1280	invalid
12.0ms	43×	body	640	valid
10.0ms	34×	body	640	invalid
7.0ms	139×	body	80	valid
3.0ms	21×	body	320	invalid
3.0ms	19×	body	320	valid
2.0ms	17×	body	160	invalid
2.0ms	15×	body	160	valid
1.0ms	17×	body	80	invalid

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5439	11

prune6.0ms (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: 0.0b

Counts

2 → 1

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (+ (exp (neg im)) (exp im)))
0.0b	(+ (exp (neg im)) (exp im))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-l` `sum-log` `*-commutative`

Counts

2 → 35

Calls

2 calls:

9.0ms	(* (* 0.5 (cos re)) (+ (exp (neg im)) (exp im)))
5.0ms	(+ (exp (neg im)) (exp im))

series17.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

13.0ms	(* (* 0.5 (cos re)) (+ (exp (neg im)) (exp im)))
4.0ms	(+ (exp (neg im)) (exp im))

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5312	437

prune67.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0b

Counts

42 → 3

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(* (exp im) (* 0.5 (cos re)))
0.0b	(+ (* 0.5 (/ (cos re) (exp im))) (* (exp im) (* 0.5 (cos re))))
0.0b	(/ (cos re) (exp im))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
7×	`add-exp-log`
5×	`add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

3 → 56

Calls

3 calls:

7.0ms	(+ (* 0.5 (/ (cos re) (exp im))) (* (exp im) (* 0.5 (cos re))))
6.0ms	(* (exp im) (* 0.5 (cos re)))
4.0ms	(/ (cos re) (exp im))

series36.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ (* 0.5 (/ (cos re) (exp im))) (* (exp im) (* 0.5 (cos re))))
9.0ms	(* (exp im) (* 0.5 (cos re)))
8.0ms	(/ (cos re) (exp im))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5028	658

prune86.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Merged error: 0b

Counts

68 → 3

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (cbrt (pow (+ (exp (neg im)) (exp im)) 3)))
0.0b	(+ (exp (neg im)) (exp im))
0.0b	(cbrt (pow (+ (exp (neg im)) (exp im)) 3))
0.0b	(pow (+ (exp (neg im)) (exp im)) 3)

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod` `*-un-lft-identity`
17×	`associate-r`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
10×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out`
6×	`cube-div` `add-log-exp`
4×	`cbrt-div` `flip3-+` `flip-+`
3×	`cube-mult` `pow-unpow` `unpow3` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`associate-*r/`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-l` `pow-exp` `sum-log` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 98

Calls

4 calls:

12.0ms	(* (* 0.5 (cos re)) (cbrt (pow (+ (exp (neg im)) (exp im)) 3)))
6.0ms	(pow (+ (exp (neg im)) (exp im)) 3)
6.0ms	(cbrt (pow (+ (exp (neg im)) (exp im)) 3))
5.0ms	(+ (exp (neg im)) (exp im))

series31.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* 0.5 (cos re)) (cbrt (pow (+ (exp (neg im)) (exp im)) 3)))
11.0ms	(pow (+ (exp (neg im)) (exp im)) 3)
4.0ms	(cbrt (pow (+ (exp (neg im)) (exp im)) 3))
3.0ms	(+ (exp (neg im)) (exp im))

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5340	1145

prune166.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	110	3	113

Merged error: 0b

Counts

113 → 3

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (+ (* 1/12 (pow im 4)) (+ 2 (* im im))))
0.1b	(* 1/12 (pow im 4))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-exp-log`
11×	`add-sqr-sqrt`
10×	`associate-r`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
4×	`unpow-prod-down` `associate-l` `cbrt-unprod`
3×	`pow-prod-down` `unswap-sqr`
2×	`associate-r/` `-commutative` `add-log-exp` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+`

Counts

2 → 47

Calls

2 calls:

10.0ms	(* (* 0.5 (cos re)) (+ (* 1/12 (pow im 4)) (+ 2 (* im im))))
5.0ms	(* 1/12 (pow im 4))

series29.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(* (* 0.5 (cos re)) (+ (* 1/12 (pow im 4)) (+ 2 (* im im))))
4.0ms	(* 1/12 (pow im 4))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5515	613

prune94.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	53	3	56

Merged error: 0b

Counts

56 → 3

regimes215.0ms (4.9%)

Accuracy

Total 0.0b remaining (54.7%)

Threshold costs 0.0b (54.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	15
1	14	15

end0.0ms (0%)

sample2.8s (63.9%)

Algorithm

1×

intervals

Results

810.0ms	1556×	body	1280	valid
511.0ms	1534×	body	1280	invalid
340.0ms	1259×	body	640	valid
291.0ms	1302×	body	640	invalid
233.0ms	4225×	body	80	valid
114.0ms	627×	body	320	valid
113.0ms	621×	body	320	invalid
40.0ms	333×	body	160	valid
38.0ms	319×	body	160	invalid
34.0ms	561×	body	80	invalid

Details

analyze350.0ms (8%)

sample84.0ms (1.9%)

simplify93.0ms (2.1%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite15.0ms (0.3%)

series17.0ms (0.4%)

simplify52.0ms (1.2%)

prune67.0ms (1.5%)

localize10.0ms (0.2%)

rewrite19.0ms (0.4%)

series36.0ms (0.8%)

simplify41.0ms (0.9%)

prune86.0ms (2%)

localize13.0ms (0.3%)

rewrite33.0ms (0.8%)

series31.0ms (0.7%)

simplify42.0ms (1%)

prune166.0ms (3.8%)

localize11.0ms (0.3%)

rewrite16.0ms (0.4%)

series29.0ms (0.7%)

simplify43.0ms (1%)

prune94.0ms (2.2%)

regimes215.0ms (4.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.8s (63.9%)

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