Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample36.0ms (1.2%)

Algorithm

1×

intervals

Results

14.0ms	54×	body	1280	valid
8.0ms	47×	body	640	valid
4.0ms	125×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5238	10

prune6.0ms (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: 30.6b

Counts

2 → 1

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

3 → 59

Calls

3 calls:

10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))

series15.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms	(+ 1.0 (exp (* -2.0 x)))

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5224	834

prune170.0ms (5.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `associate-l`
6×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`associate-*r/` `sqr-pow`
1×	`pow1` `distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-lft-in` `flip3-+` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

8.0ms

(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

series8.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

7.0ms

(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

simplify47.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4941	411
1	4941	411

prune76.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Merged error: 0.0b

Counts

42 → 4

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (pow (exp -2.0) x))
0.0b	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
3.0b	(- (cbrt (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)) 1.0)

rewrite46.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
38×	`times-frac`
30×	`add-cube-cbrt`
20×	`unpow-prod-down` `cube-prod`
11×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`difference-of-squares`
6×	`cbrt-prod` `associate-/r/`
5×	`pow1`
4×	`flip3-+` `associate-/r*` `flip-+`
3×	`pow-unpow` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `clear-num` `sum-log` `flip--` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

23.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)) 1.0)
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
6.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
5.0ms	(+ 1.0 (pow (exp -2.0) x))

series33.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)) 1.0)
11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
8.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
4.0ms	(+ 1.0 (pow (exp -2.0) x))

simplify53.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5253	1829

prune346.0ms (11.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 2) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
0.0b	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
0.0b	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
3.0b	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 2) (* 1.0 1.0))

rewrite55.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity`
62×	`times-frac`
60×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
30×	`difference-of-squares`
17×	`distribute-lft-out`
14×	`associate-/l*`
12×	`unpow-prod-down` `associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/` `unpow2` `add-log-exp` `sqr-pow`
4×	`pow1`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
2×	`flip3--` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 143

Calls

4 calls:

24.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 2) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
14.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 2) (* 1.0 1.0))
6.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
6.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))

series63.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 2) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
17.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 2) (* 1.0 1.0))
8.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
8.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4956	3516
1	4956	3516

prune631.0ms (21%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	155	4	159

Merged error: 0.0b

Counts

159 → 4

regimes125.0ms (4.2%)

Accuracy

Total 0.0b remaining (11.4%)

Threshold costs 0.0b (11.4%)

bsearch28.0ms (0.9%)

Steps

Iters	Range		Point
9	4.492822762856787e-08	0.5168984161454252	0.0007993552140358844
8	-0.05151097794333966	-1.8176653493432056e-06	-0.0008523613938262117

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	114	59
1	114	59

end0.0ms (0%)

sample995.0ms (33.1%)

Algorithm

1×

intervals

Results

425.0ms	1757×	body	1280	valid
207.0ms	1263×	body	640	valid
129.0ms	4032×	body	80	valid
70.0ms	623×	body	320	valid
27.0ms	325×	body	160	valid

Details

analyze6.0ms (0.2%)

sample36.0ms (1.2%)

simplify71.0ms (2.3%)

prune6.0ms (0.2%)

localize7.0ms (0.2%)

rewrite20.0ms (0.7%)

series15.0ms (0.5%)

simplify53.0ms (1.8%)

prune170.0ms (5.6%)

localize8.0ms (0.3%)

rewrite9.0ms (0.3%)

series8.0ms (0.3%)

simplify47.0ms (1.6%)

prune76.0ms (2.5%)

localize12.0ms (0.4%)

rewrite46.0ms (1.5%)

series33.0ms (1.1%)

simplify53.0ms (1.7%)

prune346.0ms (11.5%)

localize16.0ms (0.5%)

rewrite55.0ms (1.8%)

series63.0ms (2.1%)

simplify73.0ms (2.4%)

prune631.0ms (21%)

regimes125.0ms (4.2%)

bsearch28.0ms (0.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample995.0ms (33.1%)

Profiling