Details

analyze2.0ms (0%)

Algorithm

1×

Search

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

sample39.0ms (0.9%)

Algorithm

1×

intervals

Results

11.0ms	46×	body	1280	valid
7.0ms	19×	body	320	valid
6.0ms	39×	body	640	valid
5.0ms	138×	body	80	valid
1.0ms	14×	body	160	valid

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5238	10

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: 27.6b

Counts

2 → 1

localize7.0ms (0.1%)

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))))
3.9b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite20.0ms (0.4%)

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)))

series16.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (/ 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)))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5224	834

prune147.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Merged error: 0.0b

Counts

69 → 3

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
3.8b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite50.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity`
88×	`times-frac`
70×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`swap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
12×	`associate-/r/`
11×	`pow1`
8×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 166

Calls

4 calls:

20.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
12.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))

series32.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))
9.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5046	2518

prune699.0ms (15.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	178	3	181

Merged error: 0.0b

Counts

181 → 3

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
0.1b	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

8.0ms	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))
4.0ms	(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))

series13.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))
5.0ms	(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5070	688

prune99.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	54	3	57

Merged error: 0.0b

Counts

57 → 3

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))) (* (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))) (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0)))))
4.0b	(- (* (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))) (* (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))) (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))))) (* 1.0 1.0))
4.1b	(- (exp (* -2.0 x)) 1.0)
4.1b	(- (exp (* -2.0 x)) 1.0)

rewrite103.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`frac-times`
45×	`add-exp-log` `add-cbrt-cube`
32×	`pow1`
25×	`associate-*r/`
24×	`flip3-+` `flip-+`
23×	`prod-exp` `cbrt-unprod`
20×	`associate-*l/`
14×	`pow-prod-down`
10×	`add-log-exp`
8×	`cbrt-undiv` `distribute-rgt-in` `add-sqr-sqrt` `*-un-lft-identity` `distribute-lft-in` `div-exp`
4×	`add-cube-cbrt` `pow-plus` `associate--l+` `pow-prod-up`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`pow2` `pow-sqr` `distribute-lft-out--` `difference-of-squares`
1×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 121

Calls

4 calls:

47.0ms	(- (* (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))) (* (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))) (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))))) (* 1.0 1.0))
41.0ms	(* (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))) (* (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))) (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0)))))
4.0ms	(- (exp (* -2.0 x)) 1.0)
4.0ms	(- (exp (* -2.0 x)) 1.0)

series166.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (* (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))) (* (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))) (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))))) (* 1.0 1.0))
35.0ms	(* (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))) (* (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0))) (+ (* 1.0 1.0) (* (exp (* -2.0 x)) (- (exp (* -2.0 x)) 1.0)))))
2.0ms	(- (exp (* -2.0 x)) 1.0)
2.0ms	(- (exp (* -2.0 x)) 1.0)

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4978	6531
1	4978	6531

prune1.3s (28.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

regimes435.0ms (9.6%)

Accuracy

Total 0.5b remaining (95.6%)

Threshold costs 0.5b (95.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	132	131
1	132	131

end0.0ms (0%)

sample1.0s (22%)

Algorithm

1×

intervals

Results

428.0ms	1770×	body	1280	valid
209.0ms	1224×	body	640	valid
135.0ms	4066×	body	80	valid
69.0ms	603×	body	320	valid
25.0ms	337×	body	160	valid

Details

analyze2.0ms (0%)

sample39.0ms (0.9%)

simplify93.0ms (2%)

prune6.0ms (0.1%)

localize7.0ms (0.1%)

rewrite20.0ms (0.4%)

series16.0ms (0.4%)

simplify60.0ms (1.3%)

prune147.0ms (3.2%)

localize11.0ms (0.2%)

rewrite50.0ms (1.1%)

series32.0ms (0.7%)

simplify70.0ms (1.5%)

prune699.0ms (15.4%)

localize10.0ms (0.2%)

rewrite13.0ms (0.3%)

series13.0ms (0.3%)

simplify59.0ms (1.3%)

prune99.0ms (2.2%)

localize22.0ms (0.5%)

rewrite103.0ms (2.3%)

series166.0ms (3.7%)

simplify94.0ms (2.1%)

prune1.3s (28.1%)

regimes435.0ms (9.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (22%)

Profiling