Details

analyze6.0ms

Algorithm

Search

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

sample36.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
9.0ms	47×	body	640	valid
4.0ms	137×	body	80	valid
1.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5238	10

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 27.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4993	703
1	4993	703

prune120.0ms

Filtered

41 candidates to 53 candidates (-29.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	2	54

Merged error: 0.0b

Counts

54 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp -2.0) x)
0.0b	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
0.0b	(/ (- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
2.1b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`frac-times` `pow-pow` `distribute-lft-out`
3×	`cbrt-undiv` `unpow-prod-down` `pow-unpow` `exp-prod` `div-exp`
2×	`flip3--` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `flip--` `div-inv` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `cbrt-unprod` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

3.0ms	(pow (exp -2.0) x)
12.0ms	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
26.0ms	(/ (- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
15.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

series67.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (exp -2.0) x)
11.0ms	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
36.0ms	(/ (- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
16.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5048	2290

prune369.0ms

Filtered

81 candidates to 108 candidates (-33.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Merged error: 0.0b

Counts

110 → 2

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4))
0.0b	(/ (/ (- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 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	(/ (- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0))))))
2.0b	(- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

2130×	`times-frac`
1716×	`add-sqr-sqrt`
814×	`*-un-lft-identity`
780×	`difference-of-squares`
759×	`unpow-prod-down`
702×	`sqr-pow`
476×	`add-cube-cbrt`
207×	`cube-prod`
190×	`associate-/l*`
149×	`distribute-lft-out`
23×	`add-exp-log`
20×	`distribute-lft-out--`
15×	`associate-/r*`
14×	`associate-/r/`
13×	`div-exp` `add-cbrt-cube`
9×	`cube-mult` `unpow3`
8×	`div-inv`
7×	`flip3-+` `flip-+`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
5×	`cbrt-undiv`
4×	`pow1`
3×	`frac-2neg` `div-sub` `clear-num` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 1076

Calls

4 calls:

11.0ms	(/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4))
79.0ms	(/ (/ (- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0)))))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
48.0ms	(/ (- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0))))))
38.0ms	(- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))

series196.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4))
91.0ms	(/ (/ (- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0)))))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
70.0ms	(/ (- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0))))))
19.0ms	(- (/ (pow (* 2.0 2.0) 3) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))

simplify689.0ms

Algorithm

egg-herbie

Counts

1088 → 1088

Iterations

Useful iterations: 0 (282.0ms)

Iter	Nodes	Cost
0	4971	97675
1	4971	97675

prune20.3s

Filtered

564 candidates to 1088 candidates (-92.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1086	2	1088
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	1087	3	1090

Merged error: 0b

Counts

1090 → 3

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))))) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 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	(/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)))))
0.0b	(/ (/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))))) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0))))))
2.0b	(- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

37062×	`times-frac`
29113×	`add-sqr-sqrt`
17980×	`unpow-prod-down`
12937×	`*-un-lft-identity`
10912×	`difference-of-squares`
10540×	`sqr-pow`
9300×	`cube-prod`
8901×	`add-cube-cbrt`
2459×	`associate-/l*`
1708×	`distribute-lft-out`
310×	`distribute-lft-out--`
174×	`associate-/r/`
120×	`frac-add`
87×	`flip3-+` `flip-+`
62×	`difference-cubes`
40×	`frac-times` `associate-r/` `associate-l/`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`div-sub` `add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 11807

Calls

4 calls:

562.0ms	(/ (/ (/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))))) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0)))))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
176.0ms	(/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)))))
261.0ms	(/ (/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))))) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0))))))
116.0ms	(- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3))

series395.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (/ (/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))))) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0)))))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
80.0ms	(/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6)))))
131.0ms	(/ (/ (- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3)) (+ (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6))) (+ (pow 1.0 12) (* (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) (pow 1.0 6))))) (+ (pow 1.0 4) (* 2.0 (+ (/ (pow 2.0 3) (pow (+ 1.0 (pow (exp -2.0) x)) 4)) (* (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)) (* 1.0 1.0))))))
24.0ms	(- (pow (/ (pow 2.0 6) (pow (+ 1.0 (pow (exp -2.0) x)) 6)) 3) (pow (pow 1.0 6) 3))

simplify10.4s

Algorithm

egg-herbie

Counts

11819 → 11819

Iterations

Useful iterations: 0 (656.0ms)

Iter	Nodes	Cost
0	6561	2301583

prune1.9min

Filtered: 3687 candidates to 11819 candidates (-220.6%)

Details

analyze6.0ms

sample36.0ms

simplify72.0ms

prune7.0ms

localize7.0ms

rewrite17.0ms

series14.0ms

simplify50.0ms

prune120.0ms

localize18.0ms

rewrite59.0ms

series67.0ms

simplify34.0ms

prune369.0ms

localize34.0ms

rewrite296.0ms

series196.0ms

simplify689.0ms

prune20.3s

localize42.0ms

rewrite3.4s

series395.0ms

simplify10.4s

prune1.9min

Profiling