Details

analyze2.0ms

Algorithm

Search

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

sample35.0ms

Algorithm

intervals

Results

13.0ms	50×	body	1280	valid
6.0ms	38×	body	640	valid
5.0ms	139×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

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: 27.3b

Counts

2 → 1

localize11.0ms

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

rewrite21.0ms

Algorithm

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:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series17.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5224	834

prune163.0ms

Filtered

53 candidates to 68 candidates (-28.3%)

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: 0.1b

Counts

69 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 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)
2.1b	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
56×	`times-frac`
39×	`add-cube-cbrt`
36×	`unpow-prod-down` `cube-prod`
24×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
8×	`associate-/r*` `associate-/r/`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `flip--`

Counts

4 → 163

Calls

4 calls:

6.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
6.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
9.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
36.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

series49.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
8.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
19.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5859	2863

prune534.0ms

Filtered

97 candidates to 175 candidates (-80.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	175	4	179

Merged error: 0.1b

Counts

179 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
2.1b	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 3) (pow (pow 1.0 3) 3))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-sqr-sqrt`
274×	`unpow-prod-down`
256×	`cube-prod`
140×	`difference-of-squares`
119×	`*-un-lft-identity`
100×	`times-frac`
75×	`sqr-pow`
47×	`add-cube-cbrt`
21×	`distribute-lft-out--`
15×	`distribute-lft-out`
13×	`add-exp-log`
10×	`associate-/r/` `add-cbrt-cube`
9×	`pow-unpow`
7×	`pow1`
6×	`pow-exp` `add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`rem-cube-cbrt`
3×	`pow-to-exp` `pow-pow` `div-exp`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 318

Calls

4 calls:

8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
9.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
121.0ms	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 3) (pow (pow 1.0 3) 3))

series57.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
13.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
21.0ms	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 3) (pow (pow 1.0 3) 3))

simplify109.0ms

Algorithm

egg-herbie

Counts

330 → 330

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5203	8504

prune1.4s

Filtered

115 candidates to 330 candidates (-187.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	327	3	330
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	328	6	334

Merged error: 0.0b

Counts

334 → 6

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
0.1b	(pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 6)
2.0b	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 6) (pow (pow 1.0 3) 6))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

198×	`unpow-prod-down`
128×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
72×	`times-frac`
60×	`cube-prod`
48×	`add-cube-cbrt` `difference-of-squares`
32×	`sqr-pow`
15×	`distribute-lft-out`
14×	`add-exp-log`
10×	`pow-exp` `associate-/r/`
9×	`pow-unpow`
7×	`add-cbrt-cube`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`pow-to-exp`
3×	`pow-pow` `div-exp`
2×	`cube-mult` `unpow3` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 213

Calls

4 calls:

9.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
13.0ms	(pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 6)
50.0ms	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 6) (pow (pow 1.0 3) 6))

series70.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
14.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
19.0ms	(pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 6)
25.0ms	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 6) (pow (pow 1.0 3) 6))

simplify81.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5275	4765

prune1.3s

Filtered

92 candidates to 225 candidates (-144.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	224	7	231

Merged error: 0.0b

Counts

231 → 7

regimes241.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.0b

bsearch35.0ms

Steps

Iters	Range		Point
8	1.298035032321554e-07	0.0015820319828128906	0.0007244127199939371
8	-0.0007431259896268396	-1.1220704313385585e-07	-0.0007310721182552102

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	140	156
1	140	156

end0.0ms

sample1.0s

Algorithm

intervals

Results

429.0ms	1707×	body	1280	valid
214.0ms	1236×	body	640	valid
137.0ms	4125×	body	80	valid
72.0ms	607×	body	320	valid
24.0ms	325×	body	160	valid

Details

analyze2.0ms

sample35.0ms

simplify74.0ms

prune7.0ms

localize11.0ms

rewrite21.0ms

series17.0ms

simplify52.0ms

prune163.0ms

localize19.0ms

rewrite64.0ms

series49.0ms

simplify59.0ms

prune534.0ms

localize33.0ms

rewrite169.0ms

series57.0ms

simplify109.0ms

prune1.4s

localize36.0ms

rewrite94.0ms

series70.0ms

simplify81.0ms

prune1.3s

regimes241.0ms

bsearch35.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling