Details

sample324.0ms

Algorithm

intervals

Results

33.0ms	173×	body	10240	exit
12.0ms	381×	body	80	nan
7.0ms	237×	body	80	valid
2.0ms	23×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.1b	(- (exp (* 2.0 x)) 1.0)
5.2b	(- (exp x) 1.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
34.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify128.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune330.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
0.3b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
5.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.2b	(- (exp x) 1.0)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
67×	`sqrt-prod`
62×	`times-frac`
39×	`difference-of-squares`
29×	`add-cube-cbrt`
25×	`distribute-lft-out--`
9×	`associate-/l*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `associate-/r*`
4×	`flip3--` `flip--`
3×	`rem-sqrt-square`
2×	`sub-neg` `diff-log` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 140

Calls

4 calls:

25.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
13.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
82.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	461	1817
1	1462	1748
2	5001	1701

prune377.0ms

Filtered

152 candidates to 83 candidates (54.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (sqrt (exp (* 2.0 x))))
0.5b	(sqrt (sqrt (exp (* 2.0 x))))
5.3b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
5.3b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`sqrt-prod`
38×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`sqrt-pow1`
13×	`difference-of-squares`
10×	`add-log-exp`
8×	`pow1` `add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `rem-sqrt-square` `pow1/2` `add-cbrt-cube`
2×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--`

Counts

4 → 84

Calls

4 calls:

2.0ms	(sqrt (sqrt (exp (* 2.0 x))))
2.0ms	(sqrt (sqrt (exp (* 2.0 x))))
13.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
8.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series405.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (sqrt (exp (* 2.0 x))))
111.0ms	(sqrt (sqrt (exp (* 2.0 x))))
149.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
40.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify95.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	187	694
1	422	670
2	1031	668
3	2966	662
4	5001	662

prune350.0ms

Filtered

96 candidates to 57 candidates (59.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (exp (* 2.0 x))) (- (exp x) 1.0))
2.9b	(- (/ (sqrt (exp (* 2.0 x))) (- (exp x) 1.0)) (/ (sqrt 1.0) (- (exp x) 1.0)))
5.2b	(- (exp x) 1.0)
5.2b	(- (exp x) 1.0)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
70×	`times-frac`
38×	`sqrt-prod`
32×	`distribute-lft-out--`
27×	`add-cube-cbrt`
22×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--` `associate-/l*`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 124

Calls

4 calls:

9.0ms	(/ (sqrt (exp (* 2.0 x))) (- (exp x) 1.0))
106.0ms	(- (/ (sqrt (exp (* 2.0 x))) (- (exp x) 1.0)) (/ (sqrt 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp x) 1.0)
4.0ms	(- (exp x) 1.0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sqrt (exp (* 2.0 x))) (- (exp x) 1.0))
124.0ms	(- (/ (sqrt (exp (* 2.0 x))) (- (exp x) 1.0)) (/ (sqrt 1.0) (- (exp x) 1.0)))
17.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	363	1544
1	927	1490
2	3772	1481
3	5002	1481

prune397.0ms

Filtered

136 candidates to 87 candidates (64.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes29.0ms

Accuracy

72.1% (0.9b remaining)

Error of 1.1b against oracle of 0.2b and baseline of 3.5b

bsearch31.0ms

Steps

Iters	Range		Point
5	-7.455527952367615e-16	-3.171438052781698e-16	-7.021657331640675e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	32
1	44	32

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6785×	body	10240	exit
376.0ms	12465×	body	80	nan
227.0ms	7407×	body	80	valid
54.0ms	729×	body	160	valid