Details

sample40.0ms

Algorithm

intervals

Results

16.0ms	64×	body	1280	valid
7.0ms	41×	body	640	valid
4.0ms	127×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	5

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 30.5b

Counts

2 → 1

localize7.0ms

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))))
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite24.0ms

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 → 60

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
9.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify88.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2771	460
3	5002	460

prune131.0ms

Filtered

69 candidates to 50 candidates (27.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.1b

Counts

70 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

9.0ms	(cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
12.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series53.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	182	717
1	431	663
2	1641	624
3	5002	613

prune241.0ms

Filtered

73 candidates to 53 candidates (27.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	73	4	77

Merged error: 0.1b

Counts

77 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.0b	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
26×	`sqrt-prod`
24×	`difference-of-squares`
18×	`times-frac`
16×	`*-un-lft-identity`
14×	`associate-r`
10×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `flip3--` `add-cbrt-cube` `flip--`
5×	`sub-neg`
4×	`frac-times` `associate-l` `distribute-lft-out--`
3×	`flip3-+` `diff-log` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

51.0ms	(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
24.0ms	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series61.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
13.0ms	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	414	1851
1	1787	1713
2	5002	1700

prune537.0ms

Filtered

107 candidates to 68 candidates (36.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 0.0b

Counts

111 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.5b	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
3.0b	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
16×	`difference-of-squares`
14×	`*-un-lft-identity`
13×	`sqrt-prod`
11×	`times-frac`
10×	`add-log-exp`
7×	`log-pow`
6×	`add-cube-cbrt` `exp-prod`
5×	`pow1` `log-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out--`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 74

Calls

4 calls:

10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
13.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
12.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
25.0ms	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series36.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify69.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	268	920
1	736	855
2	2431	831
3	5001	831

prune399.0ms

Filtered

86 candidates to 57 candidates (33.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

regimes442.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	43
1	53	43

end0.0ms

sample1.1s

Algorithm

intervals

Results

407.0ms	1661×	body	1280	valid
207.0ms	1275×	body	640	valid
133.0ms	4100×	body	80	valid
70.0ms	643×	body	320	valid
23.0ms	321×	body	160	valid

Details

sample40.0ms

simplify57.0ms

prune3.0ms

localize7.0ms

rewrite24.0ms

series16.0ms

simplify88.0ms

prune131.0ms

localize11.0ms

rewrite45.0ms

series53.0ms

simplify56.0ms

prune241.0ms

localize22.0ms

rewrite100.0ms

series61.0ms

simplify53.0ms

prune537.0ms

localize26.0ms

rewrite62.0ms

series36.0ms

simplify69.0ms

prune399.0ms

regimes442.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling