Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	47×	body	1280	valid
7.0ms	50×	body	640	valid
3.0ms	125×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid

simplify58.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.3b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite22.0ms

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:

8.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series128.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
18.0ms	(+ 1.0 (exp (* -2.0 x)))
75.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5002	460

prune124.0ms

Filtered

69 candidates to 50 candidates (72.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b	(* 0.33333333333333337 (pow x 3))
7.8b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
10×	`add-log-exp`
8×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `associate-l` `prod-exp`
2×	`diff-log` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `associate--r+`

Counts

3 → 56

Calls

3 calls:

6.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
6.0ms	(* 0.33333333333333337 (pow x 3))
7.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
38.0ms	(* 0.33333333333333337 (pow x 3))
104.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify45.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	275	398
1	1164	371
2	5001	370

prune117.0ms

Filtered

65 candidates to 41 candidates (63.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.3b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
305×	`*-un-lft-identity`
233×	`sqrt-prod`
214×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
57×	`distribute-lft-out`
30×	`associate-/l*`
22×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
10×	`div-inv`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 321

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
15.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
62.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series220.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
35.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
67.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
78.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	790	5746
1	2871	5152
2	5001	4983

prune414.0ms

Filtered

333 candidates to 145 candidates (43.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	333	3	336

Merged error: 0.0b

Counts

336 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
0.8b	(* (sqrt 2.0) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))))
3.3b	(- (* (sqrt 2.0) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
52×	`times-frac`
38×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-l` `associate-/l*` `unswap-sqr`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

4 → 128

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
13.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))))
9.0ms	(- (* (sqrt 2.0) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))) 1.0)

series289.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (exp (* -2.0 x)))
66.0ms	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
96.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))))
111.0ms	(- (* (sqrt 2.0) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	406	1251
1	1673	1119
2	5001	1089

prune215.0ms

Filtered

140 candidates to 87 candidates (62.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	140	3	143

Merged error: 0.0b

Counts

143 → 3

regimes197.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample888.0ms

Algorithm

intervals

Results

361.0ms	1671×	body	1280	valid
189.0ms	1300×	body	640	valid
115.0ms	4075×	body	80	valid
57.0ms	601×	body	320	valid
21.0ms	353×	body	160	valid