Details

analyze2.0ms

Algorithm: search

sample32.0ms

Algorithm

intervals

Results

12.0ms	49×	body	1280	valid
6.0ms	37×	body	640	valid
5.0ms	146×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	8×	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

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: 25.8b

Counts

2 → 1

localize7.0ms

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)))
2.0b	(- (/ 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:

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

series17.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify91.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (18.0ms)

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

prune126.0ms

Filtered

50 candidates to 69 candidates (-38.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.0b

Counts

70 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(+ 1.0 (exp (* -2.0 x)))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.0b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
31×	`times-frac`
21×	`sqrt-prod`
20×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`associate-/r*` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`+-commutative` `sqrt-div` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 89

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
66.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series23.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
8.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
11.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	320	1064
1	949	949
2	4186	896
3	5002	896

prune197.0ms

Filtered

67 candidates to 101 candidates (-50.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	101	2	103

Merged error: 0.0b

Counts

103 → 2

localize11.0ms

Local error

Found 4 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))
0.2b	(* 5.551115123125783e-17 (pow x 4))
11.4b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

7.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(* 5.551115123125783e-17 (pow x 4))
4.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
4.0ms	(* 0.33333333333333337 (pow x 3))
4.0ms	(* 5.551115123125783e-17 (pow x 4))
9.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	344	493
1	1475	459
2	5001	459

prune133.0ms

Filtered

58 candidates to 93 candidates (-60.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Merged error: 0b

Counts

95 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

11.4b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))
16.8b	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))
16.8b	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))
16.8b	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 50

Calls

4 calls:

4.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))
5.0ms	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))
5.0ms	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))
5.0ms	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))
11.0ms	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))
11.0ms	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))
12.0ms	(cbrt (- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	315	1052
1	1140	998
2	5001	913

prune318.0ms

Filtered

55 candidates to 62 candidates (-12.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	62	3	65

Merged error: 0b

Counts

65 → 3

regimes250.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

analyze1.0ms

Algorithm: search

sample978.0ms

Algorithm

intervals

Results

412.0ms	1684×	body	1280	valid
200.0ms	1218×	body	640	valid
130.0ms	4127×	body	80	valid
74.0ms	647×	body	320	valid
26.0ms	324×	body	160	valid

Details

analyze2.0ms

sample32.0ms

simplify57.0ms

prune3.0ms

localize7.0ms

rewrite24.0ms

series17.0ms

simplify91.0ms

prune126.0ms

localize9.0ms

rewrite81.0ms

series23.0ms

simplify127.0ms

prune197.0ms

localize11.0ms

rewrite25.0ms

series22.0ms

simplify52.0ms

prune133.0ms

localize18.0ms

rewrite21.0ms

series43.0ms

simplify43.0ms

prune318.0ms

regimes250.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze1.0ms

sample978.0ms

Profiling