Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	49×	body	1280	valid
8.0ms	46×	body	640	valid
4.0ms	131×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	15	10
2	22	10
3	30	10
4	53	10
5	111	10
6	256	10
7	721	10
8	2461	10
done	5000	10

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: 29.4b

Counts

2 → 1

localize10.0ms

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)))
3.1b	(- (/ 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 → 60

Calls

3 calls:

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

series18.0ms

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)

simplify2.1s

Counts

69 → 69

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	116	947
1	252	903
2	536	847
3	1281	838
4	3775	836
done	5001	836

prune138.0ms

Filtered

51 candidates to 69 candidates (-35.3%)

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.1b	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`times-frac`
8×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`pow1` `log-prod` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-/l*`
2×	`sub-neg` `flip3-+` `exp-sum` `associate-/r/` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `log-div` `flip3--` `frac-2neg` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

4 → 81

Calls

4 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
11.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
9.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

simplify2.2s

Counts

93 → 93

Iterations

Useful iterations: 3 (242.0ms)

Iter	Nodes	Cost
0	145	1321
1	292	1228
2	589	1137
3	1359	1128
4	3947	1128
done	5001	1128

prune187.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	93	3	96

Merged error: 0.0b

Counts

96 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(+ 1.0 (exp (* -2.0 x)))
0.3b	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`sqrt-prod`
12×	`difference-of-squares`
11×	`associate-r`
10×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`flip3-+` `associate-l` `flip-+`
4×	`frac-times` `flip3--` `times-frac` `flip--` `distribute-lft-out` `distribute-lft-out--`
3×	`sub-neg`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/` `sum-log`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
35.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
16.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series52.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
34.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
14.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify602.0ms

Counts

96 → 96

Iterations

Useful iterations: done (598.0ms)

Iter	Nodes	Cost
0	148	2408
1	391	1954
2	1345	1802
done	5001	1795

prune274.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	96	3	99

Merged error: 0.0b

Counts

99 → 3

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `associate-l`
6×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`associate-*r/` `sqr-pow`
1×	`pow1` `distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-lft-in` `flip3-+` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

8.0ms

(* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x)))

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

(* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x)))

simplify1.9s

Counts

38 → 38

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	69	483
1	223	455
2	871	417
done	5000	417

prune53.0ms

Filtered

24 candidates to 38 candidates (-58.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	38	3	41

Merged error: 0.0b

Counts

41 → 3

regimes576.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	49
1	35	38
done	35	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

401.0ms	1750×	body	1280	valid
184.0ms	1182×	body	640	valid
149.0ms	4127×	body	80	valid
72.0ms	629×	body	320	valid
23.0ms	312×	body	160	valid

Details

sample38.0ms

simplify2.9s

prune3.0ms

localize10.0ms

rewrite21.0ms

series18.0ms

simplify2.1s

prune138.0ms

localize12.0ms

rewrite34.0ms

series26.0ms

simplify2.2s

prune187.0ms

localize12.0ms

rewrite61.0ms

series52.0ms

simplify602.0ms

prune274.0ms

localize9.0ms

rewrite9.0ms

series9.0ms

simplify1.9s

prune53.0ms

regimes576.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling