Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	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

simplify1.1s

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	112	10
6	268	10
7	784	10
8	2675	10
done	5001	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

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

rewrite28.0ms

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:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms	(+ 1.0 (exp (* -2.0 x)))
11.0ms	(- (/ 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)

simplify1.1s

Counts

69 → 69

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	116	947
1	255	904
2	569	850
3	1374	839
4	3611	839
done	5000	838

prune142.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

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 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)))

rewrite35.0ms

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:

7.0ms	(/ 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)))

series28.0ms

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

simplify1.2s

Counts

93 → 93

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	145	1321
1	306	1229
2	679	1140
3	1570	1129
4	4031	1129
done	5001	1128

prune186.0ms

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))

rewrite62.0ms

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

series53.0ms

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))

simplify437.0ms

Counts

96 → 96

Iterations

Useful iterations: done (434.0ms)

Iter	Nodes	Cost
0	148	2408
1	398	1972
2	1475	1818
done	5001	1795

prune259.0ms

Filtered

65 candidates to 96 candidates (-47.7%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x 4)
0.2b	(* 5.551115123125783e-17 (pow x 4))
0.3b	(* 0.33333333333333337 (pow x 3))
9.0b	(+ (* 0.33333333333333337 (pow x 3)) (* 5.551115123125783e-17 (pow x 4)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

2.0ms	(pow x 4)
6.0ms	(* 5.551115123125783e-17 (pow x 4))
9.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(+ (* 0.33333333333333337 (pow x 3)) (* 5.551115123125783e-17 (pow x 4)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow x 4)
4.0ms	(* 5.551115123125783e-17 (pow x 4))
4.0ms	(* 0.33333333333333337 (pow x 3))
11.0ms	(+ (* 0.33333333333333337 (pow x 3)) (* 5.551115123125783e-17 (pow x 4)))

simplify418.0ms

Counts

96 → 96

Iterations

Useful iterations: done (415.0ms)

Iter	Nodes	Cost
0	122	843
1	302	753
2	974	700
done	5000	694

prune145.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

99 → 3

regimes533.0ms

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	28	51
1	37	40
done	37	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

409.0ms	1750×	body	1280	valid
194.0ms	1182×	body	640	valid
150.0ms	4127×	body	80	valid
70.0ms	629×	body	320	valid
23.0ms	312×	body	160	valid

Details

sample43.0ms

simplify1.1s

prune3.0ms

localize7.0ms

rewrite28.0ms

series17.0ms

simplify1.1s

prune142.0ms

localize10.0ms

rewrite35.0ms

series28.0ms

simplify1.2s

prune186.0ms

localize12.0ms

rewrite62.0ms

series53.0ms

simplify437.0ms

prune259.0ms

localize11.0ms

rewrite25.0ms

series23.0ms

simplify418.0ms

prune145.0ms

regimes533.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.1s

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