Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	51×	body	1280	valid
6.0ms	43×	body	640	valid
3.0ms	136×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1646	5
7	5001	5
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
3.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`add-cube-cbrt`
49×	`times-frac`
18×	`fma-neg`
13×	`distribute-lft-out`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`div-inv`
3×	`fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `distribute-lft-out--`

Counts

2 → 106

Calls

2 calls:

8.0ms	(+ 1.0 (exp (* -2.0 x)))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
82.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify41.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	362	1383
1	1096	982
2	5001	948
done	5001	948

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
3.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`add-cube-cbrt`
49×	`times-frac`
18×	`fma-neg`
13×	`distribute-lft-out`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`div-inv`
3×	`fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `distribute-lft-out--`

Counts

2 → 106

Calls

2 calls:

7.0ms	(+ 1.0 (exp (* -2.0 x)))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify43.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	362	1383
1	1096	982
2	5001	948
done	5001	948

prune190.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
28.7b	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`sqrt-prod`
8×	`distribute-lft-out`
6×	`associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `fma-udef` `div-inv`

Counts

3 → 77

Calls

3 calls:

16.0ms	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
7.0ms	(+ 1.0 (exp (* -2.0 x)))
1.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

series226.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
22.0ms	(+ 1.0 (exp (* -2.0 x)))
140.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

simplify114.0ms

Counts

86 → 86

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	276	726
1	879	664
2	3543	652
3	5001	651
done	5001	651

prune233.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0)))
28.7b	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))
28.7b	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))
28.7b	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0)))
0.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))
0.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))
0.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

series742.0ms

Counts

4 → 12

Calls

4 calls:

359.0ms	(cbrt (fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0)))
130.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))
127.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))
126.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

simplify84.0ms

Counts

55 → 55

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	163	700
1	573	534
2	2622	483
3	5001	467
done	5001	467

prune244.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 28.9b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	52
1	46	52
done	46	52

end0.0ms

sample902.0ms

Algorithm

intervals

Results

351.0ms	1700×	body	1280	valid
163.0ms	1222×	body	640	valid
107.0ms	4153×	body	80	valid
60.0ms	635×	body	320	valid
19.0ms	290×	body	160	valid