Details

sample197.0ms

Algorithm

intervals

Results

87.0ms	79×	body	1280	valid
35.0ms	77×	body	640	valid
25.0ms	280×	body	80	valid
14.0ms	48×	body	320	valid
4.0ms	24×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2946
5	605
4	222
3	91
2	45
1	24
0	14

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* (cos (/ K 2.0)) J) (- (exp l) (exp (- l))) U)
0.1b	(* (cos (/ K 2.0)) J)
5.9b	(- (exp l) (exp (- l)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma (* (cos (/ K 2.0)) J) (- (exp l) (exp (- l))) U)
13.0ms	(* (cos (/ K 2.0)) J)
16.0ms	(- (exp l) (exp (- l)))

series462.0ms

Counts

3 → 9

Calls

3 calls:

299.0ms	(fma (* (cos (/ K 2.0)) J) (- (exp l) (exp (- l))) U)
85.0ms	(* (cos (/ K 2.0)) J)
78.0ms	(- (exp l) (exp (- l)))

simplify918.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1195
1	302
0	140

prune490.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (+ l l))
0.0b	(fma (* (cos (/ K 2.0)) J) (fma (pow l 5) 1/60 (fma 1/3 (pow l 3) (+ l l))) U)
0.1b	(* (cos (/ K 2.0)) J)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

0.0ms	(fma 1/3 (pow l 3) (+ l l))
0.0ms	(fma (* (cos (/ K 2.0)) J) (fma (pow l 5) 1/60 (fma 1/3 (pow l 3) (+ l l))) U)
7.0ms	(* (cos (/ K 2.0)) J)

series745.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(fma 1/3 (pow l 3) (+ l l))
570.0ms	(fma (* (cos (/ K 2.0)) J) (fma (pow l 5) 1/60 (fma 1/3 (pow l 3) (+ l l))) U)
56.0ms	(* (cos (/ K 2.0)) J)

simplify2.6s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
3	4036
2	598
1	177
0	89

prune488.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

18.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

441.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
209.0ms	(cbrt (cos (/ K 2.0)))
204.0ms	(cbrt (cos (/ K 2.0)))
197.0ms	(cbrt (cos (/ K 2.0)))

simplify2.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	3141
2	560
1	161
0	74

prune949.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.6b	(expm1 (cbrt (cos (/ K 2.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(expm1 (cbrt (cos (/ K 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (cos (/ K 2.0)))
205.0ms	(cbrt (cos (/ K 2.0)))
211.0ms	(cbrt (cos (/ K 2.0)))
515.0ms	(expm1 (cbrt (cos (/ K 2.0))))

simplify796.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
3	975
2	270
1	110
0	56

prune655.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes658.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	18

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.3s	2698×	body	640	valid
2.3s	2726×	body	1280	valid
1.7s	8322×	body	80	valid
572.0ms	1438×	body	320	valid
203.0ms	762×	body	160	valid