Details

sample315.0ms

Algorithm

intervals

Results

124.0ms	80×	body	1280	valid
70.0ms	89×	body	640	valid
54.0ms	281×	body	80	valid
25.0ms	44×	body	320	valid
9.0ms	28×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
8	2007
7	1093
6	610
5	337
4	198
3	83
2	42
1	24
0	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.2b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
0.0b	(* J (- (exp l) (exp (- l))))
6.2b	(- (exp l) (exp (- l)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `log1p-expm1-u` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 96

Calls

3 calls:

71.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
36.0ms	(* J (- (exp l) (exp (- l))))
12.0ms	(- (exp l) (exp (- l)))

series239.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
78.0ms	(* J (- (exp l) (exp (- l))))
41.0ms	(- (exp l) (exp (- l)))

simplify1.3s

Counts

105 → 105

Iterations

Iter	Nodes
3	2589
2	908
1	363
0	165

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))
0.0b	(+ (* (* J (fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))) (cos (/ K 2))) U)
0.1b	(* (* J (fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))) (cos (/ K 2)))
0.2b	(* (* l l) 1/3)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`associate-l` `*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))
35.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))) (cos (/ K 2))) U)
29.0ms	(* (* J (fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))) (cos (/ K 2)))
19.0ms	(* (* l l) 1/3)

series691.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))
352.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))) (cos (/ K 2))) U)
212.0ms	(* (* J (fma (pow l 5) 1/60 (* l (+ (* (* l l) 1/3) 2)))) (cos (/ K 2)))
42.0ms	(* (* l l) 1/3)

simplify3.7s

Counts

77 → 77

Iterations

Iter	Nodes
3	5283
2	1139
1	354
0	136

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* l (* l l)) (* l l))
0.1b	(* J (* (cos (/ K 2)) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l)))))))
0.1b	(fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))
0.1b	(* (cos (/ K 2)) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

93×	`pow1`
45×	`pow-prod-up`
32×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`pow2` `add-sqr-sqrt` `pow-plus` `pow-sqr`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt` `fma-udef`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`expm1-log1p-u` `cube-unmult` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`unswap-sqr`

Counts

4 → 106

Calls

4 calls:

74.0ms	(* (* l (* l l)) (* l l))
17.0ms	(* J (* (cos (/ K 2)) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l)))))))
0.0ms	(fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))
6.0ms	(* (cos (/ K 2)) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* l (* l l)) (* l l))
368.0ms	(* J (* (cos (/ K 2)) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l)))))))
158.0ms	(fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))
240.0ms	(* (cos (/ K 2)) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))))

simplify2.4s

Counts

118 → 118

Iterations

Iter	Nodes
3	4640
2	1221
1	438
0	178

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* l (* l l)) (* l l))
0.1b	(* (* J (cos (/ K 2))) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))))
0.1b	(* J (cos (/ K 2)))
0.1b	(fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

93×	`pow1`
45×	`pow-prod-up`
32×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`pow2` `add-sqr-sqrt` `pow-plus` `pow-sqr`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
5×	`associate-l`
4×	`expm1-log1p-u` `cube-unmult` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

62.0ms	(* (* l (* l l)) (* l l))
23.0ms	(* (* J (cos (/ K 2))) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))))
6.0ms	(* J (cos (/ K 2)))
0.0ms	(fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (* l (* l l)) (* l l))
372.0ms	(* (* J (cos (/ K 2))) (fma 2 l (fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))))
61.0ms	(* J (cos (/ K 2)))
219.0ms	(fma (* l (* l l)) 1/3 (* 1/60 (* (* l (* l l)) (* l l))))

simplify2.1s

Counts

114 → 114

Iterations

Iter	Nodes
3	3951
2	1031
1	376
0	159

prune1.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes454.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	25
1	25
0	19

end0.0ms

sample10.1s

Algorithm

intervals

Results

3.8s	2683×	body	1280	valid
2.2s	2549×	body	640	valid
1.9s	8385×	body	80	valid
1.3s	1488×	body	320	valid
275.0ms	732×	body	160	valid