Details

sample281.0ms

Algorithm

intervals

Results

82.0ms	83×	body	1280	valid
72.0ms	98×	body	640	valid
45.0ms	280×	body	80	valid
45.0ms	46×	body	320	valid
7.0ms	21×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2016
7	2016
6	1067
5	416
4	202
3	85
2	44
1	24
0	14

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
5.3b	(- (exp l) (exp (- l)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
11×	`distribute-rgt-in` `pow1` `distribute-lft-in` `add-cbrt-cube` `add-exp-log`
8×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `fma-neg` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `diff-log` `flip-+` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

39.0ms	(* J (- (exp l) (exp (- l))))
90.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
68.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
23.0ms	(- (exp l) (exp (- l)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* J (- (exp l) (exp (- l))))
302.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
133.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
46.0ms	(- (exp l) (exp (- l)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	2005
3	2005
2	1314
1	490
0	203

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

0.0ms	(fma (pow l 5) 1/60 (fma (* 1/3 (* l l)) l (+ l l)))
31.0ms	(+ (* (* J (fma (pow l 5) 1/60 (fma (* 1/3 (* l l)) l (+ l l)))) (cos (/ K 2))) U)
17.0ms	(* (* J (fma (pow l 5) 1/60 (fma (* 1/3 (* l l)) l (+ l l)))) (cos (/ K 2)))
22.0ms	(* 1/3 (* l l))

series736.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(fma (pow l 5) 1/60 (fma (* 1/3 (* l l)) l (+ l l)))
340.0ms	(+ (* (* J (fma (pow l 5) 1/60 (fma (* 1/3 (* l l)) l (+ l l)))) (cos (/ K 2))) U)
241.0ms	(* (* J (fma (pow l 5) 1/60 (fma (* 1/3 (* l l)) l (+ l l)))) (cos (/ K 2)))
44.0ms	(* 1/3 (* l l))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	2001
3	2001
2	1146
1	355
0	138

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube` `associate-l`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `prod-exp` `fma-udef`
5×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma l (fma 1/3 (* l l) 2) (* (pow l 5) 1/60))
17.0ms	(* (pow l 5) 1/60)
14.0ms	(* (cos (/ K 2)) (fma l (fma 1/3 (* l l) 2) (* (pow l 5) 1/60)))
31.0ms	(* J (* (cos (/ K 2)) (fma l (fma 1/3 (* l l) 2) (* (pow l 5) 1/60))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma l (fma 1/3 (* l l) 2) (* (pow l 5) 1/60))
91.0ms	(* (pow l 5) 1/60)
207.0ms	(* (cos (/ K 2)) (fma l (fma 1/3 (* l l) 2) (* (pow l 5) 1/60)))
369.0ms	(* J (* (cos (/ K 2)) (fma l (fma 1/3 (* l l) 2) (* (pow l 5) 1/60))))

simplify1.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	2002
3	2002
2	1216
1	386
0	165

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* l l) l)
0.1b	(* (cos (* K 1/2)) (* (* l J) 2))
2.9b	(* (* J 1/60) (pow l 5))
4.2b	(* J (* (* l l) l))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
40×	`add-exp-log`
32×	`add-cbrt-cube`
24×	`prod-exp`
18×	`cbrt-unprod`
15×	`pow-prod-down`
12×	`associate-r`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
6×	`pow-plus` `pow-prod-up`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down`
2×	`pow2` `pow-to-exp` `pow-exp` `pow-sqr`
1×	`pow3` `unswap-sqr` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

15.0ms	(* (* l l) l)
60.0ms	(* (cos (* K 1/2)) (* (* l J) 2))
20.0ms	(* (* J 1/60) (pow l 5))
49.0ms	(* J (* (* l l) l))

series315.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* l l) l)
67.0ms	(* (cos (* K 1/2)) (* (* l J) 2))
118.0ms	(* (* J 1/60) (pow l 5))
66.0ms	(* J (* (* l l) l))

simplify1.4s

Counts

118 → 118

Iterations

Iter	Nodes
done	2007
3	2007
2	1731
1	437
0	166

prune2.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes716.0ms

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
done	22
1	22
0	18

end0.0ms

sample9.8s

Algorithm

intervals

Results

4.0s	2721×	body	1280	valid
1.9s	2530×	body	640	valid
1.7s	8389×	body	80	valid
1.3s	1429×	body	320	valid
266.0ms	734×	body	160	valid