Details

sample251.0ms

Algorithm

intervals

Results

99.0ms	80×	body	1280	valid
54.0ms	81×	body	640	valid
35.0ms	255×	body	80	valid
21.0ms	49×	body	320	valid
8.0ms	28×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3163
6	1067
5	416
4	202
3	85
2	44
1	24
0	14

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.7b

localize51.0ms

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)))
7.4b	(- (exp l) (exp (- l)))

rewrite198.0ms

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:

43.0ms	(* J (- (exp l) (exp (- l))))
59.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
67.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
26.0ms	(- (exp l) (exp (- l)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* J (- (exp l) (exp (- l))))
310.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
114.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
60.0ms	(- (exp l) (exp (- l)))

simplify3.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	4948
2	1314
1	490
0	203

prune769.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (* J l))
0.0b	(+ (* (* 2 (* J l)) (cos (/ K 2))) U)
0.1b	(* (* 2 (* J l)) (cos (/ K 2)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

27.0ms	(* 2 (* J l))
44.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2))) U)
46.0ms	(* (* 2 (* J l)) (cos (/ K 2)))

series259.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 2 (* J l))
132.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2))) U)
104.0ms	(* (* 2 (* J l)) (cos (/ K 2)))

simplify3.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	4216
2	892
1	258
0	100

prune718.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* J (* l (cos (* 1/2 K)))) 2 U)
0.1b	(* J (* l (cos (* 1/2 K))))
0.1b	(* l (cos (* 1/2 K)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma (* J (* l (cos (* 1/2 K)))) 2 U)
44.0ms	(* J (* l (cos (* 1/2 K))))
14.0ms	(* l (cos (* 1/2 K)))

series235.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(fma (* J (* l (cos (* 1/2 K)))) 2 U)
58.0ms	(* J (* l (cos (* 1/2 K))))
51.0ms	(* l (cos (* 1/2 K)))

simplify2.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	1911
2	471
1	166
0	80

prune372.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt l) (cbrt l))
0.6b	(cbrt l)
0.6b	(cbrt l)
0.6b	(cbrt l)

rewrite10.0ms

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` `insert-posit16` `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 → 85

Calls

4 calls:

7.0ms	(* (cbrt l) (cbrt l))
1.0ms	(cbrt l)
1.0ms	(cbrt l)
1.0ms	(cbrt l)

series1.2s

Counts

4 → 12

Calls

4 calls:

333.0ms	(* (cbrt l) (cbrt l))
313.0ms	(cbrt l)
275.0ms	(cbrt l)
289.0ms	(cbrt l)

simplify3.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
4	4657
3	1110
2	364
1	141
0	67

prune657.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes390.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.3s	2688×	body	1280	valid
1.7s	2618×	body	640	valid
1.4s	8327×	body	80	valid
1.1s	1422×	body	320	valid
174.0ms	754×	body	160	valid