Details

sample105.0ms

Algorithm

intervals

Results

36.0ms	84×	body	1280	valid
22.0ms	84×	body	640	valid
14.0ms	249×	body	80	valid
10.0ms	40×	body	320	valid
3.0ms	26×	body	160	valid

simplify15.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	44	14
3	80	14
4	141	14
5	236	14
6	334	14
7	467	14
8	645	14
9	1090	14
10	2486	14
11	3254	14
12	3676	14
13	4546	14
14	4827	14
done	4827	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.7b	(- (exp l) (exp (- l)))

rewrite64.0ms

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-exp-log` `add-cbrt-cube`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `flip--` `log1p-expm1-u`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 96

Calls

3 calls:

24.0ms	(* J (- (exp l) (exp (- l))))
29.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
7.0ms	(- (exp l) (exp (- l)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* J (- (exp l) (exp (- l))))
91.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
37.0ms	(- (exp l) (exp (- l)))

simplify2.2s

Counts

105 → 105

Iterations

Useful iterations: 3 (918.0ms)

Iter	Nodes	Cost
0	168	2051
1	346	1619
2	985	1258
3	4153	1174
done	5000	1174

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
0.1b	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

7.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
7.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series394.0ms

Counts

2 → 6

Calls

2 calls:

234.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
161.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify2.1s

Counts

40 → 40

Iterations

Useful iterations: 3 (879.0ms)

Iter	Nodes	Cost
0	88	1117
1	228	1050
2	796	927
3	3801	880
done	5000	880

prune154.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b

(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)

0.1b

(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

0.1b

(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

6.0ms

(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)

6.0ms

(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

3.0ms

(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series481.0ms

Counts

3 → 9

Calls

3 calls:

228.0ms

(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)

164.0ms

(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

88.0ms

(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify2.4s

Counts

63 → 63

Iterations

Useful iterations: 3 (962.0ms)

Iter	Nodes	Cost
0	113	1647
1	280	1576
2	909	1379
3	4530	1322
done	5000	1322

prune254.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
0.1b	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
3.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series316.0ms

Counts

2 → 6

Calls

2 calls:

232.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
84.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify1.5s

Counts

36 → 36

Iterations

Useful iterations: 3 (340.0ms)

Iter	Nodes	Cost
0	81	877
1	174	869
2	535	752
3	2211	728
done	5000	728

prune146.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes362.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	21
1	21	21
done	21	21

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2677×	body	1280	valid
716.0ms	2657×	body	640	valid
474.0ms	8332×	body	80	valid
251.0ms	1397×	body	320	valid
95.0ms	816×	body	160	valid