Details

sample102.0ms

Algorithm

intervals

Results

32.0ms	81×	body	1280	valid
21.0ms	86×	body	640	valid
15.0ms	283×	body	80	valid
6.0ms	38×	body	320	valid
3.0ms	26×	body	160	valid

simplify376.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	44	8
2	91	8
3	195	8
4	332	8
5	652	8
6	1279	8
7	1694	8
8	4980	8
9	5001	8
done	5001	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize18.0ms

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)))
5.1b	(- (exp l) (exp (- l)))

rewrite125.0ms

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:

47.0ms	(* J (- (exp l) (exp (- l))))
59.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
15.0ms	(- (exp l) (exp (- l)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* J (- (exp l) (exp (- l))))
97.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
36.0ms	(- (exp l) (exp (- l)))

simplify45.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	348	1300
1	1396	879
2	5001	825
done	5001	825

prune258.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

9.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma 1/60 (pow l 5) (* 2 l))
17.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
17.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
132.0ms	(fma 1/60 (pow l 5) (* 2 l))
250.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
167.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify44.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	290	768
1	1274	670
2	5002	654
done	5002	654

prune296.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

7.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma 1/60 (pow l 5) (* 2 l))
0.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series519.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
126.0ms	(fma 1/60 (pow l 5) (* 2 l))
253.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify93.0ms

Counts

51 → 51

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	178	421
1	700	364
2	3483	356
3	5001	356
done	5001	356

prune346.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow l 5) (* 2 l))
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)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

0.0ms	(fma 1/60 (pow l 5) (* 2 l))
17.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
17.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
8.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma 1/60 (pow l 5) (* 2 l))
254.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
172.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
89.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify40.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	290	811
1	1017	708
2	5001	685
done	5001	685

prune269.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes195.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9
done	21	9

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2660×	body	1280	valid
661.0ms	2603×	body	640	valid
459.0ms	8399×	body	80	valid
241.0ms	1431×	body	320	valid
85.0ms	771×	body	160	valid