Details

sample110.0ms

Algorithm

intervals

Results

44.0ms	87×	body	1280	valid
24.0ms	92×	body	640	valid
14.0ms	263×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	17×	body	160	valid

simplify14.9s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	44	14
3	82	14
4	143	14
5	261	14
6	471	14
7	671	14
8	908	14
9	1444	14
10	3391	14
11	4681	14
done	5000	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
0.0b	(* J (- (exp l) (exp (- l))))
5.2b	(- (exp l) (exp (- l)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
26.0ms	(* J (- (exp l) (exp (- l))))
8.0ms	(- (exp l) (exp (- l)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
56.0ms	(* J (- (exp l) (exp (- l))))
36.0ms	(- (exp l) (exp (- l)))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: 3 (378.0ms)

Iter	Nodes	Cost
0	162	1865
1	325	1440
2	830	1116
3	3232	950
done	5000	950

prune229.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

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

rewrite4.0ms

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:

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

series421.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
236.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify729.0ms

Counts

51 → 51

Iterations

Useful iterations: 3 (171.0ms)

Iter	Nodes	Cost
0	88	1042
1	179	1027
2	513	890
3	2237	876
done	5000	876

prune216.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
14.1b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
14.1b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
14.1b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
1.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
1.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
1.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

335.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
301.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
290.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
295.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify252.0ms

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	132	2272
1	299	2080
2	835	1843