Details

sample187.0ms

Algorithm

intervals

Results

50.0ms	69×	body	1280	valid
40.0ms	96×	body	640	valid
30.0ms	261×	body	80	valid
11.0ms	38×	body	320	valid
3.0ms	16×	body	160	valid

simplify6.4s

Counts

1 → 1

Iterations

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

prune63.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (exp l))
0.0b	(fma (cos (/ K 2.0)) (- (* J (exp l)) (/ J (exp l))) U)
0.0b	(/ J (exp l))
7.4b	(- (* J (exp l)) (/ J (exp l)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
13×	`prod-diff`
8×	`add-cbrt-cube`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-r` `associate-l` `div-inv` `associate-/l`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

18.0ms	(* J (exp l))
1.0ms	(fma (cos (/ K 2.0)) (- (* J (exp l)) (/ J (exp l))) U)
10.0ms	(/ J (exp l))
50.0ms	(- (* J (exp l)) (/ J (exp l)))

series1.1s

Counts

4 → 12

Calls

4 calls:

59.0ms	(* J (exp l))
487.0ms	(fma (cos (/ K 2.0)) (- (* J (exp l)) (/ J (exp l))) U)
87.0ms	(/ J (exp l))
442.0ms	(- (* J (exp l)) (/ J (exp l)))

simplify7.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	4833
2	1447
1	506
0	205

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (cos (/ K 2.0)) (* (+ l l) J) U)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

1.0ms

(fma (cos (/ K 2.0)) (* (+ l l) J) U)

series217.0ms

Counts

1 → 3

Calls

1 calls:

217.0ms

(fma (cos (/ K 2.0)) (* (+ l l) J) U)

simplify3.8s

Counts

14 → 14

Iterations

Iter	Nodes
done	5016
4	1377
3	288
2	112
1	51
0	31

prune300.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma l (* (cos (* K 0.5)) (+ J J)) U)
0.2b	(* (cos (* K 0.5)) (+ J J))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-r`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`distribute-rgt-out` `associate-l` `distribute-lft-out`
2×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft1-in` `flip3-+` `count-2` `pow-prod-down` `distribute-rgt1-in` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `unswap-sqr`

Counts

2 → 45

Calls

2 calls:

1.0ms	(fma l (* (cos (* K 0.5)) (+ J J)) U)
69.0ms	(* (cos (* K 0.5)) (+ J J))

series340.0ms

Counts

2 → 6

Calls

2 calls:

222.0ms	(fma l (* (cos (* K 0.5)) (+ J J)) U)
119.0ms	(* (cos (* K 0.5)) (+ J J))

simplify5.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	5030
3	2656
2	692
1	206
0	86

prune825.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ J J)) (cbrt (+ J J)))
0.6b	(cbrt (+ J J))
0.6b	(cbrt (+ J J))
0.6b	(cbrt (+ J J))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cbrt-prod`
67×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
25×	`distribute-lft-out`
23×	`distribute-rgt-out`
21×	`swap-sqr`
18×	`cbrt-div`
15×	`associate-r` `associate-l`
11×	`pow1`
9×	`distribute-lft1-in` `flip3-+` `pow1/3` `distribute-rgt1-in` `flip-+`
7×	`count-2`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

81.0ms	(* (cbrt (+ J J)) (cbrt (+ J J)))
6.0ms	(cbrt (+ J J))
6.0ms	(cbrt (+ J J))
7.0ms	(cbrt (+ J J))

series1.5s

Counts

4 → 12

Calls

4 calls:

466.0ms	(* (cbrt (+ J J)) (cbrt (+ J J)))
327.0ms	(cbrt (+ J J))
363.0ms	(cbrt (+ J J))
369.0ms	(cbrt (+ J J))

simplify7.1s

Counts

171 → 171

Iterations

Iter	Nodes
done	5003
4	3816
3	1278
2	605
1	238
0	121

prune2.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes2.2s

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.6s	2748×	body	1280	valid
1.8s	2591×	body	640	valid
1.4s	8449×	body	80	valid
1.0s	1494×	body	320	valid
205.0ms	788×	body	160	valid