Details

sample314.0ms

Algorithm

intervals

Results

127.0ms	92×	body	1280	valid
74.0ms	99×	body	640	valid
44.0ms	274×	body	80	valid
30.0ms	41×	body	320	valid
7.0ms	21×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
8	2007
7	1093
6	610
5	337
4	198
3	83
2	42
1	24
0	14

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ J (exp l))
0.0b	(* J (exp l))
0.0b	(fma (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))) U)
5.4b	(- (* J (exp l)) (/ J (exp l)))

rewrite43.0ms

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:

5.0ms	(/ J (exp l))
9.0ms	(* J (exp l))
0.0ms	(fma (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))) U)
27.0ms	(- (* J (exp l)) (/ J (exp l)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ J (exp l))
28.0ms	(* J (exp l))
252.0ms	(fma (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))) U)
82.0ms	(- (* J (exp l)) (/ J (exp l)))

simplify2.3s

Counts

104 → 104

Iterations

Iter	Nodes
3	3513
2	1224
1	480
0	201

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

15.0ms	(* 2 (* J l))
0.0ms	(fma (cos (/ K 2)) (* 2 (* J l)) U)

series167.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(* 2 (* J l))
140.0ms	(fma (cos (/ K 2)) (* 2 (* J l)) U)

simplify1.9s

Counts

38 → 38

Iterations

Iter	Nodes
4	3435
3	1034
2	346
1	128
0	61

prune487.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* (* (cos (* K 1/2)) l) J) 2 U)
0.1b	(* (* (cos (* K 1/2)) l) J)
0.2b	(* (cos (* K 1/2)) l)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`associate-l` `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 (* (* (cos (* K 1/2)) l) J) 2 U)
50.0ms	(* (* (cos (* K 1/2)) l) J)
36.0ms	(* (cos (* K 1/2)) l)

series303.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(fma (* (* (cos (* K 1/2)) l) J) 2 U)
70.0ms	(* (* (cos (* K 1/2)) l) J)
67.0ms	(* (cos (* K 1/2)) l)

simplify4.1s

Counts

62 → 62

Iterations

Iter	Nodes
4	5401
3	1821
2	547
1	190
0	91

prune617.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (* K 1/2))) (cbrt (cos (* K 1/2))))
0.3b	(cbrt (cos (* K 1/2)))
0.3b	(cbrt (cos (* K 1/2)))
0.3b	(cbrt (cos (* K 1/2)))

rewrite47.0ms

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:

36.0ms	(* (cbrt (cos (* K 1/2))) (cbrt (cos (* K 1/2))))
3.0ms	(cbrt (cos (* K 1/2)))
3.0ms	(cbrt (cos (* K 1/2)))
3.0ms	(cbrt (cos (* K 1/2)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (cbrt (cos (* K 1/2))) (cbrt (cos (* K 1/2))))
152.0ms	(cbrt (cos (* K 1/2)))
136.0ms	(cbrt (cos (* K 1/2)))
144.0ms	(cbrt (cos (* K 1/2)))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
4	4254
3	1086
2	346
1	153
0	75

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes561.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	10

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.8s	2717×	body	1280	valid
2.4s	2675×	body	640	valid
1.7s	8586×	body	80	valid
748.0ms	1435×	body	320	valid
289.0ms	743×	body	160	valid