Details

sample409.0ms

Algorithm

intervals

Results

130.0ms	61×	body	1280	valid
125.0ms	198×	body	80	valid
88.0ms	55×	body	640	valid
30.0ms	22×	body	320	valid
11.0ms	15×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
4	6501
3	1077
2	185
1	54
0	19

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize70.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (sin k) (/ t l))
4.9b	(* (tan k) (* (/ t l) t))
5.4b	(* (* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
9.4b	(* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2))

rewrite496.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-cbrt-cube` `add-exp-log`
68×	`prod-exp` `cbrt-unprod`
52×	`pow1`
34×	`pow-prod-down`
24×	`associate-*l/`
19×	`add-sqr-sqrt`
18×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cbrt-undiv` `div-exp`
10×	`times-frac` `associate-*r/`
8×	`associate-l` `tan-quot`
7×	`frac-times`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `div-inv`

Counts

4 → 150

Calls

4 calls:

12.0ms	(* (sin k) (/ t l))
33.0ms	(* (tan k) (* (/ t l) t))
371.0ms	(* (* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
78.0ms	(* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2))

series823.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin k) (/ t l))
140.0ms	(* (tan k) (* (/ t l) t))
323.0ms	(* (* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
287.0ms	(* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2))

simplify1.3s

Counts

162 → 162

Iterations

Iter	Nodes
2	3565
1	770
0	262

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (* (/ t l) t) (sin k))) (cos k))) (* (sin k) (/ t l))))
4.5b	(* (sin k) (/ t l))
4.9b	(* (* (/ t l) t) (sin k))
5.4b	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (* (/ t l) t) (sin k))) (cos k))) (* (sin k) (/ t l)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
21×	`add-sqr-sqrt`
17×	`associate-r` `prod-exp` `cbrt-unprod`
16×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac`
8×	`cbrt-undiv` `div-exp`
7×	`associate-l` `pow-prod-down`
5×	`associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`associate-*l/` `div-inv` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `associate-/r/`

Counts

4 → 112

Calls

4 calls:

20.0ms	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (* (/ t l) t) (sin k))) (cos k))) (* (sin k) (/ t l))))
20.0ms	(* (sin k) (/ t l))
43.0ms	(* (* (/ t l) t) (sin k))
35.0ms	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (* (/ t l) t) (sin k))) (cos k))) (* (sin k) (/ t l)))

series1.0s

Counts

4 → 12

Calls

4 calls:

381.0ms	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (* (/ t l) t) (sin k))) (cos k))) (* (sin k) (/ t l))))
73.0ms	(* (sin k) (/ t l))
83.0ms	(* (* (/ t l) t) (sin k))
504.0ms	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (* (/ t l) t) (sin k))) (cos k))) (* (sin k) (/ t l)))

simplify764.0ms

Counts

124 → 124

Iterations

Iter	Nodes
2	2311
1	582
0	216

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.7b

localize92.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (/ t l) (* t (sin k)))) (cos k))) (* (sin k) (/ t l))))
1.2b	(* (/ t l) (* t (sin k)))
4.5b	(* (sin k) (/ t l))
5.4b	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (/ t l) (* t (sin k)))) (cos k))) (* (sin k) (/ t l)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
19×	`associate-l`
18×	`prod-exp` `cbrt-unprod`
16×	`pow1`
15×	`associate-r`
9×	`cbrt-undiv` `div-exp`
7×	`pow-prod-down`
5×	`associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
2×	`unswap-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-/r/`

Counts

4 → 124

Calls

4 calls:

19.0ms	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (/ t l) (* t (sin k)))) (cos k))) (* (sin k) (/ t l))))
37.0ms	(* (/ t l) (* t (sin k)))
24.0ms	(* (sin k) (/ t l))
45.0ms	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (/ t l) (* t (sin k)))) (cos k))) (* (sin k) (/ t l)))

series1.3s

Counts

4 → 12

Calls

4 calls:

491.0ms	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (/ t l) (* t (sin k)))) (cos k))) (* (sin k) (/ t l))))
121.0ms	(* (/ t l) (* t (sin k)))
100.0ms	(* (sin k) (/ t l))
546.0ms	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* (/ t l) (* t (sin k)))) (cos k))) (* (sin k) (/ t l)))

simplify960.0ms

Counts

136 → 136

Iterations

Iter	Nodes
2	2380
1	621
0	231

prune2.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* t (/ (* t (sin k)) l))) (cos k))) (* (sin k) (/ t l))))
0.8b	(/ (* t (sin k)) l)
4.5b	(* (sin k) (/ t l))
5.4b	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* t (/ (* t (sin k)) l))) (cos k))) (* (sin k) (/ t l)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-cbrt-cube` `add-exp-log`
22×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`times-frac`
14×	`associate-r`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
6×	`associate-l`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `*-commutative` `unswap-sqr`
1×	`associate-/r/`

Counts

4 → 112

Calls

4 calls:

41.0ms	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* t (/ (* t (sin k)) l))) (cos k))) (* (sin k) (/ t l))))
23.0ms	(/ (* t (sin k)) l)
22.0ms	(* (sin k) (/ t l))
22.0ms	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* t (/ (* t (sin k)) l))) (cos k))) (* (sin k) (/ t l)))

series1.1s

Counts

4 → 12

Calls

4 calls:

435.0ms	(/ 2 (* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* t (/ (* t (sin k)) l))) (cos k))) (* (sin k) (/ t l))))
100.0ms	(/ (* t (sin k)) l)
84.0ms	(* (sin k) (/ t l))
480.0ms	(* (fma (/ (sin k) (cos k)) (/ k (/ l k)) (/ (* 2 (* t (/ (* t (sin k)) l))) (cos k))) (* (sin k) (/ t l)))

simplify779.0ms

Counts

124 → 124

Iterations

Iter	Nodes
2	2174
1	554
0	211

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.5b

regimes337.0ms

Accuracy

-0.3% (4.3b remaining)

Error of 5.7b against oracle of 1.5b and baseline of 5.7b

bsearch396.0ms

Steps

Iters	Range		Point
7	-2.587845704498569e+199	-1.752476598521974e+197	-6.242585972483955e+198

simplify7.0ms

Iterations

Iter	Nodes
2	44
1	44
0	36

end0.0ms

sample15.0s

Algorithm

intervals

Results

6.6s	2051×	body	1280	valid
3.9s	1717×	body	640	valid
2.4s	5913×	body	80	valid
1.2s	862×	body	320	valid
501.0ms	427×	body	160	valid