Details

sample1.2s

Algorithm

intervals

Results

372.0ms	139×	body	1280	valid
343.0ms	61×	body	2560	valid
223.0ms	28×	body	5120	valid
161.0ms	68×	body	640	valid
66.0ms	24×	body	320	valid
26.0ms	62×	body	80	valid
13.0ms	14×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	1021
2	177
1	51
0	19

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 2 t) (tan k))
1.4b	(/ (* (/ l t) (/ l t)) (sin k))
2.7b	(* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k)))
30.1b	(/ (* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k))) (* (/ k t) (/ k t)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

837×	`add-cbrt-cube` `add-exp-log`
453×	`cbrt-undiv` `div-exp`
260×	`prod-exp` `cbrt-unprod`
157×	`times-frac`
103×	`add-sqr-sqrt`
85×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
15×	`associate-/l*`
12×	`div-inv`
7×	`associate-/r` `associate-r*` `associate-/l/`
6×	`pow1` `unswap-sqr`
5×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`tan-quot`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 427

Calls

4 calls:

12.0ms	(/ (/ 2 t) (tan k))
22.0ms	(/ (* (/ l t) (/ l t)) (sin k))
62.0ms	(* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k)))
60.0ms	(/ (* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k))) (* (/ k t) (/ k t)))

series1.0s

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ 2 t) (tan k))
135.0ms	(/ (* (/ l t) (/ l t)) (sin k))
359.0ms	(* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k)))
379.0ms	(/ (* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k))) (* (/ k t) (/ k t)))

simplify1.4s

Counts

439 → 439

Iterations

Iter	Nodes
done	2001
2	2001
1	1933
0	606

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.8b

localize67.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* (/ l t) (/ l t)) (sin k))
8.4b	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t)))
15.3b	(/ (/ (/ 2 t) (tan k)) (/ k t))
18.6b	(/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

4259×	`times-frac`
1922×	`add-sqr-sqrt`
1735×	`*-un-lft-identity` `add-cube-cbrt`
784×	`add-cbrt-cube` `add-exp-log`
577×	`associate-l`
507×	`cbrt-undiv` `div-exp`
244×	`div-inv`
159×	`prod-exp` `cbrt-unprod`
96×	`associate-r`
52×	`associate-/l*`
35×	`unswap-sqr`
31×	`associate-/r/`
29×	`associate-/r*`
27×	`tan-quot`
6×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 1744

Calls

4 calls:

19.0ms	(/ (* (/ l t) (/ l t)) (sin k))
121.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t)))
27.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
38.0ms	(/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t))

series803.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (* (/ l t) (/ l t)) (sin k))
396.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t)))
154.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
153.0ms	(/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t))

simplify2.2s

Counts

1756 → 1756

Iterations

Iter	Nodes
done	2416
0	2416

prune16.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.7b

localize72.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (/ l t) (sin k))
8.6b	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (/ l t) 1) 1))
15.3b	(/ (/ (/ 2 t) (tan k)) (/ k t))
16.4b	(/ (/ (/ l t) (sin k)) (/ k t))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

6327×	`times-frac`
2972×	`add-sqr-sqrt`
2625×	`*-un-lft-identity`
2562×	`add-cube-cbrt`
577×	`associate-l`
461×	`add-exp-log`
352×	`div-exp`
318×	`div-inv`
209×	`add-cbrt-cube`
135×	`cbrt-undiv`
133×	`associate-r`
100×	`associate-/l*`
77×	`prod-exp` `unswap-sqr`
63×	`1-exp`
30×	`associate-/r/`
29×	`associate-/r*`
28×	`cbrt-unprod`
27×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 2278

Calls

4 calls:

9.0ms	(/ (/ l t) (sin k))
135.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (/ l t) 1) 1))
35.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
41.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

series666.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ l t) (sin k))
244.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (/ l t) 1) 1))
182.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
121.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

simplify3.6s

Counts

2290 → 2290

Iterations

Iter	Nodes
done	3469
0	3469

prune24.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (* k (sin k)))
3.5b	(/ (/ l t) (sin k))
8.6b	(* (* 2 (/ (cos k) (* k (sin k)))) (/ (/ (/ l t) 1) 1))
16.4b	(/ (/ (/ l t) (sin k)) (/ k t))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

2284×	`times-frac`
995×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
241×	`add-exp-log`
133×	`associate-r`
130×	`div-exp`
120×	`div-inv`
115×	`add-cbrt-cube`
89×	`prod-exp`
59×	`associate-/l*`
52×	`cbrt-undiv`
36×	`1-exp`
33×	`cbrt-unprod`
17×	`associate-/r*`
9×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*r/`
2×	`associate-/l/`
1×	`frac-times` `associate-l` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 949

Calls

4 calls:

19.0ms	(/ (cos k) (* k (sin k)))
15.0ms	(/ (/ l t) (sin k))
94.0ms	(* (* 2 (/ (cos k) (* k (sin k)))) (/ (/ (/ l t) 1) 1))
27.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

series514.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (cos k) (* k (sin k)))
125.0ms	(/ (/ l t) (sin k))
190.0ms	(* (* 2 (/ (cos k) (* k (sin k)))) (/ (/ (/ l t) 1) 1))
123.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

simplify2.1s

Counts

961 → 961

Iterations

Iter	Nodes
done	2000
1	2000
0	1743

prune7.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.8b

regimes660.0ms

Accuracy

0% (1.6b remaining)

Error of 6.9b against oracle of 5.2b and baseline of 6.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample45.1s

Algorithm

intervals

Results

13.4s	4151×	body	1280	valid
11.8s	2204×	body	2560	valid
10.4s	982×	body	5120	valid
5.7s	2415×	body	640	valid
1.8s	989×	body	320	valid
1.0s	2079×	body	80	valid
455.0ms	460×	body	160	valid