Details

sample348.0ms

Algorithm

intervals

Results

131.0ms	64×	body	1280	valid
89.0ms	200×	body	80	valid
70.0ms	54×	body	640	valid
26.0ms	28×	body	320	valid
11.0ms	15×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1174
2	189
1	54
0	19

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
2.8b	(/ (tan k) (/ l t))
2.9b	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
14.4b	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
154×	`add-sqr-sqrt`
151×	`add-cbrt-cube` `add-exp-log`
118×	`*-un-lft-identity` `add-cube-cbrt`
58×	`prod-exp` `cbrt-unprod`
57×	`cbrt-undiv` `div-exp`
50×	`associate-r`
46×	`associate-l`
20×	`pow1`
13×	`associate-/r*` `div-inv`
12×	`associate-*l/`
10×	`pow-prod-down`
9×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-/r/` `-commutative` `associate-/l*`
2×	`fma-udef`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `tan-quot` `associate-/l/`

Counts

4 → 289

Calls

4 calls:

35.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
9.0ms	(/ (tan k) (/ l t))
50.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
179.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
205.0ms	(/ (tan k) (/ l t))
273.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
415.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify2.2s

Counts

301 → 301

Iterations

Iter	Nodes
done	5002
1	1545
0	465

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize55.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (tan k) (/ l t))
2.8b	(* (* t (/ (tan k) (/ l t))) (sin k))
5.2b	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
11.9b	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
103×	`add-cbrt-cube` `add-exp-log`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
43×	`prod-exp` `cbrt-unprod`
33×	`cbrt-undiv` `div-exp`
26×	`associate-/r*`
18×	`pow1`
9×	`pow-prod-down`
8×	`div-inv`
6×	`associate-r`
5×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-*r/`
2×	`clear-num` `frac-2neg` `associate-l` `associate-/r/` `*-commutative` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `tan-quot`

Counts

4 → 197

Calls

4 calls:

16.0ms	(/ (tan k) (/ l t))
61.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
162.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
150.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (tan k) (/ l t))
226.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
344.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
404.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify3.2s

Counts

209 → 209

Iterations

Iter	Nodes
done	5000
2	4856
1	1075
0	367

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin k) t) (* (sin k) t))
5.2b	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (/ (* (* k (sin k)) (* k (sin k))) l) (cos k))) (/ l t))
6.4b	(/ (* (* k (sin k)) (* k (sin k))) l)
12.0b	(/ (* (* (sin k) t) (* (sin k) t)) l)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
57×	`add-cbrt-cube` `add-exp-log`
50×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
43×	`pow1`
24×	`prod-exp` `cbrt-unprod`
19×	`associate-/r*`
17×	`pow-prod-down`
13×	`cbrt-undiv` `div-exp`
7×	`div-inv`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`pow-plus`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `associate-/r/` `*-commutative`

Counts

4 → 170

Calls

4 calls:

34.0ms	(* (* (sin k) t) (* (sin k) t))
6.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (/ (* (* k (sin k)) (* k (sin k))) l) (cos k))) (/ l t))
36.0ms	(/ (* (* k (sin k)) (* k (sin k))) l)
48.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)

series607.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (sin k) t) (* (sin k) t))
328.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (/ (* (* k (sin k)) (* k (sin k))) l) (cos k))) (/ l t))
107.0ms	(/ (* (* k (sin k)) (* k (sin k))) l)
116.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)

simplify2.7s

Counts

182 → 182

Iterations

Iter	Nodes
done	5015
2	3800
1	924
0	324

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.4b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2 (/ (fma (* (/ (* (sin k) t) l) (/ (* (sin k) t) (cos k))) 2 (* (/ (* k (sin k)) (cos k)) (/ (* k (sin k)) l))) (/ l t)))
0.9b	(/ (* (sin k) t) l)
2.9b	(/ (* k (sin k)) l)
5.2b	(/ (fma (* (/ (* (sin k) t) l) (/ (* (sin k) t) (cos k))) 2 (* (/ (* k (sin k)) (cos k)) (/ (* k (sin k)) l))) (/ l t))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

477×	`times-frac`
235×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
63×	`associate-/r*`
28×	`add-cbrt-cube` `add-exp-log`
24×	`div-inv`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`

Counts

4 → 320

Calls

4 calls:

15.0ms	(/ 2 (/ (fma (* (/ (* (sin k) t) l) (/ (* (sin k) t) (cos k))) 2 (* (/ (* k (sin k)) (cos k)) (/ (* k (sin k)) l))) (/ l t)))
33.0ms	(/ (* (sin k) t) l)
24.0ms	(/ (* k (sin k)) l)
12.0ms	(/ (fma (* (/ (* (sin k) t) l) (/ (* (sin k) t) (cos k))) 2 (* (/ (* k (sin k)) (cos k)) (/ (* k (sin k)) l))) (/ l t))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ 2 (/ (fma (* (/ (* (sin k) t) l) (/ (* (sin k) t) (cos k))) 2 (* (/ (* k (sin k)) (cos k)) (/ (* k (sin k)) l))) (/ l t)))
68.0ms	(/ (* (sin k) t) l)
86.0ms	(/ (* k (sin k)) l)
394.0ms	(/ (fma (* (/ (* (sin k) t) l) (/ (* (sin k) t) (cos k))) 2 (* (/ (* k (sin k)) (cos k)) (/ (* k (sin k)) l))) (/ l t))

simplify2.5s

Counts

332 → 332

Iterations

Iter	Nodes
done	5000
1	1630
0	594

prune3.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.3b

regimes708.0ms

Accuracy

18.6% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 7.2b

bsearch1.0s

Steps

Iters	Range		Point
7	9.218221698895833e-166	2.7565214974298962e-164	2.7233600055589613e-164
9	-8.906236421925689e-206	-3.60543208326885e-212	-2.1925115852584323e-209

simplify9.0ms

Iterations

Iter	Nodes
done	40
1	40
0	32

end0.0ms

sample14.8s

Algorithm

intervals

Results

6.0s	2050×	body	1280	valid
4.0s	1753×	body	640	valid
2.8s	5877×	body	80	valid
1.1s	875×	body	320	valid
464.0ms	445×	body	160	valid