Details

sample248.0ms

Algorithm

intervals

Results

136.0ms	77×	body	1280	valid
36.0ms	48×	body	640	valid
31.0ms	185×	body	80	valid
21.0ms	31×	body	320	valid
6.0ms	17×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.9b

localize65.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
3.4b	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
4.4b	(/ (tan k) (/ l t))
14.9b	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite346.0ms

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:

21.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
61.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
11.0ms	(/ (tan k) (/ l t))
246.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series976.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
193.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
160.0ms	(/ (tan k) (/ l t))
427.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify2.3s

Counts

301 → 301

Iterations

Iter	Nodes
done	5002
1	1545
0	465

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.1b

localize41.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* t (/ (tan k) (/ l t))) (sin k))
4.4b	(/ (tan k) (/ l t))
6.7b	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
11.3b	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite343.0ms

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:

34.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
17.0ms	(/ (tan k) (/ l t))
152.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
136.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
171.0ms	(/ (tan k) (/ l t))
368.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
403.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify2.9s

Counts

209 → 209

Iterations

Iter	Nodes
done	5002
2	4720
1	1073
0	367

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize73.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
6.7b	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
7.8b	(/ (* (* (sin k) t) (* (sin k) t)) l)
8.2b	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

475×	`times-frac`
233×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
77×	`add-cbrt-cube` `add-exp-log`
61×	`associate-/r*`
29×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `div-exp` `div-inv`
8×	`associate-/l*`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 338

Calls

4 calls:

14.0ms	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
11.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
65.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)
44.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))

series1.9s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
327.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
125.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)
120.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))

simplify2.2s

Counts

350 → 350

Iterations

Iter	Nodes
done	5001
1	1825
0	644

prune3.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.3b

localize98.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (* (/ (* (sin k) k) l) (/ (* (sin k) k) (cos k)))) (/ l t)))
3.5b	(/ (* (sin k) k) l)
6.7b	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (* (/ (* (sin k) k) l) (/ (* (sin k) k) (cos k)))) (/ l t))
7.8b	(/ (* (* (sin k) t) (* (sin k) t)) l)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 326

Calls

4 calls:

15.0ms	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (* (/ (* (sin k) k) l) (/ (* (sin k) k) (cos k)))) (/ l t)))
25.0ms	(/ (* (sin k) k) l)
11.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (* (/ (* (sin k) k) l) (/ (* (sin k) k) (cos k)))) (/ l t))
65.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)

series1.5s

Counts

4 → 12

Calls

4 calls:

930.0ms	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (* (/ (* (sin k) k) l) (/ (* (sin k) k) (cos k)))) (/ l t)))
76.0ms	(/ (* (sin k) k) l)
330.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (* (/ (* (sin k) k) l) (/ (* (sin k) k) (cos k)))) (/ l t))
120.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)

simplify2.4s

Counts

338 → 338

Iterations

Iter	Nodes
done	5000
1	1744
0	610

prune2.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.9b

regimes876.0ms

Accuracy

32% (4.4b remaining)

Error of 7.8b against oracle of 3.3b and baseline of 9.8b

bsearch366.0ms

Steps

Iters	Range		Point
7	7084540214.993224	460904679690.46906	454432954895.17645
6	-9.531452225253714e+171	-7.507359893631642e+170	-7.646207435524129e+170

simplify23.0ms

Iterations

Iter	Nodes
done	49
1	49
0	39

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.4s	2076×	body	1280	valid
2.9s	1704×	body	640	valid
1.8s	5857×	body	80	valid
786.0ms	848×	body	320	valid
414.0ms	431×	body	160	valid