Details

sample281.0ms

Algorithm

intervals

Results

106.0ms	78×	body	1280	valid
103.0ms	59×	body	640	valid
35.0ms	190×	body	80	valid
14.0ms	23×	body	320	valid
4.0ms	10×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
2.4b	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
2.7b	(/ (tan k) (/ l t))
16.7b	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite502.0ms

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:

65.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
73.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
10.0ms	(/ (tan k) (/ l t))
337.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series923.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
250.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
150.0ms	(/ (tan k) (/ l t))
349.0ms	(* (* (* (/ 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

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.4b

localize41.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* t (/ (tan k) (/ l t))) (sin k))
2.7b	(/ (tan k) (/ l t))
9.8b	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
14.3b	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite573.0ms

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:

65.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
20.0ms	(/ (tan k) (/ l t))
233.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
248.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
200.0ms	(/ (tan k) (/ l t))
422.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
311.0ms	(* (* (* 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

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
8.4b	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))
9.0b	(/ (* (* (sin k) t) (* (sin k) t)) l)
9.8b	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))

rewrite147.0ms

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:

21.0ms	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
57.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))
44.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)
9.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
123.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))
119.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)
368.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))

simplify2.1s

Counts

350 → 350

Iterations

Iter	Nodes
done	5001
1	1833
0	644

prune3.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.1b

localize92.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* t (sin k)) l)
4.0b	(/ (fma 2 (* (/ (* t (sin k)) (cos k)) (/ (* t (sin k)) l)) (* (/ (* (sin k) k) (cos k)) (/ (* (sin k) k) l))) (* (cbrt l) (cbrt l)))
4.2b	(/ (* (sin k) k) l)
5.6b	(/ (/ (fma 2 (* (/ (* t (sin k)) (cos k)) (/ (* t (sin k)) l)) (* (/ (* (sin k) k) (cos k)) (/ (* (sin k) k) l))) (* (cbrt l) (cbrt l))) (/ (cbrt l) t))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
160×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
72×	`cbrt-prod`
40×	`add-exp-log`
35×	`div-inv`
31×	`add-cbrt-cube`
29×	`associate-/r*`
19×	`cbrt-undiv` `div-exp`
12×	`associate-/l*`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 282

Calls

4 calls:

13.0ms	(/ (* t (sin k)) l)
10.0ms	(/ (fma 2 (* (/ (* t (sin k)) (cos k)) (/ (* t (sin k)) l)) (* (/ (* (sin k) k) (cos k)) (/ (* (sin k) k) l))) (* (cbrt l) (cbrt l)))
18.0ms	(/ (* (sin k) k) l)
36.0ms	(/ (/ (fma 2 (* (/ (* t (sin k)) (cos k)) (/ (* t (sin k)) l)) (* (/ (* (sin k) k) (cos k)) (/ (* (sin k) k) l))) (* (cbrt l) (cbrt l))) (/ (cbrt l) t))

series1.4s

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* t (sin k)) l)
623.0ms	(/ (fma 2 (* (/ (* t (sin k)) (cos k)) (/ (* t (sin k)) l)) (* (/ (* (sin k) k) (cos k)) (/ (* (sin k) k) l))) (* (cbrt l) (cbrt l)))
84.0ms	(/ (* (sin k) k) l)
556.0ms	(/ (/ (fma 2 (* (/ (* t (sin k)) (cos k)) (/ (* t (sin k)) l)) (* (/ (* (sin k) k) (cos k)) (/ (* (sin k) k) l))) (* (cbrt l) (cbrt l))) (/ (cbrt l) t))

simplify2.8s

Counts

294 → 294

Iterations

Iter	Nodes
done	5001
1	1654
0	534

prune2.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.1b

regimes669.0ms

Accuracy

7.8% (3.5b remaining)

Error of 7.1b against oracle of 3.6b and baseline of 7.4b

bsearch320.0ms

Steps

Iters	Range		Point
5	4.1888210936971656e+85	9.69874450483721e+85	9.580968836515877e+85
7	-8.935604087246055e+79	-5.516318892552131e+78	-3.663093566121438e+79

simplify16.0ms

Iterations

Iter	Nodes
done	40
1	40
0	31

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.3s	2045×	body	1280	valid
3.0s	1744×	body	640	valid
1.5s	5941×	body	80	valid
1.3s	851×	body	320	valid
186.0ms	410×	body	160	valid