Details

sample377.0ms

Algorithm

intervals

Results

121.0ms	63×	body	1280	valid
89.0ms	198×	body	80	valid
72.0ms	50×	body	640	valid
40.0ms	23×	body	160	valid
35.0ms	32×	body	320	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
4	2003
3	1174
2	189
1	54
0	19

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.1b

localize41.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ t (* (/ l t) (/ l t)))
2.9b	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
4.1b	(* (/ t (* (/ l t) (/ l t))) (sin k))
15.3b	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite687.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-cbrt-cube` `add-exp-log`
56×	`prod-exp` `cbrt-unprod`
36×	`cbrt-undiv` `div-exp`
20×	`pow1`
15×	`add-sqr-sqrt`
12×	`associate-l` `associate-*l/`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow-prod-down`
9×	`associate-r`
7×	`times-frac`
6×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `tan-quot` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`fma-udef` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`

Counts

4 → 146

Calls

4 calls:

10.0ms	(/ t (* (/ l t) (/ l t)))
125.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
56.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
493.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

series801.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ t (* (/ l t) (/ l t)))
202.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
108.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
448.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

simplify981.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
2	2000
1	672
0	235

prune724.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
2.9b	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
5.0b	(* (/ (cbrt t) (/ l t)) (sin k))
15.3b	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite890.0ms

Algorithm

rewrite-expression-head

Rules

284×	`add-exp-log`
230×	`add-cbrt-cube`
153×	`prod-exp` `cbrt-unprod`
138×	`times-frac`
93×	`add-sqr-sqrt`
85×	`associate-l`
81×	`cbrt-undiv` `div-exp`
77×	`*-un-lft-identity` `add-cube-cbrt`
44×	`cbrt-prod`
29×	`pow1`
26×	`associate-*l/`
17×	`pow-prod-down`
10×	`frac-times`
9×	`associate-r`
8×	`tan-quot`
7×	`div-inv`
6×	`associate-*r/`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `associate-/r/`

Counts

4 → 263

Calls

4 calls:

1.0ms	(cbrt t)
178.0ms	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
18.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
680.0ms	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt t)
233.0ms	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
157.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
440.0ms	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.7s

Counts

275 → 275

Iterations

Iter	Nodes
done	2000
2	2000
1	1350
0	453

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize63.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k))
5.0b	(* (/ (cbrt t) (/ l t)) (sin k))
8.1b	(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
11.4b	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

336×	`add-exp-log`
274×	`add-cbrt-cube`
200×	`prod-exp` `cbrt-unprod`
139×	`times-frac`
92×	`add-sqr-sqrt`
85×	`associate-l`
77×	`cbrt-undiv` `div-exp`
76×	`*-un-lft-identity` `add-cube-cbrt`
49×	`pow1`
41×	`cbrt-prod`
33×	`pow-prod-down`
10×	`associate-*l/`
9×	`associate-r`
8×	`div-inv`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `-commutative`
2×	`associate-/r/` `fma-udef`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `associate-/l` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

245.0ms	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k))
18.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
659.0ms	(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
685.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k))
236.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
444.0ms	(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
358.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify1.6s

Counts

289 → 289

Iterations

Iter	Nodes
done	2019
2	2019
1	1357
0	442

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize91.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (* (cbrt t) (sin k)) (/ l t))
4.7b	(* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t))))
8.1b	(/ (* (* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t)))) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
11.4b	(* (* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t)))) (fma (/ k t) (/ k t) 2))

rewrite883.0ms

Algorithm

rewrite-expression-head

Rules

414×	`add-exp-log`
342×	`add-cbrt-cube`
226×	`prod-exp` `cbrt-unprod`
118×	`cbrt-undiv` `div-exp`
32×	`times-frac`
27×	`pow1`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`pow-prod-down`
14×	`associate-/r*`
6×	`associate-*r/`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `associate-/r/` `-commutative` `fma-udef` `associate-/l`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`

Counts

4 → 232

Calls

4 calls:

14.0ms	(/ (* (cbrt t) (sin k)) (/ l t))
89.0ms	(* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t))))
389.0ms	(/ (* (* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t)))) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
382.0ms	(* (* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t)))) (fma (/ k t) (/ k t) 2))

series922.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (* (cbrt t) (sin k)) (/ l t))
134.0ms	(* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t))))
334.0ms	(/ (* (* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t)))) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
253.0ms	(* (* (sin k) (* (* (cbrt t) (cbrt t)) (/ (* (cbrt t) (sin k)) (/ l t)))) (fma (/ k t) (/ k t) 2))

simplify1.8s

Counts

244 → 244

Iterations

Iter	Nodes
done	2023
2	2023
1	1377
0	413

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.5b

regimes452.0ms

Accuracy

58.8% (5.2b remaining)

Error of 7.1b against oracle of 1.9b and baseline of 14.6b

bsearch640.0ms

Steps

Iters	Range		Point
8	1.269859610717766e+59	1.0392127207612875e+63	1.295357818168273e+59
8	-5.189113670411213e-20	-4.215097065401645e-23	-1.7670378365958354e-22

simplify20.0ms

Iterations

Iter	Nodes
done	50
1	50
0	39

end0.0ms

sample15.7s

Algorithm

intervals

Results

6.7s	2088×	body	1280	valid
3.6s	1733×	body	640	valid
2.9s	5927×	body	80	valid
1.7s	851×	body	320	valid
387.0ms	430×	body	160	valid