Details

sample359.0ms

Algorithm

intervals

Results

154.0ms	68×	body	1280	valid
78.0ms	63×	body	640	valid
54.0ms	185×	body	80	valid
43.0ms	25×	body	320	valid
10.0ms	15×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
4	6637
3	1079
2	183
1	52
0	19

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k)))
2.3b	(/ t (* (/ l t) (/ l t)))
3.2b	(* (/ t (* (/ l t) (/ l t))) (sin k))
16.4b	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
82×	`cbrt-undiv` `div-exp`
52×	`prod-exp` `cbrt-unprod`
24×	`times-frac`
19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-/l*`
10×	`associate-l` `associate-/r/`
7×	`associate-*l/`
6×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `associate-/r` `frac-2neg` `associate-r*`
2×	`frac-times` `associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `tan-quot` `*-commutative` `associate-/l/`

Counts

4 → 172

Calls

4 calls:

58.0ms	(/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k)))
10.0ms	(/ t (* (/ l t) (/ l t)))
52.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
63.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k)))
51.0ms	(/ t (* (/ l t) (/ l t)))
89.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
245.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify1.3s

Counts

184 → 184

Iterations

Iter	Nodes
2	3420
1	811
0	282

prune2.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
4.0b	(* (/ (cbrt t) (/ l t)) (sin k))
16.4b	(/ (/ 2 (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k)))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

329×	`add-exp-log`
275×	`add-cbrt-cube`
167×	`cbrt-undiv` `div-exp`
154×	`times-frac`
111×	`prod-exp` `cbrt-unprod`
96×	`add-sqr-sqrt`
83×	`associate-l`
80×	`*-un-lft-identity` `add-cube-cbrt`
47×	`cbrt-prod`
10×	`div-inv` `associate-/l*`
8×	`associate-*l/` `associate-/r/`
6×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`frac-times` `pow1/3` `associate-*r/`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `tan-quot` `-commutative` `associate-/l/`

Counts

4 → 262

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
17.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
119.0ms	(/ (/ 2 (* (/ (* (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:

277.0ms	(cbrt t)
267.0ms	(cbrt t)
218.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
376.0ms	(/ (/ 2 (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k)))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify3.3s

Counts

274 → 274

Iterations

Iter	Nodes
2	6969
1	1570
0	506

prune5.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.7b

localize57.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (/ (cbrt t) (/ l t)) (sin k))
4.1b	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
7.0b	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
9.3b	(* (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

2650×	`times-frac`
1028×	`add-sqr-sqrt`
942×	`*-un-lft-identity` `add-cube-cbrt`
427×	`associate-l`
405×	`sqrt-prod`
361×	`add-exp-log`
315×	`add-cbrt-cube`
218×	`cbrt-undiv` `div-exp`
124×	`associate-/l*`
109×	`div-inv`
83×	`prod-exp` `cbrt-unprod`
59×	`associate-/r/`
41×	`cbrt-prod`
40×	`associate-r`
21×	`unswap-sqr`
9×	`associate-*l/`
8×	`pow1`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `tan-quot` `*-commutative` `associate-/l/`
1×	`frac-times` `associate-*r/`

Counts

4 → 1159

Calls

4 calls:

26.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
18.0ms	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
44.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
146.0ms	(* (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
478.0ms	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
551.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
608.0ms	(* (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

simplify3.3s

Counts

1171 → 1171

Iterations

Iter	Nodes
1	4992
0	1569

prune23.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

localize71.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))) (tan k))
4.0b	(* (/ (cbrt t) (/ l t)) (sin k))
7.0b	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
8.3b	(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

rewrite814.0ms

Algorithm

rewrite-expression-head

Rules

18418×	`times-frac`
7921×	`add-sqr-sqrt`
7722×	`*-un-lft-identity` `add-cube-cbrt`
5280×	`sqrt-prod`
2510×	`cbrt-prod`
2344×	`associate-l`
763×	`associate-/l*`
466×	`div-inv`
242×	`add-exp-log`
214×	`add-cbrt-cube`
145×	`cbrt-undiv` `div-exp`
80×	`associate-/r/`
51×	`prod-exp` `cbrt-unprod`
40×	`associate-r`
39×	`unswap-sqr`
9×	`associate-*l/`
8×	`pow1`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `tan-quot` `*-commutative` `associate-/l/`
1×	`frac-times` `associate-*r/`

Counts

4 → 5622

Calls

4 calls:

42.0ms	(/ (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))) (tan k))
22.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
44.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
201.0ms	(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

358.0ms	(/ (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))) (tan k))
182.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
566.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
1.0s	(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

simplify1.9m

Counts

5634 → 5634

Iterations

Iter	Nodes
1	15700
0	5093

prune1.9m

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.4b

regimes551.0ms

Accuracy

0% (1.2b remaining)

Error of 12.5b against oracle of 11.2b and baseline of 12.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample9.7s

Algorithm

intervals

Results

4.3s	2077×	body	1280	valid
2.2s	1747×	body	640	valid
1.7s	5950×	body	80	valid
1.1s	836×	body	320	valid
258.0ms	433×	body	160	valid