Details

sample157.0ms

Algorithm

intervals

Results

49.0ms	82×	body	1280	valid
29.0ms	66×	body	640	valid
24.0ms	245×	body	80	valid
9.0ms	28×	body	320	valid
2.0ms	8×	body	160	valid

simplify401.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune65.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 180

Calls

4 calls:

81.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
58.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
18.0ms	(/ (cos th) (sqrt 2.0))
14.0ms	(/ (cos th) (sqrt 2.0))

series613.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
190.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
98.0ms	(/ (cos th) (sqrt 2.0))
106.0ms	(/ (cos th) (sqrt 2.0))

simplify3.3s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
2	1737
1	526
0	190

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 756

Calls

4 calls:

191.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
18.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
44.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
29.0ms	(/ (cos th) (sqrt 2.0))

series531.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
161.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
92.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
91.0ms	(/ (cos th) (sqrt 2.0))

simplify7.2s

Counts

768 → 768

Iterations

Iter	Nodes
done	5006
2	4912
1	1646
0	572

prune7.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize111.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

793×	`sqrt-prod`
788×	`times-frac`
434×	`add-sqr-sqrt`
429×	`*-un-lft-identity` `add-cube-cbrt`
192×	`cbrt-prod`
37×	`associate-/l*`
27×	`associate-/r*`
25×	`add-cbrt-cube` `add-exp-log`
22×	`associate-l`
17×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 577

Calls

4 calls:

80.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
36.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
56.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
29.0ms	(/ (cos th) (sqrt 2.0))

series962.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
155.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
495.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
105.0ms	(/ (cos th) (sqrt 2.0))

simplify5.5s

Counts

589 → 589

Iterations

Iter	Nodes
done	5085
2	3574
1	1420
0	627

prune5.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.7b	(log1p (expm1 (/ (cos th) (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

783×	`sqrt-prod`
768×	`times-frac`
416×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
192×	`cbrt-prod`
37×	`associate-/l*`
27×	`associate-/r*`
16×	`div-inv`
13×	`add-cbrt-cube` `add-exp-log`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`log1p-udef` `log1p-expm1` `associate-/l/`

Counts

4 → 541

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (cos th) (sqrt 2.0))))
16.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
55.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
20.0ms	(/ (cos th) (sqrt 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

868.0ms	(log1p (expm1 (/ (cos th) (sqrt 2.0))))
151.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
560.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
106.0ms	(/ (cos th) (sqrt 2.0))

simplify4.7s

Counts

553 → 553

Iterations

Iter	Nodes
done	5027
2	2759
1	1237
0	585

prune5.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes1.9s

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.0s	2565×	body	1280	valid
1.5s	8111×	body	80	valid
1.3s	2148×	body	640	valid
544.0ms	530×	body	160	valid
372.0ms	1069×	body	320	valid