Details

sample161.0ms

Algorithm

intervals

Results

65.0ms	80×	body	1280	valid
32.0ms	70×	body	640	valid
24.0ms	225×	body	80	valid
11.0ms	31×	body	320	valid
5.0ms	22×	body	160	valid

simplify162.0ms

Counts

1 → 1

Iterations

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

prune375.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite151.0ms

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:

60.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
59.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
10.0ms	(/ (cos th) (sqrt 2))
11.0ms	(/ (cos th) (sqrt 2))

series448.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
138.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
85.0ms	(/ (cos th) (sqrt 2))
78.0ms	(/ (cos th) (sqrt 2))

simplify1.6s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	1524
1	528
0	189

prune996.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
14×	`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 → 481

Calls

4 calls:

54.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
15.0ms	(/ (cos th) (sqrt (sqrt 2)))
26.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
10.0ms	(/ (cos th) (sqrt 2))

series541.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
176.0ms	(/ (cos th) (sqrt (sqrt 2)))
114.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
96.0ms	(/ (cos th) (sqrt 2))

simplify1.7s

Counts

493 → 493

Iterations

Iter	Nodes
done	5002
2	2744
1	1155
0	488

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

1143×	`sqrt-prod`
1125×	`times-frac`
615×	`add-sqr-sqrt`
581×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
41×	`add-cbrt-cube` `add-exp-log`
35×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
13×	`cbrt-undiv` `div-exp` `unswap-sqr`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
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 → 746

Calls

4 calls:

41.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
152.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
18.0ms	(/ (cos th) (sqrt (sqrt 2)))
29.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
191.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
148.0ms	(/ (cos th) (sqrt (sqrt 2)))
96.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify1.9s

Counts

758 → 758

Iterations

Iter	Nodes
done	5000
1	1744
0	595

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))))
0.2b	(/ (* a1 a1) (sqrt (sqrt 2)))
0.3b	(/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

682×	`times-frac`
677×	`sqrt-prod`
398×	`add-sqr-sqrt`
231×	`*-un-lft-identity` `add-cube-cbrt`
186×	`cbrt-prod`
160×	`associate-r`
59×	`add-cbrt-cube` `add-exp-log`
51×	`unswap-sqr`
30×	`div-inv`
27×	`associate-/r*`
24×	`cbrt-undiv` `div-exp`
16×	`associate-l`
15×	`prod-exp` `cbrt-unprod` `associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 527

Calls

4 calls:

218.0ms	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))))
26.0ms	(/ (* a1 a1) (sqrt (sqrt 2)))
25.0ms	(/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
38.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))

series982.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))))
152.0ms	(/ (* a1 a1) (sqrt (sqrt 2)))
469.0ms	(/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
150.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))

simplify1.8s

Counts

539 → 539

Iterations

Iter	Nodes
done	5002
1	1921
0	571

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes518.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.3s	2500×	body	1280	valid
1.5s	2086×	body	640	valid
1.5s	7991×	body	80	valid
306.0ms	997×	body	320	valid
117.0ms	559×	body	160	valid