Details

sample238.0ms

Algorithm

intervals

Results

76.0ms	89×	body	1280	valid
65.0ms	81×	body	640	valid
42.0ms	33×	body	320	valid
33.0ms	242×	body	80	valid
2.0ms	9×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

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))

rewrite117.0ms

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:

34.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
44.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series478.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
156.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
70.0ms	(/ (cos th) (sqrt 2))
88.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

192 → 192

Iterations

Iter	Nodes
done	2003
3	2003
2	1524
1	528
0	189

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ a2 (sqrt 2)) a2)
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.4b	(/ a2 (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

24.0ms	(* (/ a2 (sqrt 2)) a2)
34.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms	(/ a2 (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series381.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ a2 (sqrt 2)) a2)
134.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
69.0ms	(/ a2 (sqrt 2))
83.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

189 → 189

Iterations

Iter	Nodes
done	2001
3	2001
2	1685
1	546
0	219

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2)))) (* a1 a1))
0.3b	(cbrt (/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2))))
0.4b	(/ a2 (sqrt 2))
0.7b	(/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
12×	`prod-exp` `sqrt-prod` `cbrt-unprod`
11×	`cbrt-prod`
9×	`pow1`
8×	`associate-l`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-div` `clear-num` `frac-2neg` `unswap-sqr`
1×	`pow1/3` `associate-r` `associate-l/` `associate-r/` `cos-mult` `*-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

23.0ms	(* (cbrt (/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2)))) (* a1 a1))
9.0ms	(cbrt (/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2))))
5.0ms	(/ a2 (sqrt 2))
38.0ms	(/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

500.0ms	(* (cbrt (/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2)))) (* a1 a1))
481.0ms	(cbrt (/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2))))
101.0ms	(/ a2 (sqrt 2))
158.0ms	(/ (* (cos th) (* (cos th) (cos th))) (* 2 (sqrt 2)))

simplify1.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	2002
3	2002
2	1965
1	539
0	221

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ a1 (sqrt 2)) a1)
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.4b	(/ a1 (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

12.0ms	(* (/ a1 (sqrt 2)) a1)
42.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
12.0ms	(/ a1 (sqrt 2))
407.0ms	(/ (cos th) (sqrt 2))

series337.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (/ a1 (sqrt 2)) a1)
146.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
59.0ms	(/ a1 (sqrt 2))
63.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

189 → 189

Iterations

Iter	Nodes
done	2016
3	2016
2	1683
1	546
0	219

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes571.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.4s	2556×	body	1280	valid
2.0s	2152×	body	640	valid
1.9s	7805×	body	80	valid
670.0ms	1054×	body	320	valid
169.0ms	492×	body	160	valid