Details

sample175.0ms

Algorithm

intervals

Results

57.0ms	81×	body	1280	valid
36.0ms	72×	body	640	valid
31.0ms	271×	body	80	valid
13.0ms	38×	body	320	valid
4.0ms	15×	body	160	valid

simplify211.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	175
8	175
7	173
6	151
5	132
4	114
3	87
2	57
1	26
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-r` `sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `fma-udef`

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
21.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
13.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series450.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma a1 a1 (* a2 a2))
278.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
116.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2126
1	276
0	131

prune517.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

3 → 706

Calls

3 calls:

168.0ms	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
36.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
13.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))

series724.0ms

Counts

3 → 9

Calls

3 calls:

304.0ms	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
159.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
260.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))

simplify1.3s

Counts

715 → 715

Iterations

Iter	Nodes
done	5000
1	1661
0	600

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

867×	`sqrt-prod`
750×	`times-frac`
403×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
102×	`cbrt-prod`
34×	`associate-/l*`
21×	`associate-/r*`
17×	`add-exp-log`
15×	`div-inv`
11×	`sqrt-pow1` `add-cbrt-cube`
8×	`pow1` `div-exp`
7×	`pow-flip`
4×	`expm1-log1p-u` `cbrt-undiv` `pow1/3` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-div`
1×	`inv-pow` `associate-/l/`

Counts

4 → 523

Calls

4 calls:

7.0ms	(/ 1 (sqrt (sqrt 2.0)))
42.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify1.9s

Counts

527 → 527

Iterations

Iter	Nodes
done	5000
2	3994
1	1195
0	508

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))))
0.3b	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
0.3b	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0))))
0.3b	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))

rewrite871.0ms

Algorithm

rewrite-expression-head

Rules

2370×	`sqrt-prod`
1847×	`times-frac`
1373×	`add-sqr-sqrt`
842×	`*-un-lft-identity`
778×	`add-cube-cbrt`
365×	`associate-r`
144×	`unswap-sqr`
103×	`add-exp-log`
61×	`add-cbrt-cube`
43×	`associate-l` `associate-/l*`
40×	`div-exp`
37×	`prod-exp`
23×	`div-inv`
22×	`cbrt-undiv`
21×	`associate-/r*`
19×	`cbrt-unprod`
11×	`pow1`
6×	`rec-exp` `1-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`associate-/l/`

Counts

4 → 1110

Calls

4 calls:

247.0ms	(* (cos th) (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))))
384.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
8.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0))))
28.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

283.0ms	(* (cos th) (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))))
154.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
406.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0))))
629.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))

simplify2.5s

Counts

1122 → 1122

Iterations

Iter	Nodes
done	5000
1	2933
0	845

prune4.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes471.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.8s	2617×	body	1280	valid
1.1s	8062×	body	80	valid
906.0ms	2014×	body	640	valid
505.0ms	1043×	body	320	valid
185.0ms	547×	body	160	valid