Details

sample87.0ms

Algorithm

intervals

Results

28.0ms	77×	body	1280	valid
17.0ms	67×	body	640	valid
15.0ms	264×	body	80	valid
8.0ms	44×	body	320	valid
2.0ms	13×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	52	12
3	75	12
4	102	12
5	122	12
6	139	12
7	143	12
8	145	12
done	145	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.5b	(* (fma a1 a1 (* a2 a2)) (/ (cos th) (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `fma-udef`

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
13.0ms	(* (fma a1 a1 (* a2 a2)) (/ (cos th) (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series273.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma a1 a1 (* a2 a2))
175.0ms	(* (fma a1 a1 (* a2 a2)) (/ (cos th) (sqrt 2.0)))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify566.0ms

Counts

104 → 104

Iterations

Useful iterations: done (564.0ms)

Iter	Nodes	Cost
0	143	1357
1	290	1286
2	1221	1139
done	5001	1125

prune278.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.5b	(* (fma a1 a1 (* a2 a2)) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 716

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
98.0ms	(* (fma a1 a1 (* a2 a2)) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
19.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma a1 a1 (* a2 a2))
180.0ms	(* (fma a1 a1 (* a2 a2)) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
100.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
61.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify560.0ms

Counts

728 → 728

Iterations

Useful iterations: done (530.0ms)

Iter	Nodes	Cost
0	622	16144
1	1541	14198
done	5000	13538

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(/ (cos th) (cbrt (sqrt 2.0)))
0.2b	(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.5b	(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
70×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
46×	`cbrt-prod`
32×	`add-exp-log`
31×	`associate-r`
23×	`sqrt-prod`
22×	`add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`prod-exp` `cbrt-unprod`
8×	`unswap-sqr`
7×	`associate-l`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 158

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
5.0ms	(/ (cos th) (cbrt (sqrt 2.0)))
6.0ms	(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
36.0ms	(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma a1 a1 (* a2 a2))
306.0ms	(/ (cos th) (cbrt (sqrt 2.0)))
472.0ms	(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
209.0ms	(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))

simplify1.3s

Counts

170 → 170

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	230	3419
1	581	3281
2	2735	2715
done	5000	2709

prune587.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 2.0) (cos th))
0.3b	(* (sqrt (fma a1 a1 (* a2 a2))) (/ (hypot a1 a2) (/ (sqrt 2.0) (cos th))))
0.3b	(/ (hypot a1 a2) (/ (sqrt 2.0) (cos th)))
7.8b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

286×	`times-frac`
186×	`add-sqr-sqrt`
159×	`add-cube-cbrt` `*-un-lft-identity`
87×	`sqrt-prod`
71×	`associate-r`
25×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
9×	`associate-/l*`
8×	`unswap-sqr`
7×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `hypot-def`

Counts

4 → 268

Calls

4 calls:

3.0ms	(/ (sqrt 2.0) (cos th))
33.0ms	(* (sqrt (fma a1 a1 (* a2 a2))) (/ (hypot a1 a2) (/ (sqrt 2.0) (cos th))))
7.0ms	(/ (hypot a1 a2) (/ (sqrt 2.0) (cos th)))
1.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sqrt 2.0) (cos th))
263.0ms	(* (sqrt (fma a1 a1 (* a2 a2))) (/ (hypot a1 a2) (/ (sqrt 2.0) (cos th))))
172.0ms	(/ (hypot a1 a2) (/ (sqrt 2.0) (cos th)))
44.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify1.5s

Counts

280 → 280

Iterations

Useful iterations: 2 (326.0ms)

Iter	Nodes	Cost
0	341	5200
1	799	4809
2	3473	4069
done	5000	4069

prune869.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes145.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
done	11	13

end0.0ms

sample2.6s

Algorithm

intervals

Results

966.0ms	2511×	body	1280	valid
532.0ms	2041×	body	640	valid
486.0ms	8164×	body	80	valid
191.0ms	1027×	body	320	valid
71.0ms	537×	body	160	valid