Details

sample155.0ms

Algorithm

intervals

Results

47.0ms	254×	body	80	valid
40.0ms	65×	body	1280	valid
25.0ms	58×	body	640	valid
10.0ms	33×	body	320	valid
4.0ms	18×	body	160	valid

simplify274.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	12	344
1	26	304
2	57	279
3	87	279
4	114	279
5	132	279
6	151	279
7	173	279
8	175	279
done	175	279

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (fma a1 a1 (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 97

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
17.0ms	(* (/ (cos th) (sqrt 2.0)) (fma a1 a1 (* a2 a2)))
11.0ms	(/ (cos th) (sqrt 2.0))

series430.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(fma a1 a1 (* a2 a2))
302.0ms	(* (/ (cos th) (sqrt 2.0)) (fma a1 a1 (* a2 a2)))
82.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

106 → 106

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	144	35883
1	319	32333
2	1688	31467
done	5001	31313

prune723.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (fma a1 a1 (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
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-r` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`clear-num` `frac-2neg`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 718

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
165.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (fma a1 a1 (* a2 a2)))
18.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
25.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma a1 a1 (* a2 a2))
307.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (fma a1 a1 (* a2 a2)))
144.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
92.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.7s

Counts

730 → 730

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	541	404684
1	1338	372807
done	5000	360626

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 176

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
23.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
32.0ms	(/ (fma a1 a1 (* a2 a2)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
144.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (fma a1 a1 (* a2 a2)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma a1 a1 (* a2 a2))
377.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
612.0ms	(/ (fma a1 a1 (* a2 a2)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
300.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (fma a1 a1 (* a2 a2)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

simplify3.0s

Counts

188 → 188

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	246	92174
1	604	84122
2	3777	82840
done	5001	82285

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
0.3b	(/ (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (fma a1 a1 (* a2 a2))) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (fma a1 a1 (* a2 a2)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

132×	`sqrt-prod`
77×	`times-frac`
73×	`add-sqr-sqrt`
59×	`*-un-lft-identity` `add-cube-cbrt`
40×	`associate-l`
32×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
6×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `fma-udef` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 169

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
11.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
43.0ms	(/ (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (fma a1 a1 (* a2 a2))) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
35.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (fma a1 a1 (* a2 a2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

48.0ms	(fma a1 a1 (* a2 a2))
341.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
294.0ms	(/ (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (fma a1 a1 (* a2 a2))) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
714.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (fma a1 a1 (* a2 a2)))

simplify2.8s

Counts

181 → 181

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	240	85186
1	578	76417
2	4090	74006
done	5000	71611

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes515.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	439
1	16	439
done	16	439

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.0s	2548×	body	1280	valid
1.4s	7942×	body	80	valid
1.2s	2177×	body	640	valid
691.0ms	997×	body	320	valid
112.0ms	534×	body	160	valid