Details

sample149.0ms

Algorithm

intervals

Results

62.0ms	84×	body	1280	valid
25.0ms	69×	body	640	valid
19.0ms	237×	body	80	valid
9.0ms	35×	body	320	valid
4.0ms	25×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 87

Calls

2 calls:

71.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
11.0ms	(/ (cos th) (sqrt 2.0))

series345.0ms

Counts

2 → 6

Calls

2 calls:

255.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
89.0ms	(/ (cos th) (sqrt 2.0))

simplify63.0ms

Counts: 93 → 93

prune422.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`associate-r` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

3 → 706

Calls

3 calls:

219.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
48.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
13.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series584.0ms

Counts

3 → 9

Calls

3 calls:

332.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
92.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
161.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify134.0ms

Counts: 715 → 715

prune3.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
0.4b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

rewrite756.0ms

Algorithm

rewrite-expression-head

Rules

1522×	`sqrt-prod`
1510×	`times-frac`
861×	`add-sqr-sqrt`
775×	`*-un-lft-identity`
763×	`add-cube-cbrt`
392×	`cbrt-prod` `associate-l`
82×	`add-exp-log`
52×	`add-cbrt-cube`
34×	`associate-/l*`
32×	`div-exp`
29×	`div-inv` `unswap-sqr`
27×	`prod-exp`
21×	`associate-/r*`
17×	`cbrt-undiv` `cbrt-unprod`
15×	`pow1`
11×	`frac-times` `associate-*r/`
7×	`pow-flip` `sqrt-pow1`
6×	`flip3-+` `flip-+`
5×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp`
4×	`associate-r` `pow-prod-down` `associate-*l/` `add-log-exp`
3×	`pow1/2`
2×	`frac-2neg` `pow1/3` `clear-num` `*-commutative` `pow-div`
1×	`associate-/l/` `inv-pow`

Counts

4 → 987

Calls

4 calls:

324.0ms	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
222.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
19.0ms	(/ 1 (sqrt (sqrt 2.0)))
41.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

series983.0ms

Counts

4 → 8

Calls

4 calls:

331.0ms	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
651.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

simplify266.0ms

Counts: 995 → 995

prune5.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos th) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
0.3b	(* (/ (* (cos th) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (fabs (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite716.0ms

Algorithm

rewrite-expression-head

Rules

1519×	`sqrt-prod`
1501×	`times-frac`
858×	`add-sqr-sqrt`
770×	`*-un-lft-identity`
758×	`add-cube-cbrt`
392×	`cbrt-prod`
379×	`associate-r`
62×	`add-exp-log`
40×	`add-cbrt-cube`
34×	`associate-/l*`
30×	`unswap-sqr`
29×	`div-inv`
26×	`div-exp`
21×	`associate-/r*`
17×	`prod-exp`
14×	`cbrt-undiv`
12×	`pow1`
11×	`cbrt-unprod`
10×	`associate-l`
7×	`pow-flip` `sqrt-pow1`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow1/2` `associate-*r/`
2×	`frac-times` `frac-2neg` `flip3-+` `pow1/3` `pow-prod-down` `clear-num` `*-commutative` `flip-+` `pow-div`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `associate-/l/` `inv-pow`

Counts

4 → 958

Calls

4 calls:

217.0ms	(* (cos th) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
321.0ms	(* (/ (* (cos th) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (fabs (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
45.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
10.0ms	(/ 1 (sqrt (sqrt 2.0)))

series2.0s

Counts

4 → 8

Calls

4 calls:

495.0ms	(* (cos th) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
1.5s	(* (/ (* (cos th) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (fabs (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify209.0ms

Counts: 966 → 966

prune5.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes359.0ms

Accuracy

-2.5% (0.4b remaining)

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

bsearch0.0ms

simplify62.0ms

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.8s	2506×	body	1280	valid
1.7s	8004×	body	80	valid
1.6s	2088×	body	640	valid
299.0ms	1028×	body	320	valid
109.0ms	544×	body	160	valid