Details

sample217.0ms

Algorithm

intervals

Results

87.0ms	76×	body	1280	valid
52.0ms	71×	body	640	valid
42.0ms	258×	body	80	valid
15.0ms	32×	body	320	valid
4.0ms	14×	body	160	valid

simplify92.0ms

Calls

1 calls:

Slowest

92.0ms

(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt 2))
0.6b	(/ (cos th) (sqrt 2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-cube-cbrt`
34×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`associate-l`
18×	`add-exp-log`
18×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-/l*`
6×	`associate-/r*`
4×	`add-log-exp`
4×	`div-inv`
4×	`cbrt-unprod`
4×	`prod-exp`
4×	`div-exp`
4×	`cbrt-undiv`
2×	`*-commutative`
2×	`associate-*l/`
2×	`pow-prod-down`
2×	`associate-r`
2×	`frac-2neg`
2×	`clear-num`

Calls

4 calls:

Slowest

11.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
11.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
6.0ms	(/ (cos th) (sqrt 2))
6.0ms	(/ (cos th) (sqrt 2))

series226.0ms

Calls

4 calls:

Slowest

78.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
70.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
46.0ms	(/ (cos th) (sqrt 2))
32.0ms	(/ (cos th) (sqrt 2))

simplify3.0s

Calls

98 calls:

Slowest

385.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
364.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
271.0ms	(- (/ (pow a2 2) (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))
243.0ms	(- (/ (pow a1 2) (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))
230.0ms	(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt 2))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.1b	(* (cos th) (* a2 a2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-cube-cbrt`
22×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`times-frac`
18×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-l`
8×	`pow1`
6×	`associate-/r*`
4×	`add-log-exp`
4×	`associate-/l*`
4×	`cbrt-unprod`
4×	`prod-exp`
4×	`div-exp`
4×	`cbrt-undiv`
3×	`div-inv`
2×	`*-commutative`
2×	`pow-prod-down`
2×	`associate-r`
2×	`frac-2neg`
2×	`clear-num`
1×	`associate-*l/`

Calls

4 calls:

Slowest

12.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
11.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
7.0ms	(* (cos th) (* a2 a2))
6.0ms	(/ (cos th) (sqrt 2))

series242.0ms

Calls

4 calls:

Slowest

81.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
77.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
53.0ms	(/ (cos th) (sqrt 2))
31.0ms	(* (cos th) (* a2 a2))

simplify3.2s

Calls

74 calls:

Slowest

698.0ms	(- (/ (pow a1 2) (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))
452.0ms	(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
342.0ms	(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
249.0ms	(- (/ (pow a2 2) (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))
239.0ms	(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt 2))
0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b	(/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
0.2b	(/ (/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
41×	`add-exp-log`
38×	`add-cube-cbrt`
38×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
28×	`add-cbrt-cube`
18×	`cbrt-prod`
15×	`div-exp`
15×	`cbrt-undiv`
13×	`associate-l`
11×	`div-inv`
10×	`cbrt-unprod`
10×	`prod-exp`
10×	`associate-/r*`
9×	`associate-/l*`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg`
3×	`clear-num`
1×	`associate-/l/`
1×	`*-commutative`
1×	`associate-*l/`
1×	`pow-prod-down`
1×	`associate-r`

Calls

4 calls:

Slowest

24.0ms	(/ (/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
11.0ms	(/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
6.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2))

series643.0ms

Calls

4 calls:

Slowest

446.0ms	(/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
89.0ms	(/ (/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
62.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
46.0ms	(/ (cos th) (sqrt 2))

simplify12.1s

Calls

148 calls:

Slowest

429.0ms	(/ (/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2))))
425.0ms	(/ (/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (sqrt 2))))
417.0ms	(/ (/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt 2))))
405.0ms	(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))) (* (sqrt 2) (sqrt 2))) (sqrt 2))
379.0ms	(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (sqrt 2) (sqrt 2)))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
0.2b	(/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

517×	`times-frac`
279×	`add-cube-cbrt`
279×	`*-un-lft-identity`
279×	`add-sqr-sqrt`
264×	`sqrt-prod`
136×	`associate-l`
32×	`add-exp-log`
28×	`add-cbrt-cube`
26×	`associate-/l*`
17×	`div-inv`
13×	`associate-/r*`
11×	`div-exp`
11×	`cbrt-undiv`
7×	`cbrt-unprod`
7×	`prod-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg`
3×	`clear-num`
1×	`associate-/l/`
1×	`*-commutative`
1×	`associate-*l/`
1×	`pow-prod-down`
1×	`associate-r`

Calls

4 calls:

Slowest

12.0ms	(/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
9.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
7.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
3.0ms	(/ (cos th) (sqrt (sqrt 2)))

series670.0ms

Calls

4 calls:

Slowest

484.0ms	(/ (* (cos th) (* a2 a2)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
72.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
68.0ms	(/ (cos th) (sqrt (sqrt 2)))
47.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify13.3s

Calls

509 calls:

Slowest

554.0ms	(* (* (* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
360.0ms	(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (sqrt 2) (sqrt 2)))
358.0ms	(/ (* (* (/ (cos th) (sqrt (sqrt 2))) (/ (cos th) (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
329.0ms	(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))) (* (sqrt 2) (sqrt 2)))
316.0ms	(+ (log (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (log (* a1 a1)))

prune6.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes466.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end1.0ms

sample8.4s

Algorithm

intervals

Results

3.3s	2491×	body	1280	valid
2.4s	2091×	body	640	valid
1.6s	8096×	body	80	valid
549.0ms	1031×	body	320	valid
248.0ms	506×	body	160	valid