Details

sample371.0ms

Algorithm

intervals

Results

27.0ms	61×	body	1280	valid
10.0ms	36×	body	640	valid
9.0ms	135×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9
done	37	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

10.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1.0 (* (tan x) (tan x)))
103.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify41.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824
done	5001	824

prune237.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
0.2b	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
184×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
19×	`sqrt-prod` `distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
51.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
36.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
18.0ms	(* (tan x) (tan x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
198.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
112.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
37.0ms	(* (tan x) (tan x))

simplify119.0ms

Counts

236 → 236

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	735	4155
1	3740	3919
2	5001	3901
done	5001	3901

prune491.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(/ (+ (sqrt 1.0) (tan x)) (* (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`pow1` `add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/r/`
4×	`cbrt-undiv` `frac-times` `flip3-+` `times-frac` `associate-r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l`
3×	`associate-*l/` `distribute-lft-out`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv`

Counts

4 → 100

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
49.0ms	(/ (+ (sqrt 1.0) (tan x)) (* (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x))))
15.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (sqrt 1.0) (tan x))
102.0ms	(/ (+ (sqrt 1.0) (tan x)) (* (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x))))
38.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

simplify59.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	411	1028
1	2131	831
2	5001	727
done	5001	727

prune249.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`times-frac`
13×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`tan-quot` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
3×	`swap-sqr` `associate-/r*`
2×	`flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-times` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `associate-*r/` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

14.0ms	(* (tan x) (sin x))
9.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
35.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (tan x) (sin x))
56.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
117.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))

simplify48.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	402	1149
1	1438	1067
2	5002	1060
done	5002	1060

prune262.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17
done	14	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

703.0ms	1556×	body	1280	valid
363.0ms	1285×	body	640	valid
243.0ms	4264×	body	80	valid
123.0ms	623×	body	320	valid
35.0ms	272×	body	160	valid