Details

sample154.0ms

Algorithm

intervals

Results

27.0ms	45×	body	1280	valid
13.0ms	144×	body	80	valid
11.0ms	29×	body	640	valid
7.0ms	26×	body	320	valid
2.0ms	12×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
5	36
4	34
3	26
2	21
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
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` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

15.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(- 1.0 (* (tan x) (tan x)))
12.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
42.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))

simplify2.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
3	3710
2	997
1	349
0	138

prune664.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

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-cbrt-cube` `add-exp-log` `associate-/r/`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `tan-quot` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

77.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
14.0ms	(+ (sqrt 1.0) (tan x))
57.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
12.0ms	(* (tan x) (tan x))

series545.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
63.0ms	(+ (sqrt 1.0) (tan x))
152.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
41.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

236 → 236

Iterations

Iter	Nodes
done	5002
2	2956
1	846
0	313

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `pow-plus` `distribute-rgt-out--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

22.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
456.0ms	(* (tan x) (tan x))
56.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))
236.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify2.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5035
3	3187
2	866
1	299
0	118

prune680.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`associate-l`
21×	`frac-times`
20×	`add-cbrt-cube`
18×	`pow1`
17×	`add-cube-cbrt`
15×	`associate-*r/`
14×	`prod-exp`
11×	`flip3-+` `flip-+`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
9×	`times-frac` `flip3--` `flip--`
8×	`associate-*l/` `cbrt-unprod`
6×	`sub-neg` `add-log-exp`
5×	`pow-prod-down`
4×	`div-exp` `tan-quot`
3×	`swap-sqr` `*-commutative`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r/` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-sqr` `pow-prod-up` `sqrt-prod` `div-inv` `distribute-lft-out--`

Counts

4 → 137

Calls

4 calls:

74.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
7.0ms	(+ (sqrt 1.0) (tan x))
102.0ms	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))))
24.0ms	(* (tan x) (tan x))

series552.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
56.0ms	(+ (sqrt 1.0) (tan x))
281.0ms	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))))
35.0ms	(* (tan x) (tan x))

simplify2.3s

Counts

149 → 149

Iterations

Iter	Nodes
done	5002
2	2807
1	764
0	243

prune788.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes314.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	12

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.9s	1530×	body	1280	valid
697.0ms	1195×	body	640	valid
509.0ms	4291×	body	80	valid
262.0ms	655×	body	320	valid
123.0ms	329×	body	160	valid