Details

sample256.0ms

Algorithm

intervals

Results

112.0ms	50×	body	1280	valid
28.0ms	42×	body	640	valid
18.0ms	135×	body	80	valid
9.0ms	20×	body	320	valid
5.0ms	9×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	37	15
done	37	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 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))

rewrite115.0ms

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:

19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
50.0ms	(* (tan x) (tan x))

series333.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
63.0ms	(- 1.0 (* (tan x) (tan x)))
62.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

117 → 117

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	138	1632
1	351	1506
2	1541	1370
done	5002	1360

prune391.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ 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))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

41.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
11.0ms	(- 1.0 (* (tan x) (tan x)))
22.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))

series297.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
53.0ms	(- 1.0 (* (tan x) (tan x)))
52.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify2.5s

Counts

177 → 177

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	249	3696
1	635	3313
2	3444	3106
done	5002	2894

prune492.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

7.0ms	(pow (sin x) 2)
7.0ms	(pow (sin x) 2)
7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)

series119.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sin x) 2)
25.0ms	(pow (sin x) 2)
29.0ms	(pow (cos x) 2)
30.0ms	(pow (cos x) 2)

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	64	576
1	189	492
2	648	432
3	2390	432
done	5004	432

prune325.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

32.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
18.0ms	(+ (sqrt 1.0) (tan x))
90.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
16.0ms	(* (tan x) (tan x))

series526.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
58.0ms	(+ (sqrt 1.0) (tan x))
288.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
47.0ms	(* (tan x) (tan x))

simplify2.3s

Counts

144 → 144

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	215	2723
1	623	2579
2	3898	2361
done	5000	2356

prune545.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes308.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.5s	1544×	body	1280	valid
1.5s	4290×	body	80	valid
780.0ms	1255×	body	640	valid
507.0ms	624×	body	320	valid
114.0ms	287×	body	160	valid