Details

sample305.0ms

Algorithm

intervals

Results

105.0ms	64×	body	1280	valid
84.0ms	38×	body	640	valid
32.0ms	128×	body	80	valid
13.0ms	16×	body	320	valid
5.0ms	10×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	38
5	38
4	36
3	28
2	23
1	15
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`insert-posit16`
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 → 114

Calls

4 calls:

16.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
4.0ms	(- 1 (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
43.0ms	(- 1 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
69.0ms	(* (tan x) (tan x))

simplify802.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2408
2	928
1	357
0	144

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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))
0.4b	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
25×	`pow1`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
8×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--` `div-inv`
4×	`associate-/r/` `insert-posit16`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 115

Calls

4 calls:

27.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
28.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))
208.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify937.0ms

Counts

127 → 127

Iterations

Iter	Nodes
3	2764
2	789
1	294
0	121

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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))
0.4b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

13.0ms	(* (tan x) (tan x))
25.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
129.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))
62.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.6s

Counts

178 → 178

Iterations

Iter	Nodes
4	4110
3	1843
2	877
1	299
0	108

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.4b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.4b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.4b	(- (/ 1 (- 1 (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- 1 (* (* (tan x) (tan x)) (* (tan x) (tan x))))))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

233×	`pow1`
73×	`pow-prod-up`
68×	`tan-quot`
47×	`pow-prod-down`
45×	`pow-sqr`
37×	`pow-plus`
35×	`frac-times`
30×	`add-cbrt-cube` `add-exp-log`
27×	`pow2`
24×	`add-sqr-sqrt`
23×	`associate-l/` `associate-r/`
17×	`prod-exp` `cbrt-unprod`
16×	`*-un-lft-identity`
8×	`times-frac` `add-cube-cbrt`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--` `swap-sqr` `associate-r` `associate-l` `div-inv`
4×	`associate-/r/` `insert-posit16`
3×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `diff-log` `frac-sub` `sub-div`

Counts

4 → 215

Calls

4 calls:

13.0ms	(* (tan x) (tan x))
61.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
126.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
57.0ms	(- (/ 1 (- 1 (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- 1 (* (* (tan x) (tan x)) (* (tan x) (tan x))))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (tan x) (tan x))
68.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
83.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
199.0ms	(- (/ 1 (- 1 (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- 1 (* (* (tan x) (tan x)) (* (tan x) (tan x))))))

simplify2.3s

Counts

227 → 227

Iterations

Iter	Nodes
3	4157
2	1355
1	466
0	180

prune2.6s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes351.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.0s	1526×	body	1280	valid
1.7s	1238×	body	640	valid
883.0ms	4322×	body	80	valid
731.0ms	615×	body	320	valid
187.0ms	299×	body	160	valid