Details

sample173.0ms

Algorithm

intervals

Results

42.0ms	41×	body	1280	valid
27.0ms	40×	body	640	valid
22.0ms	154×	body	80	valid
7.0ms	15×	body	320	valid
2.0ms	6×	body	160	valid

simplify150.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize78.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite140.0ms

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×	`insert-posit16` `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 → 109

Calls

4 calls:

36.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
43.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

series699.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
116.0ms	(- 1.0 (* (tan x) (tan x)))
83.0ms	(* (tan x) (tan x))
114.0ms	(* (tan x) (tan x))

simplify6.4s

Counts

121 → 121

Iterations

Iter	Nodes
done	5019
3	3745
2	1002
1	352
0	141

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`*-un-lft-identity` `add-cube-cbrt`
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--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

52.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
15.0ms	(- 1.0 (* (tan x) (tan x)))
46.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

series609.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
81.0ms	(- 1.0 (* (tan x) (tan x)))
81.0ms	(* (tan x) (tan x))
76.0ms	(* (tan x) (tan x))

simplify4.4s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1811
1	631
0	252

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (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)))
0.2b	(* (tan x) (tan x))

rewrite298.0ms

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` `insert-posit16` `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 → 228

Calls

4 calls:

139.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
23.0ms	(+ (sqrt 1.0) (tan x))
63.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
21.0ms	(* (tan x) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

576.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
77.0ms	(+ (sqrt 1.0) (tan x))
294.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
80.0ms	(* (tan x) (tan x))

simplify5.2s

Counts

240 → 240

Iterations

Iter	Nodes
done	5000
2	2981
1	854
0	317

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
11.7b	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

560×	`pow1`
392×	`tan-quot`
280×	`pow-prod-up`
260×	`frac-times`
193×	`pow-plus`
176×	`associate-*l/`
112×	`associate-*r/`
94×	`pow-prod-down`
88×	`pow-sqr`
63×	`cbrt-div`
55×	`pow2`
44×	`add-cbrt-cube` `add-exp-log`
29×	`prod-exp` `cbrt-unprod`
24×	`pow3`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
7×	`swap-sqr` `associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 387

Calls

4 calls:

392.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
42.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
419.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
68.0ms	(* (tan x) (tan x))
97.0ms	(* (tan x) (tan x))
109.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

simplify11.4s

Counts

399 → 399

Iterations

Iter	Nodes
done	5000
3	4935
2	2253
1	721
0	273

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes703.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.7s	1501×	body	1280	valid
670.0ms	1261×	body	640	valid
606.0ms	4281×	body	80	valid
416.0ms	629×	body	320	valid
72.0ms	328×	body	160	valid