Details

sample362.0ms

Algorithm

intervals

Results

20.0ms	45×	body	1280	valid
11.0ms	40×	body	640	valid
10.0ms	140×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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))

rewrite66.0ms

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:

6.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1.0 (* (tan x) (tan x)))
99.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify43.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune244.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

12.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
17.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
95.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify56.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	392	1134
1	1813	1007
2	5002	951
done	5002	951

prune258.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.5b	(pow (* (tan x) (tan x)) 3)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

236×	`tan-quot`
137×	`associate-*r/`
130×	`pow1`
97×	`frac-times`
78×	`associate-*l/`
45×	`frac-sub`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
21×	`add-exp-log` `add-cbrt-cube`
20×	`pow-plus`
15×	`pow2`
14×	`sub-div`
11×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow-pow` `add-log-exp`
4×	`swap-sqr` `associate-r` `associate-l`
3×	`cube-div` `pow-unpow`
2×	`pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `distribute-rgt-out--` `diff-log` `unpow3` `cube-prod` `flip--` `sqr-pow`

Counts

4 → 207

Calls

4 calls:

17.0ms	(* (tan x) (tan x))
121.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
71.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
12.0ms	(pow (* (tan x) (tan x)) 3)

series248.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
101.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
48.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
67.0ms	(pow (* (tan x) (tan x)) 3)

simplify103.0ms

Counts

219 → 219

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	805	1700
1	3060	1367
2	5001	1356
done	5001	1356

prune376.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))) 3))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(pow (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))) 3)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
48×	`times-frac`
46×	`add-cube-cbrt` `*-un-lft-identity`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
19×	`pow1`
12×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot` `associate-/r/`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-plus` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

15.0ms	(cbrt (pow (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))) 3))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))
16.0ms	(pow (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))) 3)

series317.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (pow (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))) 3))
36.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
156.0ms	(pow (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))) 3)

simplify77.0ms

Counts

176 → 176

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	583	2240
1	2543	2087
2	5001	2063
done	5001	2063

prune286.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes162.0ms

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	13	10
1	13	10
done	13	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

688.0ms	1522×	body	1280	valid
350.0ms	1260×	body	640	valid
248.0ms	4259×	body	80	valid
127.0ms	639×	body	320	valid
42.0ms	320×	body	160	valid