Details

sample229.0ms

Algorithm

intervals

Results

62.0ms	58×	body	1280	valid
24.0ms	35×	body	640	valid
19.0ms	141×	body	80	valid
8.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	257
1	13	257
2	22	257
3	29	257
4	37	257
5	42	257
done	42	257

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-neg` `prod-diff`
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 → 119

Calls

4 calls:

4.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms	(* (tan x) (tan x))
13.0ms	(* (tan x) (tan x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1.0 (* (tan x) (tan x)))
142.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
60.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify4.5s

Counts

131 → 131

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	151	42422
1	374	35971
2	1073	35033
3	4563	34478
done	5000	34478

prune701.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow1`
6×	`associate-/r` `associate-r` `associate-l` `tan-quot` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `flip3--` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip-+` `flip--`

Counts

4 → 117

Calls

4 calls:

21.0ms	(/ (* (tan x) (sin x)) (cos x))
15.0ms	(* (tan x) (sin x))
35.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
23.0ms	(* (tan x) (tan x))

series357.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* (tan x) (sin x)) (cos x))
71.0ms	(* (tan x) (sin x))
159.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
40.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	198	55681
1	492	50140
2	1556	48232
done	5001	47677

prune860.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
9.4b	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

rewrite574.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 391

Calls

4 calls:

21.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
240.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
251.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
116.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
45.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

simplify6.3s

Counts

403 → 403

Iterations

Useful iterations: 3 (4.1s)

Iter	Nodes	Cost
0	276	122147
1	726	100699
2	2131	88963
3	4652	85608
done	5004	85608

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
40×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
23×	`frac-times`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
15×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
6×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 177

Calls

4 calls:

21.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
26.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
99.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
78.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
56.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.8s

Counts

189 → 189

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	170	47544
1	544	37157
2	1770	35569
done	5001	35049

prune774.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes437.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	457
1	14	457
done	14	457

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	1205×	body	640	valid
1.5s	1580×	body	1280	valid
699.0ms	4267×	body	80	valid
321.0ms	631×	body	320	valid
75.0ms	317×	body	160	valid