Details

sample318.0ms

Algorithm

intervals

Results

204.0ms	109×	body	2560	valid
69.0ms	83×	body	1280	valid
17.0ms	32×	body	640	valid
7.0ms	24×	body	320	valid
5.0ms	256×	pre	80	true
2.0ms	8×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
done	11	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize17.0ms

Local error

Found 1 expressions with local error:

2.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`times-frac`
5×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`add-cube-cbrt` `add-log-exp`
2×	`div-inv`
1×	`pow1` `add-exp-log` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--`

Counts

1 → 22

Calls

1 calls:

42.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

series148.0ms

Counts

1 → 3

Calls

1 calls:

147.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.4s

Counts

25 → 25

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	75	358
1	165	348
2	451	330
3	2369	330
done	5000	330

prune94.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

14.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
33.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
19.0ms	(* 0.0021164021164021165 (pow x 5))
13.0ms	(* 0.022222222222222223 (pow x 3))

series354.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
85.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
56.0ms	(* 0.0021164021164021165 (pow x 5))
54.0ms	(* 0.022222222222222223 (pow x 3))

simplify848.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (247.0ms)

Iter	Nodes	Cost
0	138	1055
1	384	935
2	1721	885
done	5002	885

prune362.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

68.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
10.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
9.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
9.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series5.5s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.3s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.5s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.2s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify1.2s

Counts

99 → 99

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	192	3092
1	517	2931
2	2029	2714
done	5001	2505

prune850.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series6.0s

Counts

4 → 12

Calls

4 calls:

1.6s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.5s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.5s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.5s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify652.0ms

Counts

64 → 64

Iterations

Useful iterations: done (648.0ms)

Iter	Nodes	Cost
0	98	1864
1	262	1828
2	961	1716
done	5001	1476

prune523.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.1b

regimes137.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	18	15
done	18	15

end0.0ms

sample13.7s

Algorithm

intervals

Results

8.2s	3252×	body	2560	valid
3.0s	2554×	body	1280	valid
1.6s	1252×	body	640	valid
292.0ms	602×	body	320	valid
209.0ms	8000×	pre	80	true
73.0ms	304×	body	160	valid
4.0ms	36×	body	80	valid