Details

sample369.0ms

Algorithm

intervals

Results

256.0ms	116×	body	2560	valid
64.0ms	71×	body	1280	valid
17.0ms	32×	body	640	valid
8.0ms	24×	body	320	valid
6.0ms	256×	pre	80	true
3.0ms	12×	body	160	valid
0.0ms	1×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize62.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

6.0ms	(/ 1.0 (tan x))
41.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series225.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ 1.0 (tan x))
153.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify2.1s

Counts

56 → 56

Iterations

Useful iterations: 3 (872.0ms)

Iter	Nodes	Cost
0	115	619
1	242	592
2	685	566
3	3990	564
done	5000	564

prune203.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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

rewrite72.0ms

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:

9.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
35.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
12.0ms	(* 0.0021164021164021165 (pow x 5))
14.0ms	(* 0.022222222222222223 (pow x 3))

series361.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
77.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
61.0ms	(* 0.0021164021164021165 (pow x 5))
40.0ms	(* 0.022222222222222223 (pow x 3))

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: 2 (306.0ms)

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

prune309.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

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))))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(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:

69.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
8.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
11.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series5.4s

Counts

4 → 12

Calls

4 calls:

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

simplify977.0ms

Counts

99 → 99

Iterations

Useful iterations: done (971.0ms)

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

prune606.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
7.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
7.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
14.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series6.9s

Counts

4 → 12

Calls

4 calls:

1.5s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.8s	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
2.0s	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.5s	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify889.0ms

Counts

73 → 73

Iterations

Useful iterations: done (883.0ms)

Iter	Nodes	Cost
0	157	2167
1	405	2113
2	1466	1968
done	5000	1791

prune554.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

regimes152.0ms

Accuracy

0% (0.2b 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

sample13.4s

Algorithm

intervals

Results

8.4s	3278×	body	2560	valid
3.4s	2543×	body	1280	valid
744.0ms	1198×	body	640	valid
343.0ms	642×	body	320	valid
163.0ms	8000×	pre	80	true
68.0ms	297×	body	160	valid
5.0ms	42×	body	80	valid