Details

sample268.0ms

Algorithm

intervals

Results

148.0ms	96×	body	2560	valid
57.0ms	90×	body	1280	valid
42.0ms	40×	body	640	valid
4.0ms	256×	pre	80	true
4.0ms	16×	body	320	valid
2.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

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: 59.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite50.0ms

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))
30.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series153.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 1.0 (tan x))
112.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.9s

Counts

56 → 56

Iterations

Useful iterations: 3 (878.0ms)

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

prune120.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

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))

rewrite64.0ms

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))
26.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
12.0ms	(* 0.0021164021164021165 (pow x 5))
13.0ms	(* 0.022222222222222223 (pow x 3))

series424.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
97.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
71.0ms	(* 0.0021164021164021165 (pow x 5))
44.0ms	(* 0.022222222222222223 (pow x 3))

simplify1.0s

Counts

92 → 92

Iterations

Useful iterations: 2 (258.0ms)

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

prune340.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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-+l+` `unpow3`

Counts

4 → 80

Calls

4 calls:

37.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
14.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
14.0ms	(* 0.0021164021164021165 (pow x 5))
25.0ms	(* 0.022222222222222223 (pow x 3))

series362.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
165.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
74.0ms	(* 0.0021164021164021165 (pow x 5))
40.0ms	(* 0.022222222222222223 (pow x 3))

simplify887.0ms

Counts

92 → 92

Iterations

Useful iterations: done (882.0ms)

Iter	Nodes	Cost
0	138	1095
1	376	979
2	1554	929
done	5000	921

prune266.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))) (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

rewrite299.0ms

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:

215.0ms	(* (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))) (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))))
20.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
33.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
28.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

361.0ms	(* (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))) (cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))))
359.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
378.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
322.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

simplify1.0s

Counts

99 → 99

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	196	4286
1	527	4077
2	2182	3842
done	5000	3517

prune517.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes107.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample12.7s

Algorithm

intervals

Results

8.3s	3158×	body	2560	valid
2.7s	2600×	body	1280	valid
783.0ms	1269×	body	640	valid
210.0ms	634×	body	320	valid
207.0ms	8000×	pre	80	true
114.0ms	290×	body	160	valid
6.0ms	49×	body	80	valid