Details

sample330.0ms

Algorithm

intervals

Results

209.0ms	89×	body	2560	valid
70.0ms	93×	body	1280	valid
16.0ms	45×	body	640	valid
4.0ms	256×	pre	80	true
4.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	1×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	8
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite58.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `tan-quot` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

9.0ms	(/ 1.0 (tan x))
46.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series492.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ 1.0 (tan x))
437.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.8s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	3982
2	685
1	242
0	115

prune261.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

43.0ms	(+ (+ (* x 0.3333333333333333) (* (pow x 3) 0.022222222222222223)) (* 0.0021164021164021165 (pow x 5)))
14.0ms	(* 0.0021164021164021165 (pow x 5))
10.0ms	(* (pow x 3) 0.022222222222222223)

series209.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(+ (+ (* x 0.3333333333333333) (* (pow x 3) 0.022222222222222223)) (* 0.0021164021164021165 (pow x 5)))
74.0ms	(* 0.0021164021164021165 (pow x 5))
57.0ms	(* (pow x 3) 0.022222222222222223)

simplify685.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1188
1	306
0	124

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

160.0ms	(* (cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165)))) (cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165)))))
12.0ms	(cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165))))
12.0ms	(cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165))))
12.0ms	(cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165))))

series1.5s

Counts

4 → 12

Calls

4 calls:

388.0ms	(* (cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165)))) (cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165)))))
397.0ms	(cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165))))
350.0ms	(cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165))))
356.0ms	(cbrt (+ (* x 0.3333333333333333) (+ (* (pow x 3) 0.022222222222222223) (* (pow x 5) 0.0021164021164021165))))

simplify907.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2276
1	531
0	196

prune854.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223))))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))
0.7b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

12.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223))))
16.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))
12.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))
15.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

355.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223))))
443.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))
449.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))
432.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (+ (* 0.3333333333333333 x) (* (pow x 3) 0.022222222222222223)))))

simplify779.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	1549
1	416
0	160

prune919.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

regimes183.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample13.4s

Algorithm

intervals

Results

8.0s	3293×	body	2560	valid
3.5s	2475×	body	1280	valid
1.1s	1259×	body	640	valid
213.0ms	642×	body	320	valid
175.0ms	8000×	pre	80	true
119.0ms	296×	body	160	valid
4.0ms	35×	body	80	valid