Details

sample273.0ms

Algorithm

intervals

Results

175.0ms	103×	body	2560	valid
57.0ms	79×	body	1280	valid
16.0ms	42×	body	640	valid
5.0ms	17×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.0ms

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: 59.4b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite78.0ms

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:

7.0ms	(/ 1.0 (tan x))
68.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series205.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ 1.0 (tan x))
146.0ms	(- (/ 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

prune296.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

13.0ms	(+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))
10.0ms	(* 0.0021164021164021165 (pow x 5))
17.0ms	(* (* x x) 0.022222222222222223)

series192.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))
63.0ms	(* 0.0021164021164021165 (pow x 5))
43.0ms	(* (* x x) 0.022222222222222223)

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
2	1765
1	309
0	115

prune368.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

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:

96.0ms	(* (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))) (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
11.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
13.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
12.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))

series1.4s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))) (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
353.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
284.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
401.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))

simplify1.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2350
1	531
0	196

prune689.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.2b

localize117.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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:

7.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
8.0ms	(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
8.0ms	(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
8.0ms	(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

379.0ms	(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
441.0ms	(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
418.0ms	(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
689.0ms	(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))

simplify2.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1640
1	414
0	160

prune732.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 0.1b

regimes183.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	12

end0.0ms

sample13.2s

Algorithm

intervals

Results

8.2s	3279×	body	2560	valid
3.5s	2515×	body	1280	valid
650.0ms	1225×	body	640	valid
306.0ms	632×	body	320	valid
161.0ms	8000×	pre	80	true
71.0ms	300×	body	160	valid
5.0ms	49×	body	80	valid