Details

sample183.0ms

Algorithm

intervals

Results

104.0ms	96×	body	1280	valid
46.0ms	88×	body	640	valid
9.0ms	39×	body	320	valid
5.0ms	256×	pre	80	true
3.0ms	24×	body	160	valid
1.0ms	9×	body	80	valid

simplify16.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
8.0b	(log (+ 1.0 x))
8.0b	(log (- 1.0 x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

33.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
10.0ms	(log (+ 1.0 x))
8.0ms	(log (- 1.0 x))

series301.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
76.0ms	(log (+ 1.0 x))
69.0ms	(log (- 1.0 x))

simplify738.0ms

Counts: 78 → 78

prune333.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 57.7b

localize34.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (- (pow 1.0 3) (pow x 3)))
7.9b	(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
8.0b	(log (+ 1.0 x))
8.0b	(log (+ 1.0 x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `log-div` `sqr-pow`
5×	`distribute-lft-out--`
4×	`rem-log-exp` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`distribute-lft-out`
1×	`difference-cubes` `flip3--` `flip--`

Counts

4 → 80

Calls

4 calls:

20.0ms	(log (- (pow 1.0 3) (pow x 3)))
43.0ms	(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
10.0ms	(log (+ 1.0 x))
10.0ms	(log (+ 1.0 x))

series626.0ms

Counts

4 → 12

Calls

4 calls:

422.0ms	(log (- (pow 1.0 3) (pow x 3)))
92.0ms	(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
44.0ms	(log (+ 1.0 x))
68.0ms	(log (+ 1.0 x))

simplify780.0ms

Counts: 92 → 92

prune607.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 57.6b

localize47.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (- (pow 1.0 3) (pow x 3)))
7.9b	(log (+ (* x (+ x 1.0)) (pow 1.0 2)))
8.0b	(log (+ 1.0 x))
8.0b	(log (+ 1.0 x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `log-div` `sqr-pow`
5×	`distribute-lft-out--`
4×	`rem-log-exp` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`distribute-lft-out`
1×	`difference-cubes` `flip3--` `flip--`

Counts

4 → 80

Calls

4 calls:

35.0ms	(log (- (pow 1.0 3) (pow x 3)))
23.0ms	(log (+ (* x (+ x 1.0)) (pow 1.0 2)))
5.0ms	(log (+ 1.0 x))
19.0ms	(log (+ 1.0 x))

series664.0ms

Counts

4 → 12

Calls

4 calls:

402.0ms	(log (- (pow 1.0 3) (pow x 3)))
101.0ms	(log (+ (* x (+ x 1.0)) (pow 1.0 2)))
78.0ms	(log (+ 1.0 x))
82.0ms	(log (+ 1.0 x))

simplify792.0ms

Counts: 92 → 92

prune593.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 57.6b

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (cbrt (- (pow 1.0 3) (pow x 3))))
7.9b	(log (+ (* x (+ x 1.0)) (pow 1.0 2)))
8.0b	(log (+ 1.0 x))
8.0b	(log (+ 1.0 x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod`
33×	`add-sqr-sqrt`
25×	`cbrt-prod`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt`
8×	`pow1` `add-exp-log` `log-div` `sqr-pow`
5×	`log-pow` `distribute-lft-out--`
4×	`rem-log-exp` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-div` `distribute-lft-out`
1×	`difference-cubes` `flip3--` `pow1/3` `flip--`

Counts

4 → 84

Calls

4 calls:

27.0ms	(log (cbrt (- (pow 1.0 3) (pow x 3))))
32.0ms	(log (+ (* x (+ x 1.0)) (pow 1.0 2)))
5.0ms	(log (+ 1.0 x))
5.0ms	(log (+ 1.0 x))

series974.0ms

Counts

4 → 12

Calls

4 calls:

776.0ms	(log (cbrt (- (pow 1.0 3) (pow x 3))))
73.0ms	(log (+ (* x (+ x 1.0)) (pow 1.0 2)))
55.0ms	(log (+ 1.0 x))
70.0ms	(log (+ 1.0 x))

simplify797.0ms

Counts: 96 → 96

prune689.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 57.6b

regimes114.0ms

Accuracy

78% (0.5b remaining)

Error of 59.2b against oracle of 58.7b and baseline of 61.0b

bsearch214.0ms

Steps

Iters	Range		Point
9	1.7032597989513092e-19	1.9251139816623773e-14	1.107680636981443e-16
8	-8.124070366127344e-17	-3.083269881977671e-21	-5.48809259434947e-17

simplify838.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.3s	3318×	body	1280	valid
1.4s	2508×	body	640	valid
428.0ms	1277×	body	320	valid
132.0ms	8000×	pre	80	true
108.0ms	665×	body	160	valid
15.0ms	232×	body	80	valid