Details

sample123.0ms

Algorithm

intervals

Results

53.0ms	58×	body	2560	valid
21.0ms	34×	body	1280	valid
18.0ms	54×	body	640	valid
8.0ms	32×	body	320	valid
5.0ms	64×	body	80	valid
2.0ms	14×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
16.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

9.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

series135.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- 1.0 (cos x))
90.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	116	808
1	301	681
2	1709	566
done	5001	553

prune259.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/720 (pow x 4) 1/2)
11.2b	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/720 (pow x 4) 1/2)
0.0ms	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

series215.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(fma 1/720 (pow x 4) 1/2)
69.0ms	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

simplify1.2s

Counts

26 → 26

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	35	298
1	58	292
2	201	255
3	1166	255
done	5001	255

prune134.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

27.0ms	(/ (/ (- 1.0 (cos x)) x) x)
26.0ms	(/ (- 1.0 (cos x)) x)
14.0ms	(- 1.0 (cos x))

series137.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (/ (- 1.0 (cos x)) x) x)
55.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

174 → 174

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	259	2577
1	621	2361
2	2999	2187
done	5000	2152

prune520.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/2 x (fma 1/720 (pow x 5) (* (pow x 3) -1/24)))
0.1b	(* (pow x 3) -1/24)
1.6b	(/ (fma 1/2 x (fma 1/720 (pow x 5) (* (pow x 3) -1/24))) x)
17.4b	(fma 1/720 (pow x 5) (* (pow x 3) -1/24))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `prod-exp` `associate-/r` `associate-/l`
2×	`fma-udef` `sqr-pow`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `frac-2neg` `unpow3` `div-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma 1/2 x (fma 1/720 (pow x 5) (* (pow x 3) -1/24)))
25.0ms	(* (pow x 3) -1/24)
9.0ms	(/ (fma 1/2 x (fma 1/720 (pow x 5) (* (pow x 3) -1/24))) x)
1.0ms	(fma 1/720 (pow x 5) (* (pow x 3) -1/24))

series483.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma 1/2 x (fma 1/720 (pow x 5) (* (pow x 3) -1/24)))
65.0ms	(* (pow x 3) -1/24)
145.0ms	(/ (fma 1/2 x (fma 1/720 (pow x 5) (* (pow x 3) -1/24))) x)
182.0ms	(fma 1/720 (pow x 5) (* (pow x 3) -1/24))

simplify703.0ms

Counts

94 → 94

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	129	1393
1	261	1342
2	1105	1228
done	5001	1225

prune245.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.1b

bsearch61.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.0325473048632644
8	-0.031678663534995	-9.641814872486784e-07	-0.03100648570835607

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	43
1	32	34
done	32	34

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	1546×	body	2560	valid
507.0ms	1267×	body	1280	valid
468.0ms	1498×	body	640	valid
161.0ms	932×	body	320	valid
122.0ms	2300×	body	80	valid
54.0ms	457×	body	160	valid