Details

sample156.0ms

Algorithm

intervals

Results

77.0ms	106×	body	1280	valid
28.0ms	58×	body	640	valid
19.0ms	16×	body	2560	valid
9.0ms	25×	body	320	valid
3.0ms	36×	body	80	valid
3.0ms	15×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize65.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

84.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

series79.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify5.4s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.3s)

Iter	Nodes	Cost
0	91	662
1	194	539
2	450	452
3	1388	388
4	4919	374
done	5000	374

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.6b	(cos (/ (fma 2 x eps) 2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

28.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
7.0ms	(cos (/ (fma 2 x eps) 2))

series98.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.6s

Counts

36 → 36

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	68	514
1	144	508
2	341	444
3	687	442
4	1340	431
5	2510	431
done	5001	430

prune158.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))
3.6b	(cos (fma 1/2 eps x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

21.0ms	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))
5.0ms	(cos (fma 1/2 eps x))

series97.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))
35.0ms	(cos (fma 1/2 eps x))

simplify3.5s

Counts

37 → 37

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	67	442
1	139	436
2	336	386
3	684	377
4	1316	370
5	2744	369
done	5001	368

prune119.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 1/2 eps)) (cos x))
0.1b	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
0.1b	(* (sin (* 1/2 eps)) (sin x))
0.2b	(* (sin (* 1/2 eps)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`fma-neg` `diff-log`

Counts

4 → 90

Calls

4 calls:

18.0ms	(* (cos (* 1/2 eps)) (cos x))
35.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
20.0ms	(* (sin (* 1/2 eps)) (sin x))
121.0ms	(* (sin (* 1/2 eps)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos (* 1/2 eps)) (cos x))
97.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
58.0ms	(* (sin (* 1/2 eps)) (sin x))
133.0ms	(* (sin (* 1/2 eps)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

simplify2.0s

Counts

102 → 102

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	154	1847
1	345	1781
2	1041	1627
3	3287	1569
done	5001	1524

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes95.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	22	22
2	24	22
done	24	22

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3220×	body	1280	valid
973.0ms	633×	body	2560	valid
750.0ms	1919×	body	640	valid
237.0ms	735×	body	320	valid
77.0ms	1139×	body	80	valid
53.0ms	354×	body	160	valid