Details

sample86.0ms

Algorithm

intervals

Results

46.0ms	149×	body	1280	valid
15.0ms	18×	body	2560	valid
11.0ms	56×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize14.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite27.0ms

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` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify71.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220
done	5001	220

prune112.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(* (cos x) (cos eps))
2.8b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
10.0ms	(* (cos x) (cos eps))
12.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(fma (sin x) (sin eps) (cos x))
40.0ms	(* (cos x) (cos eps))
136.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify119.0ms

Counts

59 → 59

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4494	406
3	5001	404
done	5001	404

prune203.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.8b	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

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 (sin x) (sin eps) (cos x))
0.0ms	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

series189.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(fma (sin x) (sin eps) (cos x))
132.0ms	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

simplify123.0ms

Counts

26 → 26

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	93	210
1	259	183
2	932	182
3	4040	180
4	5001	180
done	5001	180

prune136.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.8b	(fma (cos x) (cos eps) (- (+ (* (sin x) (sin eps)) (cos x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `sin-mult` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

12.0ms	(+ (* (sin x) (sin eps)) (cos x))
15.0ms	(* (sin x) (sin eps))
0.0ms	(fma (cos x) (cos eps) (- (+ (* (sin x) (sin eps)) (cos x))))

series240.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* (sin x) (sin eps)) (cos x))
53.0ms	(* (sin x) (sin eps))
135.0ms	(fma (cos x) (cos eps) (- (+ (* (sin x) (sin eps)) (cos x))))

simplify71.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	211	379
1	654	338
2	2502	334
3	5002	332
done	5002	332

prune155.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.4b

regimes180.0ms

Accuracy

84.2% (1.5b remaining)

Error of 16.5b against oracle of 14.9b and baseline of 24.6b

bsearch93.0ms

Steps

Iters	Range		Point
8	4.11075536510938e-11	9.85435867085541e-08	3.130998694967744e-08
6	-1.6640733670284383e-05	-3.4900073017642136e-06	-3.6584498918211995e-06

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	15
1	43	15
2	43	15
done	43	15

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4421×	body	1280	valid
562.0ms	673×	body	2560	valid
379.0ms	1889×	body	640	valid
104.0ms	662×	body	320	valid
25.0ms	280×	body	160	valid
4.0ms	75×	body	80	valid