Details

sample94.0ms

Algorithm

intervals

Results

42.0ms	128×	body	1280	valid
24.0ms	24×	body	2560	valid
12.0ms	63×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	4×	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: 40.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
4.6b	(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:

16.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify76.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (72.0ms)

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

prune123.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.9b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

11.0ms	(* (cos x) (cos eps))
19.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
69.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series317.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos eps))
88.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
52.0ms	(* (sin x) (sin eps))
135.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify47.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	989
1	1342	838
2	5002	822
done	5002	822

prune330.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.9b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.9b	(fma (cos eps) (cos x) (- (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 eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series205.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(fma (sin x) (sin eps) (cos x))
146.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify121.0ms

Counts

26 → 26

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	87	209
1	240	182
2	795	182
3	3587	180
4	5001	180
done	5001	180

prune157.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.9b	(fma (cos eps) (cos x) (- (+ (* (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:

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

series249.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ (* (sin x) (sin eps)) (cos x))
46.0ms	(* (sin x) (sin eps))
144.0ms	(fma (cos eps) (cos x) (- (+ (* (sin x) (sin eps)) (cos x))))

simplify77.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	205	378
1	645	339
2	2519	338
3	5001	336
done	5001	336

prune169.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.8b

regimes211.0ms

Accuracy

87.2% (1.3b remaining)

Error of 16.0b against oracle of 14.7b and baseline of 24.7b

bsearch93.0ms

Steps

Iters	Range		Point
9	1.7355052557369657e-07	0.016621422887445694	3.0976237051923435e-06
5	-4.560344852981834e-11	-1.324383265621001e-11	-3.2100194781168704e-11

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	42
1	63	42
2	63	42
done	63	42

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4416×	body	1280	valid
578.0ms	685×	body	2560	valid
387.0ms	1902×	body	640	valid
93.0ms	659×	body	320	valid
31.0ms	270×	body	160	valid
3.0ms	68×	body	80	valid