Details

sample94.0ms

Algorithm

intervals

Results

48.0ms	143×	body	1280	valid
20.0ms	24×	body	2560	valid
11.0ms	57×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	9×	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

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
5.0b	(cos (+ x eps))

rewrite26.0ms

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))

series76.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify75.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune119.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.8b

localize13.0ms

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))
3.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite109.0ms

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:

10.0ms	(* (cos x) (cos eps))
18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
13.0ms	(* (sin x) (sin eps))
66.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series318.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
90.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
52.0ms	(* (sin x) (sin eps))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify48.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822
done	5002	822

prune313.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.6b

localize23.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
3.4b	(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))
145.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify116.0ms

Counts

26 → 26

Iterations

Useful iterations: 3 (25.0ms)

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

prune153.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
0.2b	(* (sin eps) (sin x))
3.4b	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (* (sin x) (+ (- (sin eps)) (sin eps))) (cos x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
12.0ms	(* (sin eps) (sin x))
47.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (* (sin x) (+ (- (sin eps)) (sin eps))) (cos x)))

series282.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
46.0ms	(* (sin eps) (sin x))
144.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (* (sin x) (+ (- (sin eps)) (sin eps))) (cos x)))

simplify35.0ms

Counts

67 → 67

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	280	733
1	981	671
2	5001	608
done	5001	608

prune231.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.5b

regimes201.0ms

Accuracy

86.3% (1.4b remaining)

Error of 16.1b against oracle of 14.8b and baseline of 24.8b

bsearch114.0ms

Steps

Iters	Range		Point
7	4.000715157667192e-13	8.957781355231878e-11	8.78089823303509e-11
10	-1.7143484778777746e-14	-1.1343869170594912e-27	-1.6839546914248254e-14

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	35
1	40	35
done	40	35

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4477×	body	1280	valid
549.0ms	646×	body	2560	valid
375.0ms	1850×	body	640	valid
94.0ms	646×	body	320	valid
33.0ms	294×	body	160	valid
4.0ms	87×	body	80	valid