Details

sample88.0ms

Algorithm

intervals

Results

37.0ms	115×	body	1280	valid
20.0ms	24×	body	2560	valid
15.0ms	78×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	14×	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: 37.6b

localize14.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (cos (+ x eps)) (cos x))
3.9b	(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))

series75.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify74.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune115.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

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))

rewrite108.0ms

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))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
65.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
89.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
137.0ms	(- (- (* (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

prune300.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
3.3b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite23.0ms

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:

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

series242.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (cos x) (cos eps))
54.0ms	(fma (sin x) (sin eps) (cos x))
140.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify114.0ms

Counts

59 → 59

Iterations

Useful iterations: 3 (109.0ms)

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

prune216.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.3b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

12.0ms	(+ (* (sin x) (sin eps)) (cos x))
10.0ms	(* (cos x) (cos eps))
12.0ms	(* (sin x) (sin eps))
34.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* (sin x) (sin eps)) (cos x))
48.0ms	(* (cos x) (cos eps))
48.0ms	(* (sin x) (sin eps))
136.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify49.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	389	759
1	1561	655
2	5001	644
done	5001	644

prune241.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.0b

regimes210.0ms

Accuracy

83.4% (1.6b remaining)

Error of 16.1b against oracle of 14.5b and baseline of 24.2b

bsearch113.0ms

Steps

Iters	Range		Point
8	4.365513329072816e-10	9.67951257757751e-07	2.1207545277268232e-08
9	-2.5466144345707062e-05	-2.1789434937933663e-14	-5.83896420831228e-07

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	46
1	40	46
done	40	46

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4457×	body	1280	valid
545.0ms	646×	body	2560	valid
372.0ms	1868×	body	640	valid
105.0ms	682×	body	320	valid
25.0ms	256×	body	160	valid
10.0ms	91×	body	80	valid