Details

sample198.0ms

Algorithm

intervals

Results

76.0ms	93×	body	1280	valid
59.0ms	67×	body	640	valid
34.0ms	25×	body	2560	valid
10.0ms	25×	body	320	valid
7.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
1.9b	(sin (+ x eps))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

65.0ms	(- (sin (+ x eps)) (sin x))
13.0ms	(sin (+ x eps))

series94.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (sin (+ x eps)) (sin x))
31.0ms	(sin (+ x eps))

simplify2.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3934
3	1269
2	446
1	203
0	92

prune224.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.2b	(cos (/ (fma 2 x eps) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

14.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series95.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
36.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.9s

Counts

38 → 38

Iterations

Iter	Nodes
done	5001
4	2632
3	983
2	353
1	150
0	70

prune215.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (cos (fma eps 1/2 x)) (sin (/ eps 2)))
2.2b	(cos (fma eps 1/2 x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

15.0ms	(* (cos (fma eps 1/2 x)) (sin (/ eps 2)))
2.0ms	(cos (fma eps 1/2 x))

series70.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* (cos (fma eps 1/2 x)) (sin (/ eps 2)))
24.0ms	(cos (fma eps 1/2 x))

simplify2.5s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
4	2237
3	855
2	317
1	139
0	70

prune180.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* eps 1/2)) (cos x))
0.1b	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
0.2b	(* (sin (* eps 1/2)) (sin x))
0.3b	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (/ eps 2)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 88

Calls

4 calls:

16.0ms	(* (cos (* eps 1/2)) (cos x))
35.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
19.0ms	(* (sin (* eps 1/2)) (sin x))
107.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (/ eps 2)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos (* eps 1/2)) (cos x))
95.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
56.0ms	(* (sin (* eps 1/2)) (sin x))
127.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (/ eps 2)))

simplify1.9s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	3203
2	1027
1	370
0	165

prune462.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes110.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
2	26
1	24
0	16

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.7s	3263×	body	1280	valid
1.3s	610×	body	2560	valid
985.0ms	1816×	body	640	valid
297.0ms	770×	body	320	valid
110.0ms	1199×	body	80	valid
65.0ms	342×	body	160	valid