Details

sample187.0ms

Algorithm

intervals

Results

87.0ms	112×	body	1280	valid
48.0ms	59×	body	640	valid
25.0ms	19×	body	2560	valid
9.0ms	24×	body	320	valid
4.0ms	33×	body	80	valid
2.0ms	9×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize26.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite104.0ms

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:

88.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify1.7s

Counts

48 → 48

Iterations

Iter	Nodes
4	3108
3	1127
2	429
1	201
0	92

prune483.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.8b	(cos (/ (fma 2 x eps) 2))

rewrite23.0ms

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:

19.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series100.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
34.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.7s

Counts

38 → 38

Iterations

Iter	Nodes
5	3026
4	1701
3	796
2	336
1	148
0	70

prune557.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (cos (fma 1/2 eps x)) (sin (* eps 1/2)))
2.8b	(cos (fma 1/2 eps x))

rewrite24.0ms

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:

21.0ms	(* (cos (fma 1/2 eps x)) (sin (* eps 1/2)))
2.0ms	(cos (fma 1/2 eps x))

series77.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(* (cos (fma 1/2 eps x)) (sin (* eps 1/2)))
21.0ms	(cos (fma 1/2 eps x))

simplify2.5s

Counts

38 → 38

Iterations

Iter	Nodes
5	2761
4	1426
3	729
2	325
1	135
0	68

prune390.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite272.0ms

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:

33.0ms	(* (cos (* 1/2 eps)) (cos x))
48.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
19.0ms	(* (sin (* 1/2 eps)) (sin x))
170.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos (* 1/2 eps)) (cos x))
119.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
68.0ms	(* (sin (* 1/2 eps)) (sin x))
184.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

simplify4.0s

Counts

100 → 100

Iterations

Iter	Nodes
3	3395
2	1040
1	365
0	161

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	24
1	24
0	19

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.2s	3363×	body	1280	valid
1.5s	1858×	body	640	valid
1.2s	593×	body	2560	valid
820.0ms	762×	body	320	valid
271.0ms	1105×	body	80	valid
94.0ms	319×	body	160	valid