Details

sample249.0ms

Algorithm

intervals

Results

127.0ms	126×	body	1280	valid
54.0ms	22×	body	2560	valid
38.0ms	54×	body	640	valid
10.0ms	20×	body	320	valid
3.0ms	25×	body	80	valid
3.0ms	9×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize15.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.1b	(sin (+ x eps))

rewrite73.0ms

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:

64.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series484.0ms

Counts

2 → 6

Calls

2 calls:

458.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify1.7s

Counts

48 → 48

Iterations

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

prune384.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.1b	(cos (/ (fma 2 x eps) 2))

rewrite31.0ms

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:

24.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series95.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
28.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.8s

Counts

38 → 38

Iterations

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

prune454.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
3.1b	(cos (/ (fma 2 x eps) 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

16.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series317.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
81.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
71.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
42.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.0s

Counts

67 → 67

Iterations

Iter	Nodes
4	2346
3	1026
2	446
1	203
0	97

prune799.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cos (/ (fma x 2 eps) 2)) (* (cos (/ (fma x 2 eps) 2)) (cos (/ (fma x 2 eps) 2)))))
3.1b	(cos (/ (fma x 2 eps) 2))
3.1b	(cos (/ (fma x 2 eps) 2))
3.1b	(cos (/ (fma x 2 eps) 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `cube-unmult` `associate-*r/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

11.0ms	(cbrt (* (cos (/ (fma x 2 eps) 2)) (* (cos (/ (fma x 2 eps) 2)) (cos (/ (fma x 2 eps) 2)))))
3.0ms	(cos (/ (fma x 2 eps) 2))
3.0ms	(cos (/ (fma x 2 eps) 2))
3.0ms	(cos (/ (fma x 2 eps) 2))

series138.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (* (cos (/ (fma x 2 eps) 2)) (* (cos (/ (fma x 2 eps) 2)) (cos (/ (fma x 2 eps) 2)))))
28.0ms	(cos (/ (fma x 2 eps) 2))
32.0ms	(cos (/ (fma x 2 eps) 2))
43.0ms	(cos (/ (fma x 2 eps) 2))

simplify8.0s

Counts

56 → 56

Iterations

Iter	Nodes
8	4303
7	1857
6	1155
5	848
4	581
3	321
2	147
1	80
0	47

prune729.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes197.0ms

Accuracy

98% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 14.8b

bsearch242.0ms

Steps

Iters	Range		Point
7	1.5139611157153806e-24	8.277969008307765e-23	8.159405127878992e-23
10	-32518848344.590553	-0.0006858147917088189	-0.0006966600469417059

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.1s	3299×	body	1280	valid
2.3s	1854×	body	640	valid
1.6s	613×	body	2560	valid
395.0ms	756×	body	320	valid
166.0ms	1138×	body	80	valid
155.0ms	340×	body	160	valid