Details

sample190.0ms

Algorithm

intervals

Results

109.0ms	106×	body	1280	valid
31.0ms	58×	body	640	valid
23.0ms	16×	body	2560	valid
9.0ms	25×	body	320	valid
4.0ms	36×	body	80	valid
3.0ms	15×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite471.0ms

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` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

457.0ms	(- (sin (+ x eps)) (sin x))
12.0ms	(sin (+ x eps))

series87.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify5.2s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.2s)

Iter	Nodes	Cost
0	91	662
1	194	539
2	450	452
3	1388	388
4	4919	374
done	5000	374

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.6b	(cos (/ (fma 2 x eps) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

17.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series112.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
29.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.9s

Counts

36 → 36

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	68	514
1	144	508
2	341	444
3	687	442
4	1340	431
5	2510	431
done	5001	430

prune174.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
3.6b	(cos (/ (fma 2 x eps) 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

15.0ms	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
5.0ms	(cos (/ (fma 2 x eps) 2))

series142.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
47.0ms	(cos (/ (fma 2 x eps) 2))

simplify5.8s

Counts

35 → 35

Iterations

Useful iterations: 6 (4.4s)

Iter	Nodes	Cost
0	62	493
1	132	486
2	329	420
3	651	416
4	1254	407
5	2190	407
6	3569	406
done	5001	406

prune117.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (fma 2 x eps) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
0.5b	(log (exp (cos (/ (fma 2 x eps) 2))))
3.6b	(cos (/ (fma 2 x eps) 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

5.0ms	(exp (cos (/ (fma 2 x eps) 2)))
24.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
14.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
5.0ms	(cos (/ (fma 2 x eps) 2))

series158.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(exp (cos (/ (fma 2 x eps) 2)))
51.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
30.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.9s

Counts

81 → 81

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	112	1186
1	206	1079
2	483	949
3	952	942
4	1920	923
5	3589	923
done	5001	922

prune244.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes110.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.3b

bsearch131.0ms

Steps

Iters	Range		Point
10	7.973842016810099e-17	7.806085722401822e-05	8.837665134522453e-09
7	-0.22637101271021068	-0.008005822963963436	-0.00815188689103541

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	50
1	32	37
done	32	37

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.0s	3220×	body	1280	valid
1.1s	633×	body	2560	valid
699.0ms	1919×	body	640	valid
501.0ms	735×	body	320	valid
74.0ms	1139×	body	80	valid
49.0ms	354×	body	160	valid