Details

sample85.0ms

Algorithm

intervals

Results

42.0ms	108×	body	1280	valid
16.0ms	68×	body	640	valid
10.0ms	12×	body	2560	valid
3.0ms	21×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	6×	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: 34.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
2.4b	(sin (+ x eps))

rewrite64.0ms

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:

54.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify3.5s

Counts

46 → 46

Iterations

Useful iterations: 4 (2.1s)

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

prune100.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.2b	(cos (/ (fma 2 x eps) 2))

rewrite19.0ms

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:

14.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series79.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.2s

Counts

36 → 36

Iterations

Useful iterations: done (3.2s)

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

prune110.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.2b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
2.2b	(cos (/ (fma 2 x eps) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

13.0ms	(* (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)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series222.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
54.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
59.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.3s

Counts

63 → 63

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	93	853
1	191	763
2	443	667
3	930	659
4	1933	640
5	3785	640
done	5001	638

prune198.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
0.5b	(cbrt (pow (expm1 (cos (/ (fma 2 x eps) 2))) 3))
0.8b	(pow (expm1 (cos (/ (fma 2 x eps) 2))) 3)
2.2b	(cos (/ (fma 2 x eps) 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `expm1-log1p` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
2.0ms	(cbrt (pow (expm1 (cos (/ (fma 2 x eps) 2))) 3))
3.0ms	(pow (expm1 (cos (/ (fma 2 x eps) 2))) 3)
4.0ms	(cos (/ (fma 2 x eps) 2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
55.0ms	(cbrt (pow (expm1 (cos (/ (fma 2 x eps) 2))) 3))
138.0ms	(pow (expm1 (cos (/ (fma 2 x eps) 2))) 3)
25.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.6s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	114	1239
1	275	1039
2	856	924
3	4422	899
done	5000	899

prune222.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes89.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.8b

bsearch109.0ms

Steps

Iters	Range		Point
8	5.712072376485207e-16	7.445648313582303e-12	7.263195155747594e-12
10	-9.588134368690297e-05	-2.110491317952259e-15	-6.839223651471605e-09

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	3264×	body	1280	valid
558.0ms	641×	body	2560	valid
420.0ms	1781×	body	640	valid
147.0ms	763×	body	320	valid
66.0ms	1201×	body	80	valid
36.0ms	350×	body	160	valid