Details

sample194.0ms

Algorithm

intervals

Results

77.0ms	105×	body	1280	valid
48.0ms	59×	body	640	valid
43.0ms	28×	body	2560	valid
8.0ms	23×	body	320	valid
3.0ms	32×	body	80	valid
2.0ms	9×	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: 40.7b

localize18.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite100.0ms

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:

83.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify5.1s

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

prune125.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.4b	(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))

series113.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
39.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.8s

Counts

36 → 36

Iterations

Useful iterations: done (4.8s)

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

prune160.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (cos (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (cos (/ (fma 2 x eps) 2)))
4.4b	(cos (/ (fma 2 x eps) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`log1p-expm1-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:

0.0ms	(expm1 (log1p (cos (/ (fma 2 x eps) 2))))
26.0ms	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series274.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(expm1 (log1p (cos (/ (fma 2 x eps) 2))))
100.0ms	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
60.0ms	(log1p (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.9s

Counts

63 → 63

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	89	848
1	174	762
2	396	660
3	775	656
4	1514	637
5	2786	637
done	5000	636

prune280.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
0.5b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
4.4b	(cos (/ (fma 2 x eps) 2))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

39.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
6.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
4.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
8.0ms	(cos (/ (fma 2 x eps) 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
59.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
49.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.2s

Counts

105 → 105

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	122	1694
1	249	1400
2	717	1252
3	3873	1232
done	5000	1231

prune254.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes120.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 14.8b

bsearch160.0ms

Steps

Iters	Range		Point
10	9.030143500550019e-40	8.658023511829189e-30	8.55589437692315e-30
10	-7.35943201301068	-4.7981562703001505e-12	-8.505892634593632e-09

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	50
1	32	50
done	32	50

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3322×	body	1280	valid
1.1s	1823×	body	640	valid
829.0ms	625×	body	2560	valid
186.0ms	815×	body	320	valid
115.0ms	1062×	body	80	valid
59.0ms	353×	body	160	valid