Details

sample171.0ms

Algorithm

intervals

Results

74.0ms	96×	body	1280	valid
38.0ms	24×	body	2560	valid
27.0ms	56×	body	640	valid
11.0ms	38×	body	320	valid
3.0ms	31×	body	80	valid
2.0ms	11×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize45.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
6.1b	(sin (+ x eps))

rewrite93.0ms

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:

79.0ms	(- (sin (+ x eps)) (sin x))
12.0ms	(sin (+ x eps))

series78.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify5.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.0s)

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

prune114.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.1b	(cos (/ (fma 2 x eps) 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

25.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
21.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series177.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
58.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
30.0ms	(cos (/ (fma 2 x eps) 2))

simplify6.4s

Counts

60 → 60

Iterations

Useful iterations: done (6.4s)

Iter	Nodes	Cost
0	97	961
1	226	945
2	641	803
3	1880	800
4	4374	784
done	5000	783

prune227.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* 2 (sin (/ eps 2))) (cos (/ (fma 2 x eps) 2)))
6.1b	(cos (/ (fma 2 x eps) 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

63.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (fma 2 x eps) 2)))
8.0ms	(cos (/ (fma 2 x eps) 2))

series111.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (fma 2 x eps) 2)))
45.0ms	(cos (/ (fma 2 x eps) 2))

simplify6.1s

Counts

35 → 35

Iterations

Useful iterations: done (6.1s)

Iter	Nodes	Cost
0	70	554
1	173	538
2	535	448
3	1631	444
4	3320	435
done	5000	434

prune130.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
6.1b	(cos (/ (fma 2 x eps) 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

43.0ms	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
3.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
3.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
4.0ms	(cos (/ (fma 2 x eps) 2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
28.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
56.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
35.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	126	1623
1	287	1341
2	926	1181
done	5000	1173

prune357.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes117.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.8b

bsearch150.0ms

Steps

Iters	Range		Point
11	1.1123901126486127e-34	1.9762467893330864e-06	9.433852813731428e-09
9	-108.09236434424712	-9.640722949014248e-05	-9.760584355965869e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	3267×	body	1280	valid
1.2s	640×	body	2560	valid
865.0ms	1788×	body	640	valid
239.0ms	834×	body	320	valid
106.0ms	1105×	body	80	valid
88.0ms	366×	body	160	valid