Details

sample215.0ms

Algorithm

intervals

Results

101.0ms	109×	body	1280	valid
37.0ms	20×	body	2560	valid
31.0ms	56×	body	640	valid
12.0ms	36×	body	80	valid
10.0ms	26×	body	320	valid
2.0ms	9×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 37.4b

localize19.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite131.0ms

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:

109.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

series104.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify5.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.1s)

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

prune130.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.1b	(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))

series115.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
47.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.4s

Counts

36 → 36

Iterations

Useful iterations: done (4.4s)

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

prune189.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite48.0ms

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:

33.0ms	(* (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))

series240.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
28.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
89.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
45.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.6s

Counts

105 → 105

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	122	1694
1	250	1400
2	721	1252
3	3866	1232
done	5000	1231

prune296.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos (/ (fma 2 x eps) 2)) 2)
0.5b	(cbrt (* (pow (cos (/ (fma 2 x eps) 2)) 2) (cos (/ (fma 2 x eps) 2))))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
2×	`unpow2`
1×	`cbrt-prod` `pow-to-exp` `pow-pow` `pow1/3` `pow3` `pow-exp` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 50

Calls

4 calls:

3.0ms	(pow (cos (/ (fma 2 x eps) 2)) 2)
5.0ms	(cbrt (* (pow (cos (/ (fma 2 x eps) 2)) 2) (cos (/ (fma 2 x eps) 2))))
4.0ms	(cos (/ (fma 2 x eps) 2))
4.0ms	(cos (/ (fma 2 x eps) 2))

series132.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (cos (/ (fma 2 x eps) 2)) 2)
27.0ms	(cbrt (* (pow (cos (/ (fma 2 x eps) 2)) 2) (cos (/ (fma 2 x eps) 2))))
26.0ms	(cos (/ (fma 2 x eps) 2))
36.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.9s

Counts

62 → 62

Iterations

Useful iterations: 4 (748.0ms)

Iter	Nodes	Cost
0	63	804
1	123	625
2	243	544
3	618	539
4	2487	523
done	5001	523

prune201.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes122.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch112.0ms

Steps

Iters	Range		Point
8	2.4141069970017172e-21	1.1811762867881907e-17	1.1645375548633762e-17
8	-1550992.7687819407	-108.06719872485291	-109.79102272340833

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3289×	body	1280	valid
784.0ms	663×	body	2560	valid
682.0ms	1870×	body	640	valid
371.0ms	328×	body	160	valid
236.0ms	764×	body	320	valid
116.0ms	1086×	body	80	valid