Details

sample149.0ms

Algorithm

intervals

Results

84.0ms	144×	body	1280	valid
24.0ms	20×	body	2560	valid
20.0ms	58×	body	640	valid
5.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	4×	body	80	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: 41.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ x eps))

rewrite79.0ms

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

Counts

2 → 40

Calls

2 calls:

60.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series95.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify5.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.2s)

Iter	Nodes	Cost
0	91	664
1	194	540
2	439	453
3	1358	389
4	4783	375
done	5000	375

prune176.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.8b	(sin (/ (fma 2 x eps) 2))

rewrite98.0ms

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-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

52.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
37.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
7.0ms	(sin (/ (fma 2 x eps) 2))

series255.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
80.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
68.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.7s

Counts

60 → 60

Iterations

Useful iterations: 4 (4.2s)

Iter	Nodes	Cost
0	101	959
1	221	944
2	620	803
3	1792	799
4	3798	786
done	5000	786

prune285.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.8b	(sin (/ (fma 2 x eps) 2))

rewrite50.0ms

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:

40.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
8.0ms	(sin (/ (fma 2 x eps) 2))

series138.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
35.0ms	(sin (/ (fma 2 x eps) 2))

simplify7.0s

Counts

35 → 35

Iterations

Useful iterations: 4 (4.0s)

Iter	Nodes	Cost
0	73	552
1	170	539
2	527	447
3	1627	444
4	3483	436
done	5000	436

prune195.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
0.2b	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.8b	(sin (/ (fma 2 x eps) 2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
0.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
46.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
4.0ms	(sin (/ (fma 2 x eps) 2))

series473.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
194.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
103.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
41.0ms	(sin (/ (fma 2 x eps) 2))

simplify7.3s

Counts

63 → 63

Iterations

Useful iterations: 4 (4.6s)

Iter	Nodes	Cost
0	98	1072
1	211	1025
2	590	877
3	1704	870
4	3561	854
done	5000	854

prune312.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

regimes238.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.4b

bsearch117.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.001020768799921521	0.00022642344448914372
4	-2657796.353906291	-1550992.7687819407	-1576820.312787291

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	51
1	33	51
done	33	51

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.0s	4405×	body	1280	valid
1.5s	1886×	body	640	valid
1.4s	663×	body	2560	valid
350.0ms	700×	body	320	valid
43.0ms	248×	body	160	valid
9.0ms	98×	body	80	valid