Details

sample154.0ms

Algorithm

intervals

Results

90.0ms	145×	body	1280	valid
23.0ms	16×	body	2560	valid
18.0ms	55×	body	640	valid
6.0ms	26×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify5.0ms

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:

1.1b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite87.0ms

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:

73.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series111.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify5.3s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.3s)

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

prune145.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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)))
3.6b	(sin (/ (fma 2 x eps) 2))

rewrite114.0ms

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:

55.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
41.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
17.0ms	(sin (/ (fma 2 x eps) 2))

series232.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
71.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
44.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.8s

Counts

60 → 60

Iterations

Useful iterations: 4 (4.3s)

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

prune247.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.6b	(sin (/ (fma 2 x eps) 2))

rewrite52.0ms

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:

43.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
7.0ms	(sin (/ (fma 2 x eps) 2))

series157.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
60.0ms	(sin (/ (fma 2 x eps) 2))

simplify7.8s

Counts

35 → 35

Iterations

Useful iterations: 4 (4.5s)

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

prune183.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
0.3b	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
0.5b	(log1p (sin (/ (fma 2 x eps) 2)))
3.6b	(sin (/ (fma 2 x eps) 2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

1.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
52.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
1.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
9.0ms	(sin (/ (fma 2 x eps) 2))

series417.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
173.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
96.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
68.0ms	(sin (/ (fma 2 x eps) 2))

simplify7.3s

Counts

63 → 63

Iterations

Useful iterations: 4 (4.2s)

Iter	Nodes	Cost
0	98	906
1	205	811
2	585	688
3	1673	681
4	3448	665
done	5000	665

prune245.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.2b

regimes206.0ms

Accuracy

97.8% (0.3b remaining)

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

bsearch159.0ms

Steps

Iters	Range		Point
9	0.04058914318552966	3991008.2413703846	0.04140103919524168
7	-0.22637101271021068	-0.008005822963963436	-0.00815188689103541

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	49
1	31	49
done	31	49

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.1s	4400×	body	1280	valid
1.6s	1942×	body	640	valid
1.1s	633×	body	2560	valid
172.0ms	651×	body	320	valid
53.0ms	284×	body	160	valid
9.0ms	90×	body	80	valid