Details

sample119.0ms

Algorithm

intervals

Results

67.0ms	143×	body	1280	valid
19.0ms	62×	body	640	valid
13.0ms	14×	body	2560	valid
5.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	3×	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: 36.5b

localize10.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite57.0ms

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:

45.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series90.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify5.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (2.9s)

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

prune154.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

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)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite55.0ms

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:

28.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
20.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series243.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
90.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
41.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.9s

Counts

60 → 60

Iterations

Useful iterations: 4 (4.5s)

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

prune318.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (sin (/ eps 2)))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite72.0ms

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-r*`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`unswap-sqr`

Counts

3 → 49

Calls

3 calls:

25.0ms	(* -2 (sin (/ eps 2)))
32.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
12.0ms	(sin (/ (fma 2 x eps) 2))

series176.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* -2 (sin (/ eps 2)))
97.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
43.0ms	(sin (/ (fma 2 x eps) 2))

simplify5.9s

Counts

58 → 58

Iterations

Useful iterations: 4 (4.3s)

Iter	Nodes	Cost
0	99	754
1	221	734
2	613	621
3	1762	618
4	3721	610
done	5000	610

prune307.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

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)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite50.0ms

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)))))
44.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
4.0ms	(sin (/ (fma 2 x eps) 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
165.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
78.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
42.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.4s

Counts

63 → 63

Iterations

Useful iterations: 4 (3.7s)

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

prune287.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.4b

regimes260.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.4b

bsearch261.0ms

Steps

Iters	Range		Point
9	1.4060273304929084e-10	2.5854593811968635e-05	2.5594022594734032e-05
10	-30636816361710.875	-0.013787396536050121	-0.01398185726995361

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.3s	4485×	body	1280	valid
1.4s	603×	body	2560	valid
876.0ms	1862×	body	640	valid
186.0ms	675×	body	320	valid
51.0ms	289×	body	160	valid
8.0ms	86×	body	80	valid