Details

sample92.0ms

Algorithm

intervals

Results

47.0ms	136×	body	1280	valid
17.0ms	19×	body	2560	valid
14.0ms	60×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 38.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite13.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (241.0ms)

Iter	Nodes	Cost
0	91	664
1	189	540
2	460	453
3	1565	389
done	5001	389

prune110.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `fma-def` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`sum-log`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

43.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
15.0ms	(+ (+ x eps) x)
54.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
21.0ms	(sin (/ (+ (+ x eps) x) 2))

series179.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
27.0ms	(+ (+ x eps) x)
55.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (553.0ms)

Iter	Nodes	Cost
0	129	1298
1	300	1154
2	830	995
3	2573	908
done	5001	908

prune477.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
0.2b	(expm1 (log1p (* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2)))))
0.3b	(* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
3.6b	(sin (/ (fma 2 x eps) 2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

0.0ms	(log1p (* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
0.0ms	(expm1 (log1p (* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2)))))
9.0ms	(* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
2.0ms	(sin (/ (fma 2 x eps) 2))

series444.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(log1p (* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
160.0ms	(expm1 (log1p (* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2)))))
85.0ms	(* (sin (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
31.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.6s

Counts

64 → 64

Iterations

Useful iterations: 5 (1.6s)

Iter	Nodes	Cost
0	93	982
1	169	947
2	387	829
3	831	825
4	1738	819
5	3781	800
done	5000	800

prune247.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (- eps 0) 2)))
0.6b	(cbrt (sin (/ (- eps 0) 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.6b	(sin (/ (fma 2 x eps) 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

3.0ms	(cbrt (sin (/ (- eps 0) 2)))
3.0ms	(cbrt (sin (/ (- eps 0) 2)))
1.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(sin (/ (fma 2 x eps) 2))

series388.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (sin (/ (- eps 0) 2)))
116.0ms	(cbrt (sin (/ (- eps 0) 2)))
117.0ms	(cbrt (sin (/ eps 2)))
35.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.7s

Counts

60 → 60

Iterations

Useful iterations: 4 (740.0ms)

Iter	Nodes	Cost
0	78	670
1	139	585
2	263	541
3	715	501
4	3087	480
done	5001	480

prune281.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.2b

regimes154.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch125.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	9.949689884521833e-06
9	-0.04390830018224924	-3.199438276574562e-09	-7.455928426940857e-05

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	52
1	34	39
done	34	39

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	4395×	body	1280	valid
561.0ms	646×	body	2560	valid
434.0ms	1879×	body	640	valid
111.0ms	708×	body	320	valid
32.0ms	301×	body	160	valid
4.0ms	71×	body	80	valid