Details

sample91.0ms

Algorithm

intervals

Results

46.0ms	135×	body	1280	valid
20.0ms	24×	body	2560	valid
12.0ms	60×	body	640	valid
3.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	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: 40.0b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
1.9b	(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))

series69.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify890.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (218.0ms)

Iter	Nodes	Cost
0	91	664
1	189	540
2	460	453
3	1565	389
done	5000	389

prune112.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
2.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

15.0ms	(+ (+ x eps) x)
52.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
20.0ms	(sin (/ (+ (+ x eps) x) 2))

series106.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (+ x eps) x)
57.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
28.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

60 → 60

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	99	766
1	222	694
2	564	615
3	1469	551
done	5000	550

prune206.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (fma x 2 eps) 2))))
0.3b	(* (sin (/ (- eps 0) 2)) (expm1 (log1p (sin (/ (fma x 2 eps) 2)))))
0.5b	(log1p (sin (/ (fma x 2 eps) 2)))
2.0b	(sin (/ (fma x 2 eps) 2))

rewrite16.0ms

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` `expm1-udef` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (log1p (sin (/ (fma x 2 eps) 2))))
12.0ms	(* (sin (/ (- eps 0) 2)) (expm1 (log1p (sin (/ (fma x 2 eps) 2)))))
0.0ms	(log1p (sin (/ (fma x 2 eps) 2)))
2.0ms	(sin (/ (fma x 2 eps) 2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(expm1 (log1p (sin (/ (fma x 2 eps) 2))))
93.0ms	(* (sin (/ (- eps 0) 2)) (expm1 (log1p (sin (/ (fma x 2 eps) 2)))))
52.0ms	(log1p (sin (/ (fma x 2 eps) 2)))
30.0ms	(sin (/ (fma x 2 eps) 2))

simplify1.7s

Counts

63 → 63

Iterations

Useful iterations: 4 (571.0ms)

Iter	Nodes	Cost
0	91	891
1	171	758
2	410	660
3	907	656
4	2325	655
done	5001	655

prune212.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma x 2 eps) 2)))
0.2b	(log1p (expm1 (sin (/ (fma x 2 eps) 2))))
0.3b	(* (sin (/ (- eps 0) 2)) (log1p (expm1 (sin (/ (fma x 2 eps) 2)))))
2.0b	(sin (/ (fma x 2 eps) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (sin (/ (fma x 2 eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma x 2 eps) 2))))
15.0ms	(* (sin (/ (- eps 0) 2)) (log1p (expm1 (sin (/ (fma x 2 eps) 2)))))
2.0ms	(sin (/ (fma x 2 eps) 2))

series236.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(expm1 (sin (/ (fma x 2 eps) 2)))
67.0ms	(log1p (expm1 (sin (/ (fma x 2 eps) 2))))
92.0ms	(* (sin (/ (- eps 0) 2)) (log1p (expm1 (sin (/ (fma x 2 eps) 2)))))
29.0ms	(sin (/ (fma x 2 eps) 2))

simplify1.6s

Counts

63 → 63

Iterations

Useful iterations: 4 (552.0ms)

Iter	Nodes	Cost
0	91	891
1	174	753
2	402	660
3	885	657
4	2224	654
done	5000	654

prune187.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.5b

regimes114.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.2b

bsearch92.0ms

Steps

Iters	Range		Point
8	8.116859208030337e-08	6.379368274952145e-05	2.5399061161975948e-05
6	-2.8343233054530806e-08	-2.2450763006537216e-09	-2.7912872849602338e-08

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	54
1	36	39
done	36	39

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4415×	body	1280	valid
555.0ms	649×	body	2560	valid
378.0ms	1833×	body	640	valid
111.0ms	712×	body	320	valid
30.0ms	307×	body	160	valid
4.0ms	84×	body	80	valid