Details

sample251.0ms

Algorithm

intervals

Results

151.0ms	148×	body	1280	valid
40.0ms	22×	body	2560	valid
35.0ms	55×	body	640	valid
8.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize48.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

22.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series90.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
4	2971
3	1064
2	408
1	200
0	93

prune541.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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)))
3.1b	(sin (/ (fma 2 x eps) 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

30.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
14.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series232.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
81.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
61.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.8s

Counts

63 → 63

Iterations

Iter	Nodes
4	5559
3	1699
2	588
1	224
0	102

prune734.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.1b	(sin (/ (fma 2 x eps) 2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative`

Counts

2 → 31

Calls

2 calls:

21.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series108.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
37.0ms	(sin (/ (fma 2 x eps) 2))

simplify3.2s

Counts

37 → 37

Iterations

Iter	Nodes
4	4297
3	1550
2	472
1	171
0	73

prune412.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma 2 x eps) 2)))
0.3b	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
0.3b	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.1b	(sin (/ (fma 2 x eps) 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `associate-l` `log1p-expm1` `*-commutative` `expm1-udef`

Counts

4 → 55

Calls

4 calls:

1.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
35.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.0ms	(sin (/ (fma 2 x eps) 2))

series333.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
84.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
123.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
58.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.9s

Counts

67 → 67

Iterations

Iter	Nodes
4	3417
3	1536
2	566
1	220
0	100

prune788.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

regimes239.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.8b

bsearch210.0ms

Steps

Iters	Range		Point
8	3.2127462034754177e-10	5.6341579135238385e-06	2.8863753739128075e-06
10	-32518848344.590553	-0.0006858147917088189	-0.0006966600469417059

simplify8.0ms

Iterations

Iter	Nodes
2	31
1	31
0	26

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.6s	4494×	body	1280	valid
1.8s	1847×	body	640	valid
1.6s	613×	body	2560	valid
311.0ms	692×	body	320	valid
79.0ms	280×	body	160	valid
10.0ms	74×	body	80	valid