Details

sample206.0ms

Algorithm

intervals

Results

111.0ms	142×	body	1280	valid
50.0ms	34×	body	2560	valid
23.0ms	46×	body	640	valid
10.0ms	28×	body	320	valid
1.0ms	4×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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:

15.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series120.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (cos (+ x eps)) (cos x))
28.0ms	(cos (+ x eps))

simplify1.8s

Counts

48 → 48

Iterations

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

prune314.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

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)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite54.0ms

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:

35.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
14.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
4.0ms	(sin (/ (fma 2 x eps) 2))

series204.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
86.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
34.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.6s

Counts

63 → 63

Iterations

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

prune547.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite51.0ms

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:

44.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series135.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
38.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.9s

Counts

37 → 37

Iterations

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

prune372.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize63.0ms

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)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite53.0ms

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 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
0.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
45.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series456.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
160.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
117.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
56.0ms	(sin (/ (fma 2 x eps) 2))

simplify3.5s

Counts

67 → 67

Iterations

Iter	Nodes
4	4585
3	1752
2	528
1	216
0	98

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

regimes232.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.7b

bsearch311.0ms

Steps

Iters	Range		Point
10	1.578644681612568e-16	0.0001688282409805197	5.0711197596488575e-06
11	-145.89507053458865	-6.948120050383171e-19	-5.453340308409901e-05

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	27

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.1s	4532×	body	1280	valid
1.3s	1747×	body	640	valid
1.2s	645×	body	2560	valid
380.0ms	673×	body	320	valid
85.0ms	334×	body	160	valid
9.0ms	69×	body	80	valid