Details

sample257.0ms

Algorithm

intervals

Results

128.0ms	126×	body	1280	valid
49.0ms	20×	body	2560	valid
48.0ms	69×	body	640	valid
12.0ms	25×	body	320	valid
4.0ms	11×	body	160	valid
1.0ms	5×	body	80	valid

simplify9.0ms

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: 40.6b

localize55.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite30.0ms

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:

19.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series105.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify1.6s

Counts

48 → 48

Iterations

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

prune491.0ms

Pruning

7 alts after pruning (7 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)))
4.3b	(sin (/ (fma 2 x eps) 2))

rewrite82.0ms

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:

49.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
26.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series236.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
100.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
52.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.6s

Counts

63 → 63

Iterations

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

prune673.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
4.3b	(sin (/ (fma 2 x eps) 2))

rewrite38.0ms

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:

35.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series137.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
45.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.8s

Counts

37 → 37

Iterations

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

prune475.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

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)))))
4.3b	(sin (/ (fma 2 x eps) 2))

rewrite25.0ms

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:

0.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
21.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.0ms	(sin (/ (fma 2 x eps) 2))

series308.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
65.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
127.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
37.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.5s

Counts

67 → 67

Iterations

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

prune760.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

regimes222.0ms

Accuracy

95.5% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.0b

bsearch223.0ms

Steps

Iters	Range		Point
9	3.8140973376779237e-06	5877.37978213442	6.177621166523711e-05
9	-265991755648.13324	-2544079.157399237	-2578326.2911242372

simplify33.0ms

Iterations

Iter	Nodes
2	33
1	33
0	29

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.6s	4500×	body	1280	valid
1.5s	1823×	body	640	valid
1.1s	633×	body	2560	valid
416.0ms	83×	body	80	valid
324.0ms	685×	body	320	valid
77.0ms	276×	body	160	valid