Details

sample180.0ms

Algorithm

intervals

Results

91.0ms	147×	body	1280	valid
26.0ms	20×	body	320	valid
25.0ms	17×	body	2560	valid
23.0ms	53×	body	640	valid
3.0ms	16×	body	160	valid
0.0ms	3×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
2.2b	(cos (+ x eps))

rewrite62.0ms

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:

45.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series96.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (cos (+ x eps)) (cos x))
25.0ms	(cos (+ x eps))

simplify1.3s

Counts

48 → 48

Iterations

Iter	Nodes
4	2903
3	1052
2	410
1	202
0	93

prune493.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
0.0b	(+ x (+ eps x))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
2.5b	(sin (/ (+ x (+ eps x)) 2))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `fma-def` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

50.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
22.0ms	(+ x (+ eps x))
91.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
20.0ms	(sin (/ (+ x (+ eps x)) 2))

series270.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
28.0ms	(+ x (+ eps x))
83.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
56.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	3019
2	930
1	307
0	131

prune893.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (fma eps 1/2 x))) (sin (* eps 1/2)))
2.4b	(sin (fma eps 1/2 x))

rewrite34.0ms

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×	`sin-sum` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

31.0ms	(* (* -2 (sin (fma eps 1/2 x))) (sin (* eps 1/2)))
3.0ms	(sin (fma eps 1/2 x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(* (* -2 (sin (fma eps 1/2 x))) (sin (* eps 1/2)))
26.0ms	(sin (fma eps 1/2 x))

simplify2.7s

Counts

38 → 38

Iterations

Iter	Nodes
4	4142
3	1512
2	482
1	177
0	80

prune418.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
0.1b	(* (sin (* eps 1/2)) (cos x))
0.2b	(* (cos (* eps 1/2)) (sin x))
0.3b	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `sin-cos-mult`

Counts

4 → 81

Calls

4 calls:

33.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
36.0ms	(* (sin (* eps 1/2)) (cos x))
36.0ms	(* (cos (* eps 1/2)) (sin x))
212.0ms	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
67.0ms	(* (sin (* eps 1/2)) (cos x))
66.0ms	(* (cos (* eps 1/2)) (sin x))
213.0ms	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

simplify3.4s

Counts

93 → 93

Iterations

Iter	Nodes
3	6740
2	1620
1	438
0	168

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes442.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	16

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.7s	4481×	body	1280	valid
1.4s	630×	body	2560	valid
1.1s	1876×	body	640	valid
332.0ms	671×	body	320	valid
101.0ms	259×	body	160	valid
9.0ms	83×	body	80	valid