Details

sample156.0ms

Algorithm

intervals

Results

54.0ms	20×	body	2560	valid
53.0ms	85×	body	1280	valid
25.0ms	63×	body	640	valid
8.0ms	29×	body	320	valid
4.0ms	47×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize12.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
4.3b	(sin (+ x eps))

rewrite70.0ms

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` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

59.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	2012
4	2012
3	1269
2	446
1	203
0	92

prune424.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

23.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series134.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
43.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	2036
4	2036
3	983
2	353
1	150
0	70

prune449.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (fma eps 1/2 x)) (sin (/ eps 2)))
4.1b	(cos (fma eps 1/2 x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

16.0ms	(* (cos (fma eps 1/2 x)) (sin (/ eps 2)))
3.0ms	(cos (fma eps 1/2 x))

series110.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (cos (fma eps 1/2 x)) (sin (/ eps 2)))
32.0ms	(cos (fma eps 1/2 x))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	2000
4	2000
3	855
2	317
1	139
0	70

prune411.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 88

Calls

4 calls:

33.0ms	(* (cos (* eps 1/2)) (cos x))
24.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (/ eps 2)) (sin x)))
23.0ms	(* (sin (/ eps 2)) (sin x))
134.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (/ eps 2)) (sin x))) (sin (/ eps 2)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (cos (* eps 1/2)) (cos x))
92.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (/ eps 2)) (sin x)))
65.0ms	(* (sin (/ eps 2)) (sin x))
134.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (/ eps 2)) (sin x))) (sin (/ eps 2)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	2006
3	2006
2	1096
1	371
0	163

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
2	25
1	23
0	15

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.6s	3311×	body	1280	valid
1.2s	633×	body	2560	valid
1.2s	1788×	body	640	valid
522.0ms	822×	body	320	valid
193.0ms	1123×	body	80	valid
88.0ms	323×	body	160	valid