Details

sample259.0ms

Algorithm

intervals

Results

140.0ms	144×	body	1280	valid
43.0ms	21×	body	2560	valid
37.0ms	53×	body	640	valid
14.0ms	15×	body	160	valid
10.0ms	22×	body	320	valid
0.0ms	1×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize43.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (cos (+ x eps)) (cos x))
2.5b	(cos (+ x eps))

rewrite43.0ms

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:

23.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

series103.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (cos (+ x eps)) (cos x))
26.0ms	(cos (+ x eps))

simplify2.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3416
3	1158
2	424
1	202
0	93

prune272.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
2.5b	(sin (/ (fma 2 x eps) 2))

rewrite87.0ms

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:

57.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
24.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series213.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
67.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
44.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.5s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2020
2	602
1	226
0	102

prune343.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* (sin (/ eps 2)) -2) (sin (fma eps 1/2 x)))
2.5b	(sin (fma eps 1/2 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

21.0ms	(* (* (sin (/ eps 2)) -2) (sin (fma eps 1/2 x)))
2.0ms	(sin (fma eps 1/2 x))

series125.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(* (* (sin (/ eps 2)) -2) (sin (fma eps 1/2 x)))
37.0ms	(sin (fma eps 1/2 x))

simplify2.2s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
3	2080
2	666
1	198
0	81

prune326.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

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×	`sin-cos-mult` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r/` `-commutative`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in`

Counts

4 → 86

Calls

4 calls:

31.0ms	(+ (* (sin (/ eps 2)) (cos x)) (* (sin x) (cos (/ eps 2))))
10.0ms	(* (sin x) (cos (/ eps 2)))
11.0ms	(* (sin (/ eps 2)) (cos x))
79.0ms	(* (* (sin (/ eps 2)) -2) (+ (* (sin (/ eps 2)) (cos x)) (* (sin x) (cos (/ eps 2)))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (* (sin (/ eps 2)) (cos x)) (* (sin x) (cos (/ eps 2))))
70.0ms	(* (sin x) (cos (/ eps 2)))
66.0ms	(* (sin (/ eps 2)) (cos x))
224.0ms	(* (* (sin (/ eps 2)) -2) (+ (* (sin (/ eps 2)) (cos x)) (* (sin x) (cos (/ eps 2)))))

simplify2.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1990
1	490
0	179

prune596.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes205.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.6s	4442×	body	1280	valid
1.8s	1853×	body	640	valid
1.0s	629×	body	2560	valid
302.0ms	696×	body	320	valid
76.0ms	298×	body	160	valid
10.0ms	82×	body	80	valid