Details

sample179.0ms

Algorithm

intervals

Results

90.0ms	149×	body	1280	valid
35.0ms	23×	body	2560	valid
24.0ms	51×	body	640	valid
7.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.4b	(cos (+ x eps))

rewrite90.0ms

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` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

30.0ms	(- (cos (+ x eps)) (cos x))
58.0ms	(cos (+ x eps))

series135.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(cos (+ x eps))

simplify760.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune290.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
3.5b	(sin (/ (+ x (+ x eps)) 2))

rewrite251.0ms

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` `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 → 71

Calls

4 calls:

85.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
13.0ms	(+ x (+ x eps))
117.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
34.0ms	(sin (/ (+ x (+ x eps)) 2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
42.0ms	(+ x (+ x eps))
87.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify926.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1224
1	311
0	129

prune535.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* (sin (fma eps 1/2 x)) -2) (sin (* eps 1/2)))
3.5b	(sin (fma eps 1/2 x))

rewrite37.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`sin-sum` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

35.0ms	(* (* (sin (fma eps 1/2 x)) -2) (sin (* eps 1/2)))
2.0ms	(sin (fma eps 1/2 x))

series128.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(* (* (sin (fma eps 1/2 x)) -2) (sin (* eps 1/2)))
35.0ms	(sin (fma eps 1/2 x))

simplify675.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5000
2	939
1	180
0	78

prune269.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

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` `associate-*l/` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def`

Counts

4 → 76

Calls

4 calls:

16.0ms	(+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x)))
20.0ms	(* (cos (* eps 1/2)) (sin x))
14.0ms	(* (cos x) (sin (* eps 1/2)))
101.0ms	(* (* (+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x))) -2) (sin (* eps 1/2)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x)))
83.0ms	(* (cos (* eps 1/2)) (sin x))
93.0ms	(* (cos x) (sin (* eps 1/2)))
283.0ms	(* (* (+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x))) -2) (sin (* eps 1/2)))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	2418
1	409
0	156

prune588.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.8s	4372×	body	1280	valid
1.0s	1910×	body	640	valid
960.0ms	622×	body	2560	valid
232.0ms	733×	body	320	valid
148.0ms	290×	body	160	valid
7.0ms	73×	body	80	valid