Details

sample212.0ms

Algorithm

intervals

Results

99.0ms	133×	body	1280	valid
56.0ms	29×	body	2560	valid
30.0ms	63×	body	640	valid
6.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize11.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
2.3b	(cos (+ x eps))

rewrite73.0ms

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:

57.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series102.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(- (cos (+ x eps)) (cos x))
27.0ms	(cos (+ x eps))

simplify930.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune220.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

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))
0.3b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
2.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite295.0ms

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:

98.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
13.0ms	(+ x (+ x eps))
126.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
54.0ms	(sin (/ (+ x (+ x eps)) 2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
41.0ms	(+ x (+ x eps))
82.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
52.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify895.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1224
1	311
0	129

prune566.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* (sin (fma eps 1/2 x)) -2) (sin (* eps 1/2)))
2.1b	(sin (fma eps 1/2 x))

rewrite39.0ms

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:

36.0ms	(* (* (sin (fma eps 1/2 x)) -2) (sin (* eps 1/2)))
2.0ms	(sin (fma eps 1/2 x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(* (* (sin (fma eps 1/2 x)) -2) (sin (* eps 1/2)))
28.0ms	(sin (fma eps 1/2 x))

simplify639.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5000
2	939
1	180
0	78

prune302.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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

rewrite193.0ms

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:

26.0ms	(+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x)))
28.0ms	(* (cos x) (sin (* eps 1/2)))
20.0ms	(* (cos (* eps 1/2)) (sin x))
118.0ms	(* (* (+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x))) -2) (sin (* eps 1/2)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x)))
83.0ms	(* (cos x) (sin (* eps 1/2)))
64.0ms	(* (cos (* eps 1/2)) (sin x))
264.0ms	(* (* (+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x))) -2) (sin (* eps 1/2)))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	2423
1	409
0	156

prune461.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes332.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.8s	4407×	body	1280	valid
1.3s	633×	body	2560	valid
907.0ms	1935×	body	640	valid
184.0ms	655×	body	320	valid
53.0ms	299×	body	160	valid
7.0ms	71×	body	80	valid