Details

sample237.0ms

Algorithm

intervals

Results

129.0ms	144×	body	1280	valid
38.0ms	61×	body	640	valid
33.0ms	19×	body	2560	valid
24.0ms	22×	body	320	valid
2.0ms	7×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

45.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series460.0ms

Counts

2 → 6

Calls

2 calls:

439.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

Iter	Nodes
5	3258
4	1330
3	586
2	268
1	135
0	67

prune270.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.6b	(sin (/ (+ x (+ x eps)) 2))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

53.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
11.0ms	(+ x (+ x eps))
80.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
24.0ms	(sin (/ (+ x (+ x eps)) 2))

series249.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
45.0ms	(+ x (+ x eps))
67.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify830.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2396
2	826
1	289
0	123

prune858.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
2.6b	(sin (+ x (* eps 1/2)))

rewrite66.0ms

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`
2×	`insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 30

Calls

2 calls:

49.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
16.0ms	(sin (+ x (* eps 1/2)))

series144.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
39.0ms	(sin (+ x (* eps 1/2)))

simplify3.2s

Counts

36 → 36

Iterations

Iter	Nodes
4	4094
3	1842
2	563
1	190
0	76

prune425.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 86

Calls

4 calls:

18.0ms	(* (sin x) (cos (* eps 1/2)))
17.0ms	(* (cos x) (sin (* eps 1/2)))
60.0ms	(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
77.0ms	(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (sin x) (cos (* eps 1/2)))
71.0ms	(* (cos x) (sin (* eps 1/2)))
96.0ms	(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
138.0ms	(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))

simplify5.4s

Counts

98 → 98

Iterations

Iter	Nodes
3	7422
2	1629
1	415
0	165

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	15

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.6s	4529×	body	1280	valid
1.1s	1881×	body	640	valid
1.1s	593×	body	2560	valid
340.0ms	657×	body	320	valid
65.0ms	264×	body	160	valid
9.0ms	76×	body	80	valid