Details

sample251.0ms

Algorithm

intervals

Results

125.0ms	145×	body	1280	valid
63.0ms	53×	body	640	valid
37.0ms	19×	body	2560	valid
11.0ms	24×	body	320	valid
3.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

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: 38.7b

localize13.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite25.0ms

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:

10.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series125.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (cos (+ x eps)) (cos x))
36.0ms	(cos (+ x eps))

simplify1.2s

Counts

32 → 32

Iterations

Iter	Nodes
done	2044
5	2044
4	1424
3	658
2	282
1	137
0	67

prune179.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite174.0ms

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:

72.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
11.0ms	(+ x (+ x eps))
57.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
32.0ms	(sin (/ (+ x (+ x eps)) 2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
31.0ms	(+ x (+ x eps))
61.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
33.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	2008
3	2008
2	826
1	291
0	123

prune306.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
2.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`sum-log` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 43

Calls

3 calls:

10.0ms	(+ x (+ x eps))
44.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
22.0ms	(sin (/ (+ x (+ x eps)) 2))

series156.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ x (+ x eps))
95.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
31.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify921.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	2000
3	2000
2	743
1	241
0	96

prune292.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

2.8b	(sin (/ (+ x (+ x eps)) 2))
2.8b	(sin (/ (+ x (+ x eps)) 2))
2.8b	(sin (/ (+ x (+ x eps)) 2))
8.7b	(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))) (sin (/ (+ x (+ x eps)) 2))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `rem-cbrt-cube` `sin-mult`

Counts

4 → 36

Calls

4 calls:

19.0ms	(sin (/ (+ x (+ x eps)) 2))
37.0ms	(sin (/ (+ x (+ x eps)) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))
151.0ms	(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))) (sin (/ (+ x (+ x eps)) 2))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sin (/ (+ x (+ x eps)) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))
31.0ms	(sin (/ (+ x (+ x eps)) 2))
35.0ms	(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))) (sin (/ (+ x (+ x eps)) 2))))

simplify931.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	2001
5	2001
4	691
3	250
2	137
1	78
0	45

prune265.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes177.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.7b

bsearch233.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	3231.8276777318033	8.193560063624595e-05
10	-190824653340.76273	-0.005838610583870787	-0.005924238612320757

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.7s	4480×	body	1280	valid
1.6s	1864×	body	640	valid
1.1s	641×	body	2560	valid
229.0ms	640×	body	320	valid
75.0ms	305×	body	160	valid
8.0ms	70×	body	80	valid