Details

sample162.0ms

Algorithm

intervals

Results

93.0ms	135×	body	1280	valid
32.0ms	24×	body	2560	valid
20.0ms	63×	body	640	valid
5.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify5.0ms

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: 39.3b

localize27.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite46.0ms

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:

27.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series97.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(- (cos (+ x eps)) (cos x))
35.0ms	(cos (+ x eps))

simplify2.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	3787
4	1424
3	658
2	282
1	137
0	67

prune198.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x eps))
0.0b	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
2.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite634.0ms

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:

31.0ms	(+ x (+ x eps))
103.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
463.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
36.0ms	(sin (/ (+ x (+ x eps)) 2))

series248.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ x (+ x eps))
94.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
87.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
41.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5048
3	3581
2	854
1	289
0	121

prune421.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (+ x (/ eps 2)))) (sin (/ eps 2)))
2.7b	(sin (+ x (/ eps 2)))

rewrite109.0ms

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×	`insert-posit16` `add-log-exp`
1×	`sin-sum` `associate-l` `*-commutative`

Counts

2 → 28

Calls

2 calls:

91.0ms	(* (* -2 (sin (+ x (/ eps 2)))) (sin (/ eps 2)))
17.0ms	(sin (+ x (/ eps 2)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

147.0ms	(* (* -2 (sin (+ x (/ eps 2)))) (sin (/ eps 2)))
30.0ms	(sin (+ x (/ eps 2)))

simplify3.0s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	1721
2	462
1	171
0	73

prune233.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin (/ eps 2)))
0.1b	(+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))
0.2b	(* (sin x) (cos (/ eps 2)))
0.3b	(* (* -2 (+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))) (sin (/ eps 2)))

rewrite136.0ms

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×	`insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `sin-cos-mult`

Counts

4 → 72

Calls

4 calls:

18.0ms	(* (cos x) (sin (/ eps 2)))
15.0ms	(+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))
11.0ms	(* (sin x) (cos (/ eps 2)))
89.0ms	(* (* -2 (+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))) (sin (/ eps 2)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cos x) (sin (/ eps 2)))
139.0ms	(+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))
73.0ms	(* (sin x) (cos (/ eps 2)))
281.0ms	(* (* -2 (+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))) (sin (/ eps 2)))

simplify1.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1453
1	414
0	157

prune531.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes206.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.4s	4388×	body	1280	valid
1.3s	1901×	body	640	valid
947.0ms	649×	body	2560	valid
182.0ms	689×	body	320	valid
91.0ms	290×	body	160	valid
8.0ms	83×	body	80	valid