Details

sample196.0ms

Algorithm

intervals

Results

84.0ms	144×	body	1280	valid
54.0ms	61×	body	640	valid
37.0ms	25×	body	2560	valid
6.0ms	23×	body	320	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite27.0ms

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

Counts

2 → 24

Calls

2 calls:

18.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series146.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (cos (+ x eps)) (cos x))
53.0ms	(cos (+ x eps))

simplify1.0s

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1232
2	337
1	135
0	65

prune189.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite259.0ms

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`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

91.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
13.0ms	(+ x (+ x eps))
104.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
48.0ms	(sin (/ (+ x (+ x eps)) 2))

series331.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
40.0ms	(+ x (+ x eps))
122.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
57.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1135
1	288
0	118

prune497.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.1b	(sin (/ (+ x (+ x eps)) 2))
3.1b	(sin (/ (+ x (+ x eps)) 2))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

23.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
46.0ms	(sin (/ (+ x (+ x eps)) 2))
37.0ms	(sin (/ (+ x (+ x eps)) 2))
25.0ms	(sin (/ (+ x (+ x eps)) 2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
31.0ms	(sin (/ (+ x (+ x eps)) 2))
32.0ms	(sin (/ (+ x (+ x eps)) 2))
56.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify3.3s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	4851
3	1071
2	308
1	121
0	57

prune435.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

3.0ms	(cbrt (sin (/ eps 2)))
3.0ms	(cbrt (sin (/ eps 2)))
3.0ms	(cbrt (sin (/ eps 2)))
52.0ms	(sin (/ (+ x (+ x eps)) 2))

series571.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (sin (/ eps 2)))
156.0ms	(cbrt (sin (/ eps 2)))
183.0ms	(cbrt (sin (/ eps 2)))
52.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1283
2	299
1	123
0	60

prune404.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.3b

regimes267.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch273.0ms

Steps

Iters	Range		Point
11	5.267526695779846e-25	1126.7541422477805	8.24866037662799e-05
10	-3.2052418334402957e-07	-8.353467643873847e-20	-3.15657623230093e-07

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.9s	4442×	body	1280	valid
1.0s	651×	body	2560	valid
842.0ms	1861×	body	640	valid
223.0ms	683×	body	320	valid
104.0ms	299×	body	160	valid
6.0ms	64×	body	80	valid