Details

sample248.0ms

Algorithm

intervals

Results

127.0ms	101×	body	1280	valid
49.0ms	28×	body	2560	valid
35.0ms	55×	body	640	valid
16.0ms	33×	body	320	valid
4.0ms	30×	body	80	valid
3.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize25.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

58.0ms	(- (sin (+ x eps)) (sin x))
12.0ms	(sin (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify1.5s

Counts

32 → 32

Iterations

Iter	Nodes
5	3343
4	1447
3	634
2	296
1	137
0	65

prune289.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
4.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

13.0ms	(+ x (+ x eps))
16.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series174.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ x (+ x eps))
87.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
41.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify4.1s

Counts

53 → 53

Iterations

Iter	Nodes
4	6965
3	1694
2	567
1	224
0	94

prune559.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
4.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

36.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
46.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
60.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
29.0ms	(cos (/ (+ x (+ x eps)) 2))

series178.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
65.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
29.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
5	3052
4	1882
3	1074
2	511
1	233
0	111

prune772.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (+ x (* eps 1/2))))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (+ x (* eps 1/2))))))
0.5b	(log (exp (cos (+ x (* eps 1/2)))))
4.3b	(cos (+ x (* eps 1/2)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 68

Calls

4 calls:

9.0ms	(exp (cos (+ x (* eps 1/2))))
24.0ms	(* (sin (/ eps 2)) (log (exp (cos (+ x (* eps 1/2))))))
17.0ms	(log (exp (cos (+ x (* eps 1/2)))))
14.0ms	(cos (+ x (* eps 1/2)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp (cos (+ x (* eps 1/2))))
379.0ms	(* (sin (/ eps 2)) (log (exp (cos (+ x (* eps 1/2))))))
23.0ms	(log (exp (cos (+ x (* eps 1/2)))))
24.0ms	(cos (+ x (* eps 1/2)))

simplify796.0ms

Counts

80 → 80

Iterations

Iter	Nodes
4	2038
3	1151
2	519
1	236
0	118

prune698.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes122.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	3293×	body	1280	valid
1.2s	1758×	body	640	valid
993.0ms	660×	body	2560	valid
242.0ms	808×	body	320	valid
104.0ms	1111×	body	80	valid
72.0ms	370×	body	160	valid