Details

sample194.0ms

Algorithm

intervals

Results

111.0ms	111×	body	1280	valid
30.0ms	21×	body	2560	valid
29.0ms	55×	body	640	valid
7.0ms	19×	body	320	valid
4.0ms	35×	body	80	valid
4.0ms	15×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	24
2	24
1	21
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize55.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite59.0ms

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:

43.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

series87.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (sin (+ x eps)) (sin x))
30.0ms	(sin (+ x eps))

simplify1.3s

Counts

32 → 32

Iterations

Iter	Nodes
5	3270
4	1578
3	831
2	446
1	257
0	65

prune320.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite89.0ms

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:

11.0ms	(+ x (+ x eps))
36.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
40.0ms	(cos (/ (+ x (+ x eps)) 2))

series143.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ x (+ x eps))
82.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
35.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.1s

Counts

53 → 53

Iterations

Iter	Nodes
4	6052
3	1812
2	804
1	391
0	94

prune632.0ms

Pruning

9 alts after pruning (8 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)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.6b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite174.0ms

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:

46.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
45.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
51.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
32.0ms	(cos (/ (+ x (+ x eps)) 2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
69.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
33.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify965.0ms

Counts

77 → 77

Iterations

Iter	Nodes
4	2007
3	1248
2	729
1	414
0	111

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow E (cos (/ (+ x (+ x eps)) 2)))
0.2b	(* (sin (/ eps 2)) (log (pow E (cos (/ (+ x (+ x eps)) 2)))))
0.6b	(log (pow E (cos (/ (+ x (+ x eps)) 2))))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

27.0ms	(pow E (cos (/ (+ x (+ x eps)) 2)))
47.0ms	(* (sin (/ eps 2)) (log (pow E (cos (/ (+ x (+ x eps)) 2)))))
65.0ms	(log (pow E (cos (/ (+ x (+ x eps)) 2))))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series319.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(pow E (cos (/ (+ x (+ x eps)) 2)))
117.0ms	(* (sin (/ eps 2)) (log (pow E (cos (/ (+ x (+ x eps)) 2)))))
82.0ms	(log (pow E (cos (/ (+ x (+ x eps)) 2))))
36.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify787.0ms

Counts

93 → 93

Iterations

Iter	Nodes
3	2096
2	999
1	537
0	134

prune978.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

regimes183.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.1b

bsearch214.0ms

Steps

Iters	Range		Point
9	2.817105925958348e-12	6.676551468262503e-06	1.2991744042388225e-08
8	-4.564155152621576e-09	-3.3752683627201123e-12	-4.4887063267839754e-09

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	3248×	body	1280	valid
1.2s	1842×	body	640	valid
1.0s	643×	body	2560	valid
296.0ms	785×	body	320	valid
160.0ms	1141×	body	80	valid
84.0ms	341×	body	160	valid