Details

sample185.0ms

Algorithm

intervals

Results

89.0ms	103×	body	1280	valid
28.0ms	16×	body	2560	valid
26.0ms	49×	body	640	valid
22.0ms	35×	body	320	valid
5.0ms	41×	body	80	valid
3.0ms	12×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize58.0ms

Local error

Found 2 expressions with local error:

2.6b	(sin (+ x eps))
1.9b	(- (sin (+ x eps)) (sin x))

rewrite37.0ms

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:

Slowest

29.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series109.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

73.0ms	(- (sin (+ x eps)) (sin x))
36.0ms	(sin (+ x eps))

simplify1.3s

Counts: 32 → 32

prune368.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 3 expressions with local error:

2.6b	(cos (/ (+ x (+ x eps)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))

rewrite59.0ms

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:

Slowest

34.0ms	(cos (/ (+ x (+ x eps)) 2))
15.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
10.0ms	(+ x (+ x eps))

series134.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

69.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
38.0ms	(+ x (+ x eps))
27.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.7s

Counts: 53 → 53

prune642.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

rewrite98.0ms

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/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 36

Calls

4 calls:

Slowest

39.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
19.0ms	(cos (/ (+ x (+ x eps)) 2))
11.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

41.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.6s

Counts: 48 → 48

prune554.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize67.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))
0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

Slowest

30.0ms	(cos (/ (+ x (+ x eps)) 2))
22.0ms	(cos (/ (+ x (+ x eps)) 2))
18.0ms	(cos (/ (+ x (+ x eps)) 2))
1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify756.0ms

Counts: 48 → 48

prune629.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes178.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.3b

bsearch224.0ms

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.7s	3343×	body	1280	valid
1.4s	650×	body	2560	valid
1.1s	1847×	body	640	valid
340.0ms	766×	body	320	valid
129.0ms	358×	body	160	valid
110.0ms	1036×	body	80	valid