Details

sample272.0ms

Algorithm

intervals

Results

106.0ms	88×	body	1280	valid
75.0ms	27×	body	2560	valid
51.0ms	61×	body	640	valid
16.0ms	28×	body	320	valid
7.0ms	41×	body	80	valid
4.0ms	11×	body	160	valid

simplify9.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize14.0ms

Local error

Found 2 expressions with local error:

4.7b	(sin (+ x eps))
1.2b	(- (sin (+ x eps)) (sin x))

rewrite67.0ms

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

37.0ms	(sin (+ x eps))
29.0ms	(- (sin (+ x eps)) (sin x))

series95.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify1.8s

Counts: 32 → 32

prune280.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 3 expressions with local error:

4.6b	(cos (/ (+ x (+ x eps)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))

rewrite62.0ms

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

26.0ms	(cos (/ (+ x (+ x eps)) 2))
20.0ms	(+ x (+ x eps))
14.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

74.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
45.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(+ x (+ x eps))

simplify2.9s

Counts: 53 → 53

prune648.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ x (+ x eps)) 2))
4.6b	(cos (/ (+ x (+ x eps)) 2))
4.6b	(cos (/ (+ x (+ x eps)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

rewrite97.0ms

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

45.0ms	(cos (/ (+ x (+ x eps)) 2))
19.0ms	(cos (/ (+ x (+ x eps)) 2))
18.0ms	(cos (/ (+ x (+ x eps)) 2))
14.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

43.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
36.0ms	(cos (/ (+ x (+ x eps)) 2))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.7s

Counts: 48 → 48

prune646.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ x (+ x eps)) 2))
4.6b	(cos (/ (+ x (+ x eps)) 2))
4.6b	(cos (/ (+ x (+ x eps)) 2))
4.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite114.0ms

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`

Counts

4 → 32

Calls

4 calls:

Slowest

36.0ms	(cos (/ (+ x (+ x eps)) 2))
34.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))
18.0ms	(cos (/ (+ x (+ x eps)) 2))

series135.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

35.0ms	(cos (/ (+ x (+ x eps)) 2))
34.0ms	(cos (/ (+ x (+ x eps)) 2))
33.0ms	(cos (/ (+ x (+ x eps)) 2))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.4s

Counts: 44 → 44

prune612.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes195.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch259.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.7s	3308×	body	1280	valid
1.8s	635×	body	2560	valid
1.7s	1875×	body	640	valid
346.0ms	748×	body	320	valid
140.0ms	1072×	body	80	valid
97.0ms	362×	body	160	valid