Details

sample254.0ms

Algorithm

intervals

Results

154.0ms	116×	body	1280	valid
37.0ms	20×	body	2560	valid
34.0ms	52×	body	640	valid
7.0ms	43×	body	80	valid
6.0ms	15×	body	320	valid
3.0ms	10×	body	160	valid

simplify17.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize26.0ms

Local error

Found 2 expressions with local error:

3.2b	(sin (+ x eps))
0.6b	(- (sin (+ x eps)) (sin x))

rewrite87.0ms

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

72.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series109.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

71.0ms	(- (sin (+ x eps)) (sin x))
38.0ms	(sin (+ x eps))

simplify1.4s

Counts: 32 → 32

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite56.0ms

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

23.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
22.0ms	(cos (/ (+ x (+ x eps)) 2))
10.0ms	(+ x (+ x eps))

series143.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

72.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
36.0ms	(cos (/ (+ x (+ x eps)) 2))
35.0ms	(+ x (+ x eps))

simplify3.0s

Counts: 53 → 53

prune594.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ x (+ x eps)) 2))
3.1b	(cos (/ (+ x (+ x eps)) 2))
3.1b	(cos (/ (+ x (+ x eps)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

rewrite137.0ms

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

43.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
17.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

33.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
28.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.6s

Counts: 48 → 48

prune618.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ x (+ x eps)) 2))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))

rewrite185.0ms

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:

Slowest

70.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
52.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
41.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
57.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))

simplify1.1s

Counts: 77 → 77

prune970.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

regimes227.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.5b

bsearch262.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.7s	3322×	body	1280	valid
2.0s	1841×	body	640	valid
1.2s	628×	body	2560	valid
342.0ms	751×	body	320	valid
136.0ms	1098×	body	80	valid
88.0ms	360×	body	160	valid