Details

sample260.0ms

Algorithm

intervals

Results

133.0ms	148×	body	1280	valid
63.0ms	59×	body	640	valid
39.0ms	20×	body	2560	valid
6.0ms	13×	body	320	valid
5.0ms	15×	body	160	valid
0.0ms	1×	body	80	valid

simplify13.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize28.0ms

Local error

Found 2 expressions with local error:

3.2b	(cos (+ x eps))
2.0b	(- (cos (+ x eps)) (cos x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

Slowest

42.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series85.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

66.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify1.3s

Counts: 32 → 32

prune379.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

3.1b	(sin (/ (+ x (+ x eps)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

Slowest

72.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
71.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
21.0ms	(+ x (+ x eps))
19.0ms	(sin (/ (+ x (+ x eps)) 2))

series286.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
85.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
49.0ms	(sin (/ (+ x (+ x eps)) 2))
35.0ms	(+ x (+ x eps))

simplify1.2s

Counts: 76 → 76

prune961.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 3 expressions with local error:

3.1b	(sin (/ (+ x (+ x eps)) 2))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`sum-log` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 43

Calls

3 calls:

Slowest

93.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))
20.0ms	(+ x (+ x eps))

series171.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

85.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
51.0ms	(sin (/ (+ x (+ x eps)) 2))
35.0ms	(+ x (+ x eps))

simplify1.1s

Counts: 52 → 52

prune477.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
6.2b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
6.2b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite68.0ms

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`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 41

Calls

4 calls:

Slowest

20.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
19.0ms	(sin (/ (+ x (+ x eps)) 2))
16.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
12.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

613.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
199.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
187.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
40.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify751.0ms

Counts: 53 → 53

prune724.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes206.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch258.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.3s	4466×	body	1280	valid
1.6s	628×	body	2560	valid
1.6s	1855×	body	640	valid
430.0ms	688×	body	320	valid
118.0ms	290×	body	160	valid
10.0ms	73×	body	80	valid