Details

sample208.0ms

Algorithm

intervals

Results

107.0ms	103×	body	1280	valid
36.0ms	22×	body	2560	valid
31.0ms	52×	body	640	valid
16.0ms	31×	body	320	valid
6.0ms	41×	body	80	valid
2.0ms	7×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize28.0ms

Local error

Found 2 expressions with local error:

4.4b	(sin (+ x eps))
0.9b	(- (sin (+ x eps)) (sin x))

rewrite54.0ms

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

43.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series90.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

70.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.3s

Counts: 32 → 32

prune309.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 3 expressions with local error:

4.2b	(cos (/ (+ x (+ x eps)) 2))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))

rewrite65.0ms

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

25.0ms	(cos (/ (+ x (+ x eps)) 2))
24.0ms	(+ x (+ x eps))
15.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))

series103.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

49.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(+ x (+ x eps))

simplify2.7s

Counts: 53 → 53

prune661.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ x (+ x eps)) 2))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))

rewrite163.0ms

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

47.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
44.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
32.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

62.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
56.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
35.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify954.0ms

Counts: 77 → 77

prune870.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize89.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ x (+ x eps)) 2))
4.2b	(cos (/ (+ x (+ x eps)) 2))
4.2b	(cos (/ (+ x (+ x eps)) 2))
0.6b	(* (exp (cos (/ (+ x (+ x eps)) 2))) (exp (cos (/ (+ x (+ x eps)) 2))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

18×	`exp-prod`
16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`add-cbrt-cube`
4×	`pow-prod-down` `add-exp-log` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

Slowest

141.0ms	(* (exp (cos (/ (+ x (+ x eps)) 2))) (exp (cos (/ (+ x (+ x eps)) 2))))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
23.0ms	(cos (/ (+ x (+ x eps)) 2))
19.0ms	(cos (/ (+ x (+ x eps)) 2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(* (exp (cos (/ (+ x (+ x eps)) 2))) (exp (cos (/ (+ x (+ x eps)) 2))))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.9s

Counts: 71 → 71

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes284.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch123.0ms

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.2s	3363×	body	1280	valid
1.1s	1785×	body	640	valid
1.1s	648×	body	2560	valid
259.0ms	751×	body	320	valid
126.0ms	1108×	body	80	valid
82.0ms	345×	body	160	valid