Details

sample243.0ms

Algorithm

intervals

Results

102.0ms	103×	body	1280	valid
77.0ms	70×	body	640	valid
32.0ms	16×	body	2560	valid
11.0ms	25×	body	320	valid
6.0ms	35×	body	80	valid
2.0ms	7×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

(- (sin (+ x eps)) (sin x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize27.0ms

Local error

Found 2 expressions with local error:

4.3b	(sin (+ x eps))
1.0b	(- (sin (+ x eps)) (sin x))

rewrite86.0ms

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))

series82.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

49.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify712.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

346.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
210.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
55.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
28.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
15.0ms	(- (sin (+ x eps)) (sin x))

prune278.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize48.0ms

Local error

Found 3 expressions with local error:

4.5b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite60.0ms

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-+` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

Slowest

34.0ms	(cos (/ (+ x (+ eps x)) 2))
14.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
10.0ms	(+ x (+ eps x))

series200.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

117.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
42.0ms	(cos (/ (+ x (+ eps x)) 2))
41.0ms	(+ x (+ eps x))

simplify1.3s

Counts

23 → 52

Calls

23 calls:

Slowest

358.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
278.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
152.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
60.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
60.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune652.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize70.0ms

Local error

Found 4 expressions with local error:

4.5b	(cos (/ (+ x (+ eps x)) 2))
4.5b	(cos (/ (+ x (+ eps x)) 2))
4.5b	(cos (/ (+ x (+ eps x)) 2))
0.4b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite105.0ms

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

44.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
20.0ms	(cos (/ (+ x (+ eps x)) 2))
18.0ms	(cos (/ (+ x (+ eps x)) 2))

series134.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

37.0ms	(cos (/ (+ x (+ eps x)) 2))
37.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
34.0ms	(cos (/ (+ x (+ eps x)) 2))
26.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.6s

Counts

15 → 48

Calls

15 calls:

Slowest

296.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
286.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
284.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
252.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
60.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune659.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize75.0ms

Local error

Found 4 expressions with local error:

4.5b	(cos (/ (+ x (+ eps x)) 2))
4.5b	(cos (/ (+ x (+ eps x)) 2))
4.5b	(cos (/ (+ x (+ eps x)) 2))
4.5b	(cos (/ (+ x (+ eps x)) 2))

rewrite133.0ms

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

43.0ms	(cos (/ (+ x (+ eps x)) 2))
39.0ms	(cos (/ (+ x (+ eps x)) 2))
30.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(cos (/ (+ x (+ eps x)) 2))

series144.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

42.0ms	(cos (/ (+ x (+ eps x)) 2))
40.0ms	(cos (/ (+ x (+ eps x)) 2))
34.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.4s

Counts

12 → 44

Calls

12 calls:

Slowest

290.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
267.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
263.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
254.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
61.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune763.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.6b

regimes190.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.2b

bsearch123.0ms

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.4s	3319×	body	1280	valid
1.9s	1876×	body	640	valid
1.3s	619×	body	2560	valid
864.0ms	760×	body	320	valid
201.0ms	1081×	body	80	valid
101.0ms	345×	body	160	valid