Details

sample235.0ms

Algorithm

intervals

Results

147.0ms	146×	body	1280	valid
36.0ms	62×	body	640	valid
31.0ms	18×	body	2560	valid
7.0ms	19×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

8.0ms

(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize13.0ms

Local error

Found 2 expressions with local error:

3.3b	(cos (+ x eps))
0.6b	(- (cos (+ x eps)) (cos x))

rewrite35.0ms

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

27.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series89.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

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

simplify479.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

202.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
130.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
44.0ms	(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(/ (exp (cos (+ x eps))) (exp (cos x)))
15.0ms	(- (cos (+ x eps)) (cos x))

prune330.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

3.3b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite112.0ms

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-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

Slowest

63.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
29.0ms	(sin (/ (+ x (+ eps x)) 2))
19.0ms	(+ x (+ eps x))

series219.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

138.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms	(+ x (+ eps x))
39.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.3s

Counts

24 → 53

Calls

24 calls:

Slowest

368.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
262.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
231.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
56.0ms	(sin (* 1/2 (+ (* 2 x) eps)))
49.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune547.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

3.3b	(sin (/ (+ x (+ eps x)) 2))
3.3b	(sin (/ (+ x (+ eps x)) 2))
3.3b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

Slowest

28.0ms	(sin (/ (+ x (+ eps x)) 2))
23.0ms	(sin (/ (+ x (+ eps x)) 2))
19.0ms	(sin (/ (+ x (+ eps x)) 2))
18.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
58.0ms	(sin (/ (+ x (+ eps x)) 2))
51.0ms	(sin (/ (+ x (+ eps x)) 2))
36.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.9s

Counts

15 → 48

Calls

15 calls:

Slowest

419.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
234.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
228.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)
224.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
224.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)

prune891.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.3b

localize76.0ms

Local error

Found 4 expressions with local error:

3.3b	(sin (/ (+ x (+ eps x)) 2))
3.3b	(sin (/ (+ x (+ eps x)) 2))
3.3b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

Slowest

31.0ms	(sin (/ (+ x (+ eps x)) 2))
30.0ms	(sin (/ (+ x (+ eps x)) 2))
22.0ms	(sin (/ (+ x (+ eps x)) 2))
8.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
45.0ms	(sin (/ (+ x (+ eps x)) 2))
38.0ms	(sin (/ (+ x (+ eps x)) 2))
32.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.8s

Counts

15 → 48

Calls

15 calls:

Slowest

408.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
233.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)
232.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
229.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
226.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune651.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 0.3b

regimes496.0ms

Accuracy

96.8% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.1b

bsearch167.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.9s	4456×	body	1280	valid
1.5s	1865×	body	640	valid
1.1s	644×	body	2560	valid
317.0ms	659×	body	320	valid
69.0ms	290×	body	160	valid
17.0ms	86×	body	80	valid