Details

sample230.0ms

Algorithm

intervals

Results

119.0ms	107×	body	1280	valid
40.0ms	60×	body	640	valid
33.0ms	18×	body	2560	valid
14.0ms	29×	body	320	valid
5.0ms	15×	body	160	valid
5.0ms	27×	body	80	valid

simplify16.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize20.0ms

Local error

Found 2 expressions with local error:

3.1b	(sin (+ x eps))
1.6b	(- (sin (+ x eps)) (sin x))

rewrite47.0ms

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

39.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series79.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

53.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify1.8s

Counts

36 → 32

Calls

36 calls:

Slowest

420.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
296.0ms	(* (* (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x))) (- (sin (+ x eps)) (sin x)))
263.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
208.0ms	(- (pow (sin (+ x eps)) 3) (pow (sin x) 3))
100.0ms	(- (* (sin (+ x eps)) (sin (+ x eps))) (* (sin x) (sin x)))

prune314.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 3 expressions with local error:

3.0b	(cos (/ (+ x (+ eps x)) 2))
0.3b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

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-+` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

Slowest

34.0ms	(cos (/ (+ x (+ eps x)) 2))
11.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
10.0ms	(+ x (+ eps x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

97.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms	(+ x (+ eps x))
36.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify4.2s

Counts

53 → 52

Calls

53 calls:

Slowest

850.0ms	(* (* (+ x (+ eps x)) (+ x (+ eps x))) (+ x (+ eps x)))
549.0ms	(- (* x x) (* (+ eps x) (+ eps x)))
465.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
256.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
250.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

prune563.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize57.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (/ (+ x (+ eps x)) 2))
3.0b	(cos (/ (+ x (+ eps x)) 2))
3.0b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite88.0ms

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

27.0ms	(cos (/ (+ x (+ eps x)) 2))
23.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
19.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(cos (/ (+ x (+ eps x)) 2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

47.0ms	(cos (/ (+ x (+ eps x)) 2))
43.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
41.0ms	(cos (/ (+ x (+ eps x)) 2))
41.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify3.1s

Counts

48 → 48

Calls

48 calls:

Slowest

265.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
265.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
260.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
203.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
127.0ms	(log (cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2)))))

prune634.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (/ (+ x (+ eps x)) 2))
3.0b	(cos (/ (+ x (+ eps x)) 2))
3.0b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (cos (/ (+ x (+ eps x)) 2)))

rewrite81.0ms

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

39.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(cos (/ (+ x (+ eps x)) 2))
20.0ms	(cos (/ (+ x (+ eps x)) 2))
1.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))
39.0ms	(cos (/ (+ x (+ eps x)) 2))
30.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify3.0s

Counts

50 → 48

Calls

50 calls:

Slowest

278.0ms	(- 1 (+ (* 1/6 (* x eps)) (* 1/6 (pow x 2))))
265.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
262.0ms	(pow (cos (* 1/2 (+ (* 2 x) eps))) 1/3)
262.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
257.0ms	(pow (cos (* 1/2 (+ (* 2 x) eps))) 1/3)

prune609.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes228.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.6b

bsearch282.0ms

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.8s	3186×	body	1280	valid
1.7s	1804×	body	640	valid
1.4s	689×	body	2560	valid
785.0ms	821×	body	320	valid
509.0ms	355×	body	160	valid
155.0ms	1145×	body	80	valid