Details

sample262.0ms

Algorithm

intervals

Results

114.0ms	107×	body	1280	valid
71.0ms	18×	body	2560	valid
47.0ms	63×	body	640	valid
10.0ms	23×	body	320	valid
5.0ms	33×	body	80	valid
4.0ms	12×	body	160	valid

simplify13.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

12.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize13.0ms

Local error

Found 2 expressions with local error:

3.4b	(sin (+ x eps))
1.2b	(- (sin (+ x eps)) (sin x))

rewrite65.0ms

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

58.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

51.0ms	(- (sin (+ x eps)) (sin x))
24.0ms	(sin (+ x eps))

simplify831.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

380.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
235.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
61.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
58.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
21.0ms	(- (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune290.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite87.0ms

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

37.0ms	(cos (/ (+ x (+ eps x)) 2))
27.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
21.0ms	(+ x (+ eps x))

series160.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

100.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
34.0ms	(cos (/ (+ x (+ eps x)) 2))
26.0ms	(+ x (+ eps x))

simplify1.4s

Counts

23 → 52

Calls

23 calls:

Slowest

394.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
280.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
197.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
75.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
67.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune572.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ x (+ eps x)) 2))
3.3b	(cos (/ (+ x (+ eps x)) 2))
3.3b	(cos (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite132.0ms

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

45.0ms	(cos (/ (+ x (+ eps x)) 2))
38.0ms	(cos (/ (+ x (+ eps x)) 2))
38.0ms	(cos (/ (+ x (+ eps x)) 2))
12.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series141.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

43.0ms	(cos (/ (+ x (+ eps x)) 2))
33.0ms	(cos (/ (+ x (+ eps x)) 2))
33.0ms	(cos (/ (+ x (+ eps x)) 2))
32.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

simplify1.7s

Counts

15 → 48

Calls

15 calls:

Slowest

301.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
295.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
286.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
267.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
65.0ms	(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune635.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ x (+ eps x)) 2))
3.3b	(cos (/ (+ x (+ eps x)) 2))
3.3b	(cos (/ (+ x (+ eps x)) 2))
3.3b	(cos (/ (+ x (+ eps x)) 2))

rewrite128.0ms

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

42.0ms	(cos (/ (+ x (+ eps x)) 2))
37.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
20.0ms	(cos (/ (+ x (+ eps x)) 2))

series151.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

44.0ms	(cos (/ (+ x (+ eps x)) 2))
42.0ms	(cos (/ (+ x (+ eps x)) 2))
34.0ms	(cos (/ (+ x (+ eps x)) 2))
30.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.6s

Counts

12 → 44

Calls

12 calls:

Slowest

324.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
321.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
318.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
286.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
62.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune682.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes258.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.1b

bsearch273.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.6s	3263×	body	1280	valid
1.3s	644×	body	2560	valid
1.2s	1872×	body	640	valid
331.0ms	757×	body	320	valid
142.0ms	1114×	body	80	valid
92.0ms	350×	body	160	valid