Details

sample183.0ms

Algorithm

intervals

Results

104.0ms	105×	body	1280	valid
30.0ms	64×	body	640	valid
23.0ms	18×	body	2560	valid
9.0ms	20×	body	320	valid
4.0ms	39×	body	80	valid
2.0ms	10×	body	160	valid

simplify16.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize15.0ms

Local error

Found 2 expressions with local error:

3.8b	(sin (+ x eps))
0.6b	(- (sin (+ x eps)) (sin x))

rewrite70.0ms

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

62.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

51.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify783.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

379.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
229.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
58.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
36.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
15.0ms	(- (sin (+ x eps)) (sin x))

prune318.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ x (+ eps x)) 2))
0.3b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

Slowest

41.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
16.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
12.0ms	(+ x (+ eps x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

111.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
89.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
46.0ms	(+ x (+ eps x))
40.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify3.0s

Counts

35 → 74

Calls

35 calls:

Slowest

622.0ms	(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
470.0ms	(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
386.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
375.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
260.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune668.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ x (+ eps x)) 2))
4.0b	(cos (/ (+ x (+ eps x)) 2))
4.0b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite121.0ms

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

39.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

43.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
40.0ms	(cos (/ (+ x (+ eps x)) 2))
39.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.4s

Counts

15 → 48

Calls

15 calls:

Slowest

265.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
262.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
246.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
224.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
59.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune563.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize73.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ x (+ eps x)) 2))
4.0b	(cos (/ (+ x (+ eps x)) 2))
4.0b	(cos (/ (+ x (+ eps x)) 2))
4.0b	(cos (/ (+ x (+ eps x)) 2))

rewrite95.0ms

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

26.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(cos (/ (+ x (+ eps x)) 2))
22.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(cos (/ (+ x (+ eps x)) 2))

series133.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

42.0ms	(cos (/ (+ x (+ eps x)) 2))
35.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.3s

Counts

12 → 44

Calls

12 calls:

Slowest

262.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
258.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
247.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
221.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
56.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune705.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes239.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.3b

bsearch321.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.8s	3332×	body	1280	valid
1.4s	606×	body	2560	valid
1.3s	1806×	body	640	valid
667.0ms	761×	body	320	valid
184.0ms	1131×	body	80	valid
141.0ms	364×	body	160	valid