Details

sample222.0ms

Algorithm

intervals

Results

111.0ms	100×	body	1280	valid
45.0ms	68×	body	640	valid
30.0ms	16×	body	2560	valid
14.0ms	28×	body	320	valid
5.0ms	35×	body	80	valid
3.0ms	9×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

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

prune54.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize31.0ms

Local error

Found 2 expressions with local error:

2.6b	(sin (+ x eps))
1.4b	(- (sin (+ x eps)) (sin x))

rewrite69.0ms

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

55.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series109.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

67.0ms	(- (sin (+ x eps)) (sin x))
42.0ms	(sin (+ x eps))

simplify815.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

445.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
210.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
41.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
41.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
20.0ms	(- (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune304.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite105.0ms

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

33.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(+ x (+ eps x))
25.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
21.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
90.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
27.0ms	(cos (/ (+ x (+ eps x)) 2))
27.0ms	(+ x (+ eps x))

simplify3.2s

Counts

35 → 74

Calls

35 calls:

Slowest

633.0ms	(* (* (* 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)))))
567.0ms	(* (* (* 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)))))
475.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
331.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
238.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune897.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
0.4b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite127.0ms

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

42.0ms	(cos (/ (+ x (+ eps x)) 2))
38.0ms	(cos (/ (+ x (+ eps x)) 2))
24.0ms	(cos (/ (+ x (+ eps x)) 2))
23.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

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))))
25.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.7s

Counts

15 → 48

Calls

15 calls:

Slowest

294.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
287.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
282.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
281.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
60.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune681.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

rewrite120.0ms

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` `cos-mult`

Counts

4 → 35

Calls

4 calls:

Slowest

38.0ms	(cos (/ (+ x (+ eps x)) 2))
38.0ms	(cos (/ (+ x (+ eps x)) 2))
37.0ms	(cos (/ (+ x (+ eps x)) 2))
6.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

series218.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))
41.0ms	(cos (/ (+ x (+ eps x)) 2))
30.0ms	(cos (/ (+ x (+ eps x)) 2))
29.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.2s

Counts

14 → 47

Calls

14 calls:

Slowest

410.0ms	(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
321.0ms	(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
303.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
299.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
267.0ms	(- 1 (+ (* 1/3 (* x eps)) (* 1/3 (pow x 2))))

prune677.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

regimes185.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch221.0ms

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.2s	3343×	body	1280	valid
1.9s	1822×	body	640	valid
1.6s	600×	body	2560	valid
437.0ms	744×	body	320	valid
196.0ms	1153×	body	80	valid
101.0ms	338×	body	160	valid