Details

sample228.0ms

Algorithm

intervals

Results

134.0ms	148×	body	1280	valid
36.0ms	22×	body	2560	valid
32.0ms	55×	body	640	valid
8.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize26.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite19.0ms

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:

11.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series97.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (cos (+ x eps)) (cos x))
25.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

Iter	Nodes
5	3258
4	1330
3	586
2	268
1	135
0	67

prune300.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x eps))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
3.2b	(sin (/ (+ x (+ x eps)) 2))

rewrite205.0ms

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` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

15.0ms	(+ x (+ x eps))
55.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
88.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
45.0ms	(sin (/ (+ x (+ x eps)) 2))

series309.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ x (+ x eps))
116.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
95.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
56.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
3	2455
2	838
1	289
0	123

prune896.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
3.2b	(sin (/ (+ x (+ x eps)) 2))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

22.0ms	(+ x (+ x eps))
90.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
41.0ms	(sin (/ (+ x (+ x eps)) 2))

series155.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ x (+ x eps))
76.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
43.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify955.0ms

Counts

52 → 52

Iterations

Iter	Nodes
3	2381
2	732
1	239
0	96

prune561.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.2b	(sin (/ (+ x (+ x eps)) 2))
3.2b	(sin (/ (+ x (+ x eps)) 2))
3.2b	(sin (/ (+ x (+ x eps)) 2))

rewrite86.0ms

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:

9.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
21.0ms	(sin (/ (+ x (+ x eps)) 2))
31.0ms	(sin (/ (+ x (+ x eps)) 2))
24.0ms	(sin (/ (+ x (+ x eps)) 2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))
50.0ms	(sin (/ (+ x (+ x eps)) 2))
47.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.8s

Counts

48 → 48

Iterations

Iter	Nodes
5	4346
4	1461
3	536
2	249
1	121
0	59

prune657.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.3b

regimes353.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.8b

bsearch191.0ms

Steps

Iters	Range		Point
8	3.2127462034754177e-10	5.6341579135238385e-06	2.8863753739128075e-06
10	-32518848344.590553	-0.0006858147917088189	-0.0006966600469417059

simplify8.0ms

Iterations

Iter	Nodes
2	35
1	35
0	28

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.1s	4494×	body	1280	valid
1.7s	613×	body	2560	valid
1.6s	1847×	body	640	valid
356.0ms	692×	body	320	valid
68.0ms	280×	body	160	valid
10.0ms	74×	body	80	valid