Details

sample213.0ms

Algorithm

intervals

Results

94.0ms	126×	body	1280	valid
59.0ms	54×	body	640	valid
33.0ms	22×	body	2560	valid
8.0ms	20×	body	320	valid
3.0ms	25×	body	80	valid
2.0ms	9×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.1b	(sin (+ x eps))

rewrite56.0ms

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:

47.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify1.5s

Counts

32 → 32

Iterations

Iter	Nodes
5	3374
4	1441
3	637
2	294
1	137
0	65

prune286.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite75.0ms

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-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

28.0ms	(+ x (+ x eps))
26.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series139.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ x (+ x eps))
62.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
44.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify4.7s

Counts

53 → 53

Iterations

Iter	Nodes
4	7454
3	1757
2	596
1	221
0	94

prune577.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
3.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

21.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
44.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
69.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
38.0ms	(cos (/ (+ x (+ x eps)) 2))

series210.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
76.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
33.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.6s

Counts

77 → 77

Iterations

Iter	Nodes
5	3227
4	1985
3	1107
2	503
1	232
0	111

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
3.1b	(cos (/ (+ x (+ x eps)) 2))
3.1b	(cos (/ (+ x (+ x eps)) 2))
3.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite117.0ms

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:

12.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
21.0ms	(cos (/ (+ x (+ x eps)) 2))
45.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

series140.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.6s

Counts

48 → 48

Iterations

Iter	Nodes
8	4119
7	1495
6	924
5	652
4	431
3	248
2	129
1	80
0	45

prune576.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.2b

regimes259.0ms

Accuracy

98% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 14.8b

bsearch245.0ms

Steps

Iters	Range		Point
7	1.5139611157153806e-24	8.277969008307765e-23	8.159405127878992e-23
10	-32518848344.590553	-0.0006858147917088189	-0.0006966600469417059

simplify7.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.1s	3299×	body	1280	valid
1.5s	1854×	body	640	valid
1.2s	613×	body	2560	valid
692.0ms	756×	body	320	valid
221.0ms	1138×	body	80	valid
80.0ms	340×	body	160	valid