Details

sample237.0ms

Algorithm

intervals

Results

121.0ms	129×	body	1280	valid
48.0ms	25×	body	2560	valid
45.0ms	69×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize34.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
1.9b	(cos (+ x eps))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `cos-sum` `*-un-lft-identity` `add-log-exp`
2×	`associate--l-` `pow1` `+-commutative` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

28.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

series107.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify2.6s

Counts

34 → 34

Iterations

Iter	Nodes
done	5015
5	3954
4	1427
3	659
2	282
1	138
0	70

prune156.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (* eps 1/2)) (sin (/ (+ x (+ x eps)) 2)))
1.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`associate-r`
15×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `*-commutative` `distribute-lft-out`
2×	`+-commutative` `associate-+r+` `sin-mult`
1×	`flip3-+` `associate-*r/` `flip-+`

Counts

4 → 78

Calls

4 calls:

599.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (+ x (+ x eps)) 2))))
29.0ms	(+ x (+ x eps))
220.0ms	(* (sin (* eps 1/2)) (sin (/ (+ x (+ x eps)) 2)))
149.0ms	(sin (/ (+ x (+ x eps)) 2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (+ x (+ x eps)) 2))))
44.0ms	(+ x (+ x eps))
100.0ms	(* (sin (* eps 1/2)) (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5031
3	3455
2	942
1	332
0	136

prune477.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (* -2 (sin (/ (+ x (+ x eps)) 2))) (sin (* eps 1/2)))
1.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite769.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

24.0ms	(+ x (+ x eps))
623.0ms	(* (* -2 (sin (/ (+ x (+ x eps)) 2))) (sin (* eps 1/2)))
120.0ms	(sin (/ (+ x (+ x eps)) 2))

series199.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ x (+ x eps))
138.0ms	(* (* -2 (sin (/ (+ x (+ x eps)) 2))) (sin (* eps 1/2)))
34.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.5s

Counts

66 → 66

Iterations

Iter	Nodes
done	5004
3	3590
2	845
1	280
0	114

prune372.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
1.8b	(sin (/ (+ x (+ x eps)) 2))
1.8b	(sin (/ (+ x (+ x eps)) 2))
1.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite442.0ms

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:

48.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
123.0ms	(sin (/ (+ x (+ x eps)) 2))
146.0ms	(sin (/ (+ x (+ x eps)) 2))
124.0ms	(sin (/ (+ x (+ x eps)) 2))

series314.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
54.0ms	(sin (/ (+ x (+ x eps)) 2))
50.0ms	(sin (/ (+ x (+ x eps)) 2))
44.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.4s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
4	2826
3	747
2	260
1	123
0	59

prune324.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

regimes188.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.3b

bsearch244.0ms

Steps

Iters	Range		Point
7	4.263740854872979e-07	7.143616659564812e-05	1.4877491964720032e-05
9	-101227.54480913779	-0.0005350557287305616	-0.0008099166487036783

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.6s	4444×	body	1280	valid
1.2s	1831×	body	640	valid
1.0s	610×	body	2560	valid
374.0ms	737×	body	320	valid
108.0ms	281×	body	160	valid
12.0ms	97×	body	80	valid