Details

sample155.0ms

Algorithm

intervals

Results

75.0ms	105×	body	1280	valid
27.0ms	59×	body	640	valid
27.0ms	17×	body	2560	valid
7.0ms	23×	body	320	valid
4.0ms	42×	body	80	valid
2.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite80.0ms

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`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

64.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series112.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(- (sin (+ x eps)) (sin x))
45.0ms	(sin (+ x eps))

simplify951.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1449
2	381
1	135
0	63

prune160.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite66.0ms

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` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

20.0ms	(+ x (+ x eps))
11.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

series198.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ x (+ x eps))
113.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
37.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify849.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
2	993
1	211
0	86

prune386.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

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))))
3.2b	(cos (/ (+ x (+ x eps)) 2))
3.2b	(cos (/ (+ x (+ x eps)) 2))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 32

Calls

4 calls:

12.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
43.0ms	(cos (/ (+ x (+ x eps)) 2))
32.0ms	(cos (/ (+ x (+ x eps)) 2))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

series169.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
43.0ms	(cos (/ (+ x (+ x eps)) 2))
46.0ms	(cos (/ (+ x (+ x eps)) 2))
34.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.6s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	2950
3	656
2	181
1	81
0	43

prune341.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.2b	(* (log (exp (cos (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2)))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

31.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
85.0ms	(* (log (exp (cos (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2)))
74.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
29.0ms	(cos (/ (+ x (+ x eps)) 2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
87.0ms	(* (log (exp (cos (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2)))
35.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.8s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	3215
2	654
1	204
0	97

prune374.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes257.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.0b

bsearch193.0ms

Steps

Iters	Range		Point
11	2.0892179653459966e-19	4.9803363081918155	1.3935314959670237e-08
7	-0.16269631706675922	-0.007136466459190441	-0.007204743972663667

simplify7.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	3248×	body	1280	valid
841.0ms	650×	body	2560	valid
811.0ms	1858×	body	640	valid
258.0ms	778×	body	320	valid
130.0ms	326×	body	160	valid
84.0ms	1140×	body	80	valid