Details

sample164.0ms

Algorithm

intervals

Results

79.0ms	110×	body	1280	valid
31.0ms	22×	body	2560	valid
23.0ms	50×	body	640	valid
8.0ms	28×	body	320	valid
4.0ms	18×	body	160	valid
3.0ms	28×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize20.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite124.0ms

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:

69.0ms	(- (sin (+ x eps)) (sin x))
54.0ms	(sin (+ x eps))

series99.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify1.1s

Counts

30 → 30

Iterations

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

prune199.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite99.0ms

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:

24.0ms	(+ x (+ x eps))
22.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
52.0ms	(cos (/ (+ x (+ x eps)) 2))

series157.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ x (+ x eps))
97.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify850.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
2	993
1	211
0	86

prune307.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize54.0ms

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))))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite124.0ms

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:

17.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
28.0ms	(cos (/ (+ x (+ x eps)) 2))
47.0ms	(cos (/ (+ x (+ x eps)) 2))

series143.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
28.0ms	(cos (/ (+ x (+ x eps)) 2))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
40.0ms	(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

prune470.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (log (exp (cos (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2)))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite248.0ms

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:

36.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
91.0ms	(* (log (exp (cos (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2)))
67.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
53.0ms	(cos (/ (+ x (+ x eps)) 2))

series189.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
72.0ms	(* (log (exp (cos (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2)))
29.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
34.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

67 → 67

Iterations

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

prune356.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.3b

regimes266.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 15.1b

bsearch223.0ms

Steps

Iters	Range		Point
10	2.765405219724019e-10	1875.4132169206714	9.294677533277006e-09
9	-245180560723.46045	-1212215.9807367995	-1230266.9135965805

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.3s	3302×	body	1280	valid
1.2s	1847×	body	640	valid
1.1s	655×	body	2560	valid
325.0ms	772×	body	320	valid
94.0ms	1102×	body	80	valid
59.0ms	322×	body	160	valid