Details

sample162.0ms

Algorithm

intervals

Results

75.0ms	99×	body	1280	valid
33.0ms	76×	body	640	valid
23.0ms	15×	body	2560	valid
9.0ms	27×	body	320	valid
3.0ms	13×	body	160	valid
3.0ms	26×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize23.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
3.9b	(sin (+ x eps))

rewrite45.0ms

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:

37.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series77.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify820.0ms

Counts

30 → 30

Iterations

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

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite73.0ms

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:

12.0ms	(+ x (+ x eps))
11.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
48.0ms	(cos (/ (+ x (+ x eps)) 2))

series167.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ x (+ x eps))
98.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify530.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
2	993
1	211
0	86

prune351.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (* 2 x) eps) 2)))
0.2b	(* (log (exp (cos (/ (+ (* 2 x) eps) 2)))) (sin (/ eps 2)))
0.5b	(log (exp (cos (/ (+ (* 2 x) eps) 2))))
3.7b	(cos (/ (+ (* 2 x) eps) 2))

rewrite106.0ms

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:

20.0ms	(exp (cos (/ (+ (* 2 x) eps) 2)))
39.0ms	(* (log (exp (cos (/ (+ (* 2 x) eps) 2)))) (sin (/ eps 2)))
26.0ms	(log (exp (cos (/ (+ (* 2 x) eps) 2))))
19.0ms	(cos (/ (+ (* 2 x) eps) 2))

series226.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(exp (cos (/ (+ (* 2 x) eps) 2)))
84.0ms	(* (log (exp (cos (/ (+ (* 2 x) eps) 2)))) (sin (/ eps 2)))
37.0ms	(log (exp (cos (/ (+ (* 2 x) eps) 2))))
36.0ms	(cos (/ (+ (* 2 x) eps) 2))

simplify1.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	3134
2	631
1	198
0	95

prune437.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ (* 2 x) eps) 2)))
3.7b	(cos (/ (+ (* 2 x) eps) 2))
3.7b	(cos (/ (+ (* 2 x) eps) 2))
3.7b	(cos (/ (+ (* 2 x) eps) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ (* 2 x) eps) 2)))
10.0ms	(cos (/ (+ (* 2 x) eps) 2))
10.0ms	(cos (/ (+ (* 2 x) eps) 2))
13.0ms	(cos (/ (+ (* 2 x) eps) 2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (cos (/ (+ (* 2 x) eps) 2)))
25.0ms	(cos (/ (+ (* 2 x) eps) 2))
31.0ms	(cos (/ (+ (* 2 x) eps) 2))
36.0ms	(cos (/ (+ (* 2 x) eps) 2))

simplify1.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	3472
3	678
2	189
1	83
0	40

prune336.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes225.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.5b

bsearch162.0ms

Steps

Iters	Range		Point
10	1.3677800180115613e-22	7.547849388716505e-12	7.420855731105884e-12
9	-1.188249318842855e+20	-33326255562.233612	-33857598964.282944

simplify3.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.0s	3313×	body	1280	valid
1.1s	1776×	body	640	valid
1.1s	656×	body	2560	valid
243.0ms	771×	body	320	valid
160.0ms	1118×	body	80	valid
79.0ms	366×	body	160	valid