Details

sample174.0ms

Algorithm

intervals

Results

74.0ms	106×	body	1280	valid
49.0ms	56×	body	640	valid
29.0ms	21×	body	2560	valid
6.0ms	21×	body	320	valid
4.0ms	37×	body	80	valid
3.0ms	15×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize13.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
2.5b	(sin (+ x eps))

rewrite70.0ms

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:

62.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify2.9s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	4407
4	1723
3	751
2	308
1	137
0	65

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
2.5b	(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` `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:

19.0ms	(+ x (+ x eps))
43.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
37.0ms	(cos (/ (+ x (+ x eps)) 2))

series137.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ x (+ x eps))
69.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
29.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

53 → 53

Iterations

Iter	Nodes
done	5004
3	2890
2	654
1	221
0	92

prune262.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.4b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.5b	(cos (/ (+ x (+ x eps)) 2))

rewrite131.0ms

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:

22.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
45.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
42.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series235.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
87.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
31.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
32.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	5006
4	3634
3	1389
2	517
1	231
0	109

prune440.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow E (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (sin (* 1/2 eps)) (log (pow E (cos (/ (+ x (+ x eps)) 2)))))
0.4b	(log (pow E (cos (/ (+ x (+ x eps)) 2))))
2.5b	(cos (/ (+ x (+ x eps)) 2))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

26.0ms	(pow E (cos (/ (+ x (+ x eps)) 2)))
61.0ms	(* (sin (* 1/2 eps)) (log (pow E (cos (/ (+ x (+ x eps)) 2)))))
76.0ms	(log (pow E (cos (/ (+ x (+ x eps)) 2))))
23.0ms	(cos (/ (+ x (+ x eps)) 2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(pow E (cos (/ (+ x (+ x eps)) 2)))
113.0ms	(* (sin (* 1/2 eps)) (log (pow E (cos (/ (+ x (+ x eps)) 2)))))
64.0ms	(log (pow E (cos (/ (+ x (+ x eps)) 2))))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5018
3	2238
2	674
1	302
0	132

prune421.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

regimes278.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.6b

bsearch204.0ms

Steps

Iters	Range		Point
4	7.81566744931325e-09	1.2368458821499648e-08	1.1087986248072222e-08
11	-3168283.462966651	-1.7028068208877994e-13	-1.1998709236678226e-08

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	3281×	body	1280	valid
1.0s	1826×	body	640	valid
880.0ms	629×	body	2560	valid
295.0ms	762×	body	320	valid
233.0ms	1144×	body	80	valid
104.0ms	358×	body	160	valid