Details

sample167.0ms

Algorithm

intervals

Results

70.0ms	93×	body	1280	valid
36.0ms	67×	body	640	valid
34.0ms	25×	body	2560	valid
9.0ms	25×	body	320	valid
4.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize45.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
1.9b	(sin (+ x eps))

rewrite42.0ms

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:

33.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (sin (+ x eps)) (sin x))
28.0ms	(sin (+ x eps))

simplify2.6s

Counts

32 → 32

Iterations

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

prune109.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
2.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite72.0ms

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:

11.0ms	(+ x (+ x eps))
22.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

series119.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ x (+ x eps))
62.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

53 → 53

Iterations

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

prune318.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize62.0ms

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)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite179.0ms

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)))
63.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
48.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
46.0ms	(cos (/ (+ x (+ x eps)) 2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
60.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
31.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.8s

Counts

77 → 77

Iterations

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

prune520.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (* 1/2 eps)) (log (log (exp (exp (cos (/ (+ x (+ x eps)) 2)))))))
0.5b	(exp (exp (cos (/ (+ x (+ x eps)) 2))))
0.5b	(log (log (exp (exp (cos (/ (+ x (+ x eps)) 2))))))
2.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
15×	`add-sqr-sqrt`
14×	`log-pow`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`exp-prod`
11×	`pow1`
7×	`distribute-rgt-in` `distribute-lft-in` `add-exp-log`
6×	`add-cbrt-cube`
5×	`add-log-exp`
4×	`associate-r` `insert-posit16`
3×	`associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 71

Calls

4 calls:

37.0ms	(* (sin (* 1/2 eps)) (log (log (exp (exp (cos (/ (+ x (+ x eps)) 2)))))))
48.0ms	(exp (exp (cos (/ (+ x (+ x eps)) 2))))
15.0ms	(log (log (exp (exp (cos (/ (+ x (+ x eps)) 2))))))
23.0ms	(cos (/ (+ x (+ x eps)) 2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin (* 1/2 eps)) (log (log (exp (exp (cos (/ (+ x (+ x eps)) 2)))))))
106.0ms	(exp (exp (cos (/ (+ x (+ x eps)) 2))))
41.0ms	(log (log (exp (exp (cos (/ (+ x (+ x eps)) 2))))))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.8s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
3	1922
2	669
1	277
0	136

prune530.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes297.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.2b

bsearch137.0ms

Steps

Iters	Range		Point
7	4.263740854872979e-07	7.143616659564812e-05	4.3324917171030357e-07
6	-0.0005350557287305616	-5.532094628653386e-05	-5.6103683390120787e-05

simplify36.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.9s	3263×	body	1280	valid
1.7s	1816×	body	640	valid
968.0ms	610×	body	2560	valid
285.0ms	770×	body	320	valid
177.0ms	342×	body	160	valid
144.0ms	1199×	body	80	valid