Details

sample219.0ms

Algorithm

intervals

Results

101.0ms	130×	body	1280	valid
56.0ms	72×	body	640	valid
29.0ms	17×	body	2560	valid
9.0ms	29×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize23.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

30.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series153.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(- (cos (+ x eps)) (cos x))
54.0ms	(cos (+ x eps))

simplify1.1s

Counts

46 → 46

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	91	664
1	202	543
2	726	453
done	5000	389

prune284.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
3.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`fma-def` `distribute-lft-out`
3×	`expm1-log1p-u` `associate-r` `associate-l` `sum-log` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

57.0ms	(+ (+ x eps) x)
190.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
86.0ms	(sin (/ (+ (+ x eps) x) 2))

series203.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (+ x eps) x)
108.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
53.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify885.0ms

Counts

60 → 60

Iterations

Useful iterations: done (882.0ms)

Iter	Nodes	Cost
0	99	766
1	231	694
2	832	617
done	5000	591

prune524.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
3.1b	(sin (/ (+ (+ x eps) x) 2))
3.1b	(sin (/ (+ (+ x eps) x) 2))
3.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

36.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
86.0ms	(sin (/ (+ (+ x eps) x) 2))
89.0ms	(sin (/ (+ (+ x eps) x) 2))
85.0ms	(sin (/ (+ (+ x eps) x) 2))

series355.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))
60.0ms	(sin (/ (+ (+ x eps) x) 2))
56.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

52 → 52

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	61	644
1	127	629
2	323	563
3	1147	535
done	5001	480

prune660.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

localize60.0ms

Local error

Found 4 expressions with local error:

3.1b	(sin (/ (+ (+ x eps) x) 2))
4.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
4.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
4.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 45

Calls

4 calls:

84.0ms	(sin (/ (+ (+ x eps) x) 2))
43.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
60.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
43.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

series831.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sin (/ (+ (+ x eps) x) 2))
247.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
256.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
278.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

simplify1.1s

Counts

57 → 57

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	70	1032
1	143	1014
2	334	914
3	1201	849
done	5001	770

prune605.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.5b

regimes402.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch261.0ms

Steps

Iters	Range		Point
10	5.024206171497321e-19	2.8868360106527892e-08	2.860803493028998e-08
10	-4.26929226401081	-4.5846337071089676e-10	-3.597466725231278e-05

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	27	51
1	36	37
2	37	37
done	37	37

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.5s	4495×	body	1280	valid
1.7s	633×	body	2560	valid
1.3s	1850×	body	640	valid
282.0ms	672×	body	320	valid
131.0ms	281×	body	160	valid
8.0ms	69×	body	80	valid