Details

sample175.0ms

Algorithm

intervals

Results

102.0ms	144×	body	1280	valid
25.0ms	19×	body	2560	valid
22.0ms	57×	body	640	valid
7.0ms	25×	body	320	valid
1.0ms	9×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize12.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

39.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series139.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (cos (+ x eps)) (cos x))
42.0ms	(cos (+ x eps))

simplify2.7s

Counts

30 → 30

Iterations

Useful iterations: 4 (425.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	266	283
3	540	275
4	1076	273
5	2577	273
done	5001	273

prune132.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(/ (+ (+ x eps) x) 2)
0.3b	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
3.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `sum-log`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

34.0ms	(+ (+ x eps) x)
154.0ms	(/ (+ (+ x eps) x) 2)
134.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
63.0ms	(sin (/ (+ (+ x eps) x) 2))

series239.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ x eps) x)
50.0ms	(/ (+ (+ x eps) x) 2)
109.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.9s

Counts

90 → 90

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	133	1130
1	287	1101
2	764	997
3	1927	973
done	5001	963

prune392.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
3.4b	(sin (/ (+ (+ x eps) x) 2))
3.4b	(sin (/ (+ (+ x eps) x) 2))
3.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

23.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
47.0ms	(sin (/ (+ (+ x eps) x) 2))
57.0ms	(sin (/ (+ (+ x eps) x) 2))
69.0ms	(sin (/ (+ (+ x eps) x) 2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
42.0ms	(sin (/ (+ (+ x eps) x) 2))
37.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.8s

Counts

44 → 44

Iterations

Useful iterations: 4 (541.0ms)

Iter	Nodes	Cost
0	57	570
1	120	567
2	251	501
3	519	477
4	1308	467
5	3961	467
done	5000	467

prune313.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

4.0ms	(cbrt (sin (/ eps 2)))
4.0ms	(cbrt (sin (/ eps 2)))
4.0ms	(cbrt (sin (/ eps 2)))
80.0ms	(sin (/ (+ (+ x eps) x) 2))

series547.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (sin (/ eps 2)))
156.0ms	(cbrt (sin (/ eps 2)))
187.0ms	(cbrt (sin (/ eps 2)))
39.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.4s

Counts

52 → 52

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	60	558
1	122	549
2	232	503
3	540	457
4	1795	439
done	5001	430

prune298.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.2b

regimes318.0ms

Accuracy

93.7% (0.9b remaining)

Error of 1.3b against oracle of 0.4b and baseline of 15.1b

bsearch132.0ms

Steps

Iters	Range		Point
9	3.487234927462356e-05	1902.9075791774285	0.0157429896569327
7	-1.4853052640572707e+23	-5.683048547362338e+21	-5.770898450817316e+21

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	51
1	35	51
done	35	51

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	4523×	body	1280	valid
1.5s	1821×	body	640	valid
886.0ms	611×	body	2560	valid
240.0ms	670×	body	320	valid
52.0ms	292×	body	160	valid
7.0ms	83×	body	80	valid