Details

sample143.0ms

Algorithm

intervals

Results

76.0ms	121×	body	1280	valid
22.0ms	57×	body	640	valid
20.0ms	17×	body	2560	valid
4.0ms	15×	body	320	valid
4.0ms	37×	body	80	valid
1.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	202
1	9	202
2	10	202
done	10	202

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize16.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite73.0ms

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:

64.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series91.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
45.0ms	(sin (+ x eps))

simplify4.1s

Counts

30 → 30

Iterations

Useful iterations: 4 (780.0ms)

Iter	Nodes	Cost
0	63	8462
1	135	7579
2	305	7579
3	755	7539
4	1781	7460
5	4797	7460
done	5000	7460

prune142.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (cos (/ (+ (+ x eps) x) 2)) (sin (* eps 1/2))))
0.0b	(+ (+ x eps) x)
0.2b	(* (cos (/ (+ (+ x eps) x) 2)) (sin (* eps 1/2)))
4.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

29.0ms	(* 2 (* (cos (/ (+ (+ x eps) x) 2)) (sin (* eps 1/2))))
20.0ms	(+ (+ x eps) x)
21.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (* eps 1/2)))
33.0ms	(cos (/ (+ (+ x eps) x) 2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* 2 (* (cos (/ (+ (+ x eps) x) 2)) (sin (* eps 1/2))))
30.0ms	(+ (+ x eps) x)
76.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (* eps 1/2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.6s

Counts

70 → 70

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	111	22660
1	282	20767
2	819	20607
3	3561	19998
done	5001	16860

prune351.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (+ x (* 1/2 eps))) (* (sin (* 1/2 eps)) 2))
4.4b	(cos (+ x (* 1/2 eps)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`add-log-exp`
1×	`cos-sum` `associate-r` `*-commutative`

Counts

2 → 26

Calls

2 calls:

33.0ms	(* (cos (+ x (* 1/2 eps))) (* (sin (* 1/2 eps)) 2))
16.0ms	(cos (+ x (* 1/2 eps)))

series111.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(* (cos (+ x (* 1/2 eps))) (* (sin (* 1/2 eps)) 2))
29.0ms	(cos (+ x (* 1/2 eps)))

simplify4.3s

Counts

32 → 32

Iterations

Useful iterations: 4 (2.9s)

Iter	Nodes	Cost
0	62	9997
1	155	9115
2	432	9034
3	1511	8834
4	4909	8819
done	5002	8819

prune143.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos (* 1/2 eps)))
0.2b	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
0.2b	(* (sin x) (sin (* 1/2 eps)))
0.2b	(* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (* (sin (* 1/2 eps)) 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cos-mult` `cbrt-unprod` `sin-mult`
4×	`associate-*l/`
3×	`*-commutative`
2×	`flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `diff-log`

Counts

4 → 74

Calls

4 calls:

13.0ms	(* (cos x) (cos (* 1/2 eps)))
24.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
14.0ms	(* (sin x) (sin (* 1/2 eps)))
100.0ms	(* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (* (sin (* 1/2 eps)) 2))

series344.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos (* 1/2 eps)))
91.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
54.0ms	(* (sin x) (sin (* 1/2 eps)))
154.0ms	(* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (* (sin (* 1/2 eps)) 2))

simplify3.3s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	139	34071
1	355	31954
2	1058	31633
3	4746	30837
done	5001	30837

prune327.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes179.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	484
1	19	484
done	19	484

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.1s	3270×	body	1280	valid
1.2s	1838×	body	640	valid
798.0ms	675×	body	2560	valid
212.0ms	759×	body	320	valid
77.0ms	1124×	body	80	valid
50.0ms	334×	body	160	valid