Details

sample176.0ms

Algorithm

intervals

Results

86.0ms	109×	body	1280	valid
35.0ms	23×	body	2560	valid
23.0ms	57×	body	640	valid
7.0ms	20×	body	320	valid
3.0ms	35×	body	80	valid
3.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize12.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ eps x)) (sin x))
3.6b	(sin (+ eps x))

rewrite87.0ms

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:

78.0ms	(- (sin (+ eps x)) (sin x))
8.0ms	(sin (+ eps x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(- (sin (+ eps x)) (sin x))
30.0ms	(sin (+ eps x))

simplify3.1s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
4	4832
3	1014
2	314
1	126
0	63

prune161.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
0.1b	(* (cos eps) (sin x))
0.1b	(* (sin eps) (cos x))
1.1b	(- (* (cos eps) (sin x)) (sin x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
9×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
3×	`sin-cos-mult`
2×	`associate-+r+` `sum-log` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `distribute-rgt-out--` `flip-+`

Counts

4 → 67

Calls

4 calls:

44.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
9.0ms	(* (cos eps) (sin x))
9.0ms	(* (sin eps) (cos x))
10.0ms	(- (* (cos eps) (sin x)) (sin x))

series369.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
53.0ms	(* (cos eps) (sin x))
64.0ms	(* (sin eps) (cos x))
88.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify812.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1478
1	354
0	139

prune468.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (sin eps) (cos x))
1.1b	(- (cos eps) 1)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*r/` `difference-of-squares`
3×	`flip3--` `sin-cos-mult` `flip--`
2×	`difference-of-sqr-1` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `diff-log` `flip-+`

Counts

4 → 80

Calls

4 calls:

18.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
30.0ms	(* (sin x) (- (cos eps) 1))
17.0ms	(* (sin eps) (cos x))
10.0ms	(- (cos eps) 1)

series314.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
63.0ms	(* (sin x) (- (cos eps) 1))
59.0ms	(* (sin eps) (cos x))
21.0ms	(- (cos eps) 1)

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5003
2	2155
1	420
0	155

prune616.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ 1 (cos eps))))
0.2b	(/ (- (* (sin eps) (sin eps))) (+ 1 (cos eps)))
0.3b	(* (sin eps) (sin eps))
0.4b	(+ 1 (cos eps))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
49×	`times-frac`
39×	`add-sqr-sqrt`
33×	`associate-r`
32×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
6×	`associate-l` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `swap-sqr` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `distribute-frac-neg` `*-commutative` `div-inv` `sin-mult`
1×	`pow2` `neg-sub0` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out` `sqr-sin` `distribute-neg-frac` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

32.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ 1 (cos eps))))
27.0ms	(/ (- (* (sin eps) (sin eps))) (+ 1 (cos eps)))
19.0ms	(* (sin eps) (sin eps))
16.0ms	(+ 1 (cos eps))

series322.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ 1 (cos eps))))
100.0ms	(/ (- (* (sin eps) (sin eps))) (+ 1 (cos eps)))
36.0ms	(* (sin eps) (sin eps))
14.0ms	(+ 1 (cos eps))

simplify3.5s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	4503
1	591
0	212

prune997.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	15

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.6s	3204×	body	1280	valid
1.1s	622×	body	2560	valid
687.0ms	1922×	body	640	valid
225.0ms	829×	body	320	valid
192.0ms	353×	body	160	valid
77.0ms	1070×	body	80	valid