Details

sample216.0ms

Algorithm

intervals

Results

75.0ms	100×	body	1280	valid
61.0ms	62×	body	640	valid
48.0ms	29×	body	2560	valid
8.0ms	24×	body	320	valid
4.0ms	33×	body	80	valid
2.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize11.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ eps x)) (sin x))
2.2b	(sin (+ eps x))

rewrite57.0ms

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:

49.0ms	(- (sin (+ eps x)) (sin x))
8.0ms	(sin (+ eps x))

series90.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (sin (+ eps x)) (sin x))
20.0ms	(sin (+ eps x))

simplify2.9s

Counts

30 → 30

Iterations

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

prune146.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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))
0.2b	(* (sin eps) (cos x))
2.0b	(- (* (cos eps) (sin x)) (sin x))

rewrite74.0ms

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:

25.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
9.0ms	(* (cos eps) (sin x))
20.0ms	(* (sin eps) (cos x))
18.0ms	(- (* (cos eps) (sin x)) (sin x))

series443.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
66.0ms	(* (cos eps) (sin x))
77.0ms	(* (sin eps) (cos x))
109.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify829.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1478
1	354
0	139

prune495.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
0.2b	(* (sin eps) (cos x))
0.2b	(* (sin x) (- (cos eps) 1))
1.9b	(- (cos eps) 1)

rewrite93.0ms

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:

15.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
16.0ms	(* (sin eps) (cos x))
43.0ms	(* (sin x) (- (cos eps) 1))
16.0ms	(- (cos eps) 1)

series312.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
68.0ms	(* (sin eps) (cos x))
53.0ms	(* (sin x) (- (cos eps) 1))
28.0ms	(- (cos eps) 1)

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
2	2155
1	420
0	155

prune591.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
0.3b	(cbrt (pow (- (cos eps) 1) 3))
0.3b	(pow (- (cos eps) 1) 3)
1.9b	(- (cos eps) 1)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
44×	`cbrt-prod`
36×	`*-un-lft-identity`
23×	`associate-r`
22×	`unpow-prod-down` `cube-prod`
15×	`add-cube-cbrt`
14×	`difference-of-squares`
7×	`pow1` `difference-of-sqr-1` `add-exp-log` `distribute-lft-out--`
6×	`cube-div` `add-cbrt-cube` `add-log-exp`
5×	`unswap-sqr`
4×	`cbrt-div` `flip3--` `flip--` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
2×	`associate-*r/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 124

Calls

4 calls:

58.0ms	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
8.0ms	(cbrt (pow (- (cos eps) 1) 3))
9.0ms	(pow (- (cos eps) 1) 3)
6.0ms	(- (cos eps) 1)

series175.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
32.0ms	(cbrt (pow (- (cos eps) 1) 3))
57.0ms	(pow (- (cos eps) 1) 3)
20.0ms	(- (cos eps) 1)

simplify1.9s

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	2518
1	406
0	151

prune728.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes260.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.3s	3226×	body	1280	valid
1.1s	633×	body	2560	valid
987.0ms	1875×	body	640	valid
208.0ms	760×	body	320	valid
98.0ms	1143×	body	80	valid
65.0ms	363×	body	160	valid