Details

sample198.0ms

Algorithm

intervals

Results

114.0ms	143×	body	1280	valid
33.0ms	21×	body	2560	valid
26.0ms	46×	body	640	valid
11.0ms	28×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	5×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize57.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series98.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify780.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	1205
2	338
1	137
0	67

prune214.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

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-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

11.0ms	(+ x (+ x eps))
55.0ms	(/ (+ x (+ x eps)) 2)
63.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
21.0ms	(sin (/ (+ x (+ x eps)) 2))

series216.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ x (+ x eps))
58.0ms	(/ (+ x (+ x eps)) 2)
95.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify942.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
2	1236
1	304
0	136

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))))
0.3b	(* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps)))
3.4b	(sin (+ (* 1/2 eps) x))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`insert-posit16` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`sin-sum` `associate-*r/` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

90.0ms	(* -2 (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))))
60.0ms	(* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps)))
25.0ms	(sin (+ (* 1/2 eps) x))

series240.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(* -2 (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))))
91.0ms	(* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps)))
43.0ms	(sin (+ (* 1/2 eps) x))

simplify1.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
2	833
1	215
0	97

prune311.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
0.1b	(* (sin (* 1/2 eps)) (cos x))
0.1b	(* (cos (* 1/2 eps)) (sin x))
0.3b	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (* 1/2 eps)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `sum-log` `sin-cos-mult`

Counts

4 → 72

Calls

4 calls:

32.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
19.0ms	(* (sin (* 1/2 eps)) (cos x))
37.0ms	(* (cos (* 1/2 eps)) (sin x))
140.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (* 1/2 eps)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
81.0ms	(* (sin (* 1/2 eps)) (cos x))
64.0ms	(* (cos (* 1/2 eps)) (sin x))
216.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (* 1/2 eps)))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1687
1	350
0	143

prune423.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes285.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.8s	4357×	body	1280	valid
1.3s	1935×	body	640	valid
1.1s	617×	body	2560	valid
365.0ms	707×	body	320	valid
74.0ms	294×	body	160	valid
12.0ms	90×	body	80	valid