Details

sample195.0ms

Algorithm

intervals

Results

111.0ms	111×	body	1280	valid
30.0ms	20×	body	2560	valid
25.0ms	56×	body	640	valid
7.0ms	23×	body	320	valid
4.0ms	36×	body	80	valid
2.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ eps x)) (sin x))
2.3b	(sin (+ eps x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

89.0ms	(- (sin (+ eps x)) (sin x))
8.0ms	(sin (+ eps x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (sin (+ eps x)) (sin x))
26.0ms	(sin (+ eps x))

simplify758.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	705
1	195
0	90

prune283.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
0.1b	(* (sin eps) (cos x))
0.2b	(* (sin x) (- (cos eps) 1))
1.2b	(- (cos eps) 1)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity` `prod-diff`
39×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
10×	`associate-r`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `fma-neg` `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` `expm1-def` `sum-log` `fma-def` `flip3-+` `diff-log` `flip-+`

Counts

4 → 138

Calls

4 calls:

28.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
9.0ms	(* (sin eps) (cos x))
28.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(- (cos eps) 1)

series291.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
56.0ms	(* (sin eps) (cos x))
72.0ms	(* (sin x) (- (cos eps) 1))
21.0ms	(- (cos eps) 1)

simplify1.8s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	3018
1	591
0	228

prune951.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (sin eps) (cos x)))
0.1b	(* (sin eps) (cos x))
1.2b	(- (cos eps) 1)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`expm1-def` `sub-neg` `flip3--` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-cos-mult` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

0.0ms	(fma (sin x) (- (cos eps) 1) (* (sin eps) (cos x)))
18.0ms	(* (sin eps) (cos x))
14.0ms	(- (cos eps) 1)

series282.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(fma (sin x) (- (cos eps) 1) (* (sin eps) (cos x)))
70.0ms	(* (sin eps) (cos x))
29.0ms	(- (cos eps) 1)

simplify801.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1077
1	307
0	136

prune559.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (cos x) (sin eps) (fma (sin x) (cos eps) (- (sin x))))
1.2b	(fma (sin x) (cos eps) (- (sin x)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma (cos x) (sin eps) (fma (sin x) (cos eps) (- (sin x))))
1.0ms	(fma (sin x) (cos eps) (- (sin x)))

series268.0ms

Counts

2 → 6

Calls

2 calls:

191.0ms	(fma (cos x) (sin eps) (fma (sin x) (cos eps) (- (sin x))))
77.0ms	(fma (sin x) (cos eps) (- (sin x)))

simplify804.0ms

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	1200
2	256
1	79
0	43

prune187.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes207.0ms

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	32
3	32
2	29
1	25
0	14

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.9s	3320×	body	1280	valid
1.2s	1868×	body	640	valid
1.0s	637×	body	2560	valid
229.0ms	725×	body	320	valid
95.0ms	1106×	body	80	valid
62.0ms	344×	body	160	valid