Details

sample154.0ms

Algorithm

intervals

Results

94.0ms	140×	body	1280	valid
19.0ms	17×	body	2560	valid
18.0ms	60×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	5×	body	80	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite37.0ms

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` `cos-sum` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

24.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series110.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify1.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune299.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b	(* (sin x) (sin eps))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

13.0ms	(* (cos x) (cos eps))
15.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
65.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series473.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos x) (cos eps))
114.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
81.0ms	(* (sin x) (sin eps))
206.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify2.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1785
1	407
0	168

prune727.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin eps) (sin x))
0.3b	(* (sin eps) (sin x))
2.6b	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))) (cos x)))
52.2b	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`associate-+r+`
9×	`prod-diff` `add-log-exp`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-udef`
2×	`sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `associate--l+` `flip-+` `distribute-lft-out--`

Counts

4 → 85

Calls

4 calls:

18.0ms	(* (sin eps) (sin x))
18.0ms	(* (sin eps) (sin x))
28.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))) (cos x)))
0.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin eps) (sin x))
86.0ms	(* (sin eps) (sin x))
269.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))) (cos x)))
69.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1169
1	296
0	129

prune842.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.1b

localize68.0ms

Local error

Found 4 expressions with local error:

2.6b	(fma (cos x) (cos eps) (fma (- (sin eps)) (sin x) (- (* (* (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))) (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))))) (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))))) (cos x))))
52.2b	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))
52.2b	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))
52.2b	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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

4 → 40

Calls

4 calls:

0.0ms	(fma (cos x) (cos eps) (fma (- (sin eps)) (sin x) (- (* (* (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))) (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))))) (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))))) (cos x))))
0.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))
0.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))
1.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(fma (cos x) (cos eps) (fma (- (sin eps)) (sin x) (- (* (* (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))) (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))))) (cbrt (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))))) (cos x))))
79.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))
81.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))
77.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

simplify1.3s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	961
2	234
1	92
0	49

prune430.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 15.1b

regimes412.0ms

Accuracy

84.3% (1.6b remaining)

Error of 16.2b against oracle of 14.6b and baseline of 24.7b

bsearch231.0ms

Steps

Iters	Range		Point
9	3.4817375791661903e-26	2.0892179653459966e-19	2.0653104270896466e-19
9	-0.007136466459190441	-3.2432757514909933e-09	-8.743701952491837e-07

simplify24.0ms

Iterations

Iter	Nodes
done	61
3	61
2	57
1	49
0	35

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.7s	4431×	body	1280	valid
1.1s	1841×	body	640	valid
879.0ms	650×	body	2560	valid
181.0ms	743×	body	320	valid
41.0ms	255×	body	160	valid
7.0ms	80×	body	80	valid