Details

sample189.0ms

Algorithm

intervals

Results

110.0ms	148×	body	1280	valid
32.0ms	19×	body	2560	valid
27.0ms	60×	body	640	valid
6.0ms	19×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

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: 40.2b

localize25.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite65.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series94.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify3.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3416
3	1158
2	424
1	202
0	93

prune183.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

36.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
8.0ms	(sin (/ (fma 2 x eps) 2))

series113.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
40.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.6s

Counts

38 → 38

Iterations

Iter	Nodes
done	5001
4	2076
3	859
2	333
1	147
0	71

prune317.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
0.1b	(expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `sin-mult` `expm1-udef` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

0.0ms	(log1p (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
1.0ms	(expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
51.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
7.0ms	(sin (/ (fma 2 x eps) 2))

series359.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(log1p (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
100.0ms	(expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
66.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
45.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.7s

Counts

68 → 68

Iterations

Iter	Nodes
done	5004
4	2685
3	995
2	393
1	195
0	98

prune551.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

3.0b	(sin (/ (fma 2 x eps) 2))
5.7b	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
5.7b	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
5.7b	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 52

Calls

4 calls:

8.0ms	(sin (/ (fma 2 x eps) 2))
2.0ms	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
2.0ms	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
2.0ms	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))

series788.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sin (/ (fma 2 x eps) 2))
250.0ms	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
273.0ms	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))
231.0ms	(cbrt (expm1 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))))

simplify2.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5019
4	2380
3	808
2	282
1	134
0	69

prune591.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

regimes300.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.5b

bsearch198.0ms

Steps

Iters	Range		Point
8	0.113095154289168	29.100869698027953	0.11407284983207572
10	-1.4244285555183042e-05	-9.550132857780223e-23	-4.028105222915818e-06

simplify7.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.9s	4454×	body	1280	valid
1.5s	658×	body	2560	valid
960.0ms	1824×	body	640	valid
245.0ms	696×	body	320	valid
55.0ms	286×	body	160	valid
8.0ms	82×	body	80	valid