Details

sample204.0ms

Algorithm

intervals

Results

125.0ms	157×	body	1280	valid
30.0ms	59×	body	640	valid
26.0ms	17×	body	2560	valid
3.0ms	11×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	4×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	202
1	9	202
2	10	202
done	10	202

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize24.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
4.4b	(cos (+ x eps))

rewrite20.0ms

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:

12.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series114.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

simplify4.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	91	15621
1	200	13865
2	423	12143
3	1175	11978
4	3416	10474
done	5001	10474

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
4.3b	(sin (/ (fma 2 x eps) 2))

rewrite63.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

32.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
27.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series234.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
85.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
48.0ms	(sin (/ (fma 2 x eps) 2))

simplify3.6s

Counts

60 → 60

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	99	21123
1	221	19859
2	588	19567
3	1898	19542
done	5003	19266

prune365.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* 1/2 eps))) (sin (fma eps 1/2 x)))
4.3b	(sin (fma eps 1/2 x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `sin-sum` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 32

Calls

2 calls:

47.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (fma eps 1/2 x)))
2.0ms	(sin (fma eps 1/2 x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (fma eps 1/2 x)))
43.0ms	(sin (fma eps 1/2 x))

simplify6.3s

Counts

38 → 38

Iterations

Useful iterations: 4 (4.8s)

Iter	Nodes	Cost
0	77	12594
1	194	11540
2	581	11460
3	1902	11355
4	4868	11325
done	5000	11325

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (* 1/2 eps)) (cos x))
0.1b	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
0.2b	(* (cos (* eps 1/2)) (sin x))
0.2b	(* (* -2 (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* eps 1/2)) (sin x))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in` `sin-cos-mult`

Counts

4 → 79

Calls

4 calls:

21.0ms	(* (sin (* 1/2 eps)) (cos x))
21.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
14.0ms	(* (cos (* eps 1/2)) (sin x))
98.0ms	(* (* -2 (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* eps 1/2)) (sin x))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin (* 1/2 eps)) (cos x))
158.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
58.0ms	(* (cos (* eps 1/2)) (sin x))
171.0ms	(* (* -2 (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* eps 1/2)) (sin x))))

simplify3.1s

Counts

91 → 91

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	164	37656
1	458	34430
2	1588	32979
done	5000	32809

prune572.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes425.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	499
1	17	499
done	17	499

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.4s	4415×	body	1280	valid
1.4s	675×	body	2560	valid
959.0ms	1868×	body	640	valid
231.0ms	685×	body	320	valid
46.0ms	268×	body	160	valid
8.0ms	89×	body	80	valid