Details

sample160.0ms

Algorithm

intervals

Results

87.0ms	121×	body	1280	valid
24.0ms	57×	body	640	valid
23.0ms	17×	body	2560	valid
5.0ms	15×	body	320	valid
3.0ms	37×	body	80	valid
2.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize22.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite123.0ms

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:

107.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series111.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (sin (+ x eps)) (sin x))
31.0ms	(sin (+ x eps))

simplify3.5s

Counts

46 → 46

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	90	15578
1	201	13858
2	445	12111
3	1287	11911
4	3880	10418
done	5002	10394

prune200.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2))))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
4.4b	(cos (/ (fma 2 x eps) 2))

rewrite57.0ms

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-cos-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

34.0ms	(* 2 (* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2))))
17.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series175.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* 2 (* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2))))
62.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
30.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.0s

Counts

60 → 60

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	95	21181
1	231	19837
2	630	19732
3	2134	19500
done	5001	19166

prune420.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (fma 1/2 eps x)) (* 2 (sin (* 1/2 eps))))
4.4b	(cos (fma 1/2 eps x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

38.0ms	(* (cos (fma 1/2 eps x)) (* 2 (sin (* 1/2 eps))))
2.0ms	(cos (fma 1/2 eps x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(* (cos (fma 1/2 eps x)) (* 2 (sin (* 1/2 eps))))
27.0ms	(cos (fma 1/2 eps x))

simplify5.6s

Counts

36 → 36

Iterations

Useful iterations: 4 (3.9s)

Iter	Nodes	Cost
0	69	11075
1	160	10222
2	440	10141
3	1318	10031
4	4771	9964
done	5000	9964

prune218.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cos-mult` `cbrt-unprod` `sin-mult`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (cos (* 1/2 eps)) (cos x))
40.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
27.0ms	(* (sin (* 1/2 eps)) (sin x))
152.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (* 2 (sin (* 1/2 eps))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (cos (* 1/2 eps)) (cos x))
147.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
91.0ms	(* (sin (* 1/2 eps)) (sin x))
188.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (* 2 (sin (* 1/2 eps))))

simplify2.4s

Counts

96 → 96

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	156	38302
1	393	36139
2	1248	35964
done	5000	35062

prune712.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes248.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	499
1	22	499
2	24	499
done	24	499

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.9s	3270×	body	1280	valid
1.5s	675×	body	2560	valid
1.1s	1838×	body	640	valid
294.0ms	759×	body	320	valid
97.0ms	1124×	body	80	valid
59.0ms	334×	body	160	valid