Details

sample177.0ms

Algorithm

intervals

Results

88.0ms	143×	body	1280	valid
34.0ms	25×	body	2560	valid
32.0ms	50×	body	640	valid
8.0ms	29×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite54.0ms

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:

43.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series96.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (cos (+ x eps)) (cos x))
25.0ms	(cos (+ x eps))

simplify3.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3416
3	1175
2	423
1	200
0	91

prune234.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
3.7b	(sin (/ (fma 2 x eps) 2))

rewrite100.0ms

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:

54.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
39.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series222.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
84.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
39.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	2079
2	599
1	222
0	97

prune496.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
0.1b	(expm1 (log1p (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
3.7b	(sin (/ (fma 2 x eps) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `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 → 52

Calls

4 calls:

0.0ms	(log1p (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (log1p (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))))
17.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(log1p (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
142.0ms	(expm1 (log1p (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))))
87.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
37.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.7s

Counts

64 → 64

Iterations

Iter	Nodes
done	5002
4	2230
3	977
2	385
1	183
0	91

prune545.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* 1/2 eps)) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
0.5b	(log1p (sin (/ (fma 2 x eps) 2)))
3.7b	(sin (/ (fma 2 x eps) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
15.0ms	(* (sin (* 1/2 eps)) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
1.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
13.0ms	(sin (/ (fma 2 x eps) 2))

series314.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
137.0ms	(* (sin (* 1/2 eps)) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
54.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
40.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.1s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
4	2018
3	898
2	403
1	173
0	86

prune415.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes212.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch185.0ms

Steps

Iters	Range		Point
8	9.663324920224664e-10	1.054768169099283e-06	1.0360142885107461e-06
10	-2.725519985046895e-08	-4.357977289634356e-25	-2.6849380613362534e-08

simplify7.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.4s	4429×	body	1280	valid
1.2s	671×	body	2560	valid
876.0ms	1838×	body	640	valid
169.0ms	710×	body	320	valid
46.0ms	284×	body	160	valid
5.0ms	68×	body	80	valid