Details

sample168.0ms

Algorithm

intervals

Results

75.0ms	100×	body	1280	valid
39.0ms	29×	body	2560	valid
28.0ms	62×	body	640	valid
6.0ms	24×	body	320	valid
3.0ms	33×	body	80	valid
2.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize20.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
2.2b	(sin (+ x eps))

rewrite96.0ms

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:

87.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series85.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify851.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune250.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `sum-log` `fma-def` `associate-r` `associate-l` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

21.0ms	(+ x (+ x eps))
54.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

series141.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ x (+ x eps))
66.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify890.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
2	1082
1	242
0	99

prune361.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.5b	(expm1 (cos (/ (fma 2 x eps) 2)))
2.3b	(cos (/ (fma 2 x eps) 2))

rewrite36.0ms

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` `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:

28.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
1.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series270.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
83.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
67.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
28.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.3s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	3330
2	667
1	206
0	95

prune450.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.5b	(expm1 (cos (/ (fma 2 x eps) 2)))
2.3b	(cos (/ (fma 2 x eps) 2))

rewrite39.0ms

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` `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:

33.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series326.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
73.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
94.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
43.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.7s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	3330
2	667
1	206
0	95

prune403.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

regimes212.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 15.0b

bsearch170.0ms

Steps

Iters	Range		Point
10	6.967356414530657e-12	13.800596953327334	3.3945064243833135e-09
7	-185496355225.45163	-876554076.2144383	-892737702.6104735

simplify7.0ms

Iterations

Iter	Nodes
done	43
2	43
1	42
0	33

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	3226×	body	1280	valid
1.5s	633×	body	2560	valid
841.0ms	1875×	body	640	valid
225.0ms	760×	body	320	valid
134.0ms	1143×	body	80	valid
57.0ms	363×	body	160	valid