Details

sample137.0ms

Algorithm

intervals

Results

55.0ms	109×	body	1280	valid
43.0ms	63×	body	640	valid
14.0ms	14×	body	2560	valid
5.0ms	23×	body	320	valid
3.0ms	38×	body	80	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize11.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.0b	(sin (+ x eps))

rewrite62.0ms

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:

53.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify838.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune177.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
2.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite70.0ms

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:

14.0ms	(+ x (+ x eps))
24.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
30.0ms	(cos (/ (+ x (+ x eps)) 2))

series154.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ x (+ x eps))
85.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
41.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify902.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
2	1082
1	242
0	99

prune418.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.5b	(expm1 (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite33.0ms

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:

0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
27.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
1.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series280.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
96.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
90.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
31.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.8s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	3316
2	662
1	206
0	95

prune388.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ (+ eps 0) 2)) (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite40.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

36.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series91.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (fma 2 x eps) 2)))
33.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.3s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	3222
2	521
1	152
0	70

prune183.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

regimes215.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.9b

bsearch199.0ms

Steps

Iters	Range		Point
8	3.3185797753340088e-09	5.09324609688744e-06	6.520854844146571e-09
11	-938.9819325385033	-2.717163482503313e-19	-1.3793080901766334e-08

simplify3.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.4s	3263×	body	1280	valid
1.1s	652×	body	2560	valid
880.0ms	1858×	body	640	valid
205.0ms	768×	body	320	valid
129.0ms	370×	body	160	valid
81.0ms	1089×	body	80	valid