Details

sample146.0ms

Algorithm

intervals

Results

70.0ms	109×	body	1280	valid
28.0ms	23×	body	2560	valid
23.0ms	57×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	35×	body	80	valid
2.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize18.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite71.0ms

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:

61.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify729.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

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)))
3.4b	(cos (/ (+ x (+ x eps)) 2))

rewrite93.0ms

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:

24.0ms	(+ x (+ x eps))
30.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
36.0ms	(cos (/ (+ x (+ x eps)) 2))

series131.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ x (+ x eps))
50.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ x eps)) 2)))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify926.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
2	1082
1	242
0	99

prune338.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (cos (/ (fma 2 x eps) 2))))
0.2b	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
0.4b	(log1p (cos (/ (fma 2 x eps) 2)))
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite26.0ms

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 (cos (/ (fma 2 x eps) 2))))
22.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series306.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(expm1 (log1p (cos (/ (fma 2 x eps) 2))))
110.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
92.0ms	(log1p (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.2s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	3215
2	620
1	190
0	91

prune488.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(log1p (cbrt (pow (cos (/ (fma x 2 eps) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (fma x 2 eps) 2)) 3))
0.5b	(pow (cos (/ (fma x 2 eps) 2)) 3)
3.4b	(cos (/ (fma x 2 eps) 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`unpow-prod-down` `cube-prod`
5×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log`
4×	`log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `log1p-udef` `pow-pow` `pow1/3` `pow-exp` `log1p-expm1` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

0.0ms	(log1p (cbrt (pow (cos (/ (fma x 2 eps) 2)) 3)))
3.0ms	(cbrt (pow (cos (/ (fma x 2 eps) 2)) 3))
5.0ms	(pow (cos (/ (fma x 2 eps) 2)) 3)
6.0ms	(cos (/ (fma x 2 eps) 2))

series219.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(log1p (cbrt (pow (cos (/ (fma x 2 eps) 2)) 3)))
42.0ms	(cbrt (pow (cos (/ (fma x 2 eps) 2)) 3))
59.0ms	(pow (cos (/ (fma x 2 eps) 2)) 3)
39.0ms	(cos (/ (fma x 2 eps) 2))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1120
1	224
0	91

prune505.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

regimes255.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.2b

bsearch241.0ms

Steps

Iters	Range		Point
10	4.323010966332037e-21	8.465211478171325e-06	8.245159560248623e-09
11	-496427297.3881253	-4.632829109756021e-12	-8.79028981561156e-09

simplify4.0ms

Iterations

Iter	Nodes
done	38
1	38
0	31

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.2s	3204×	body	1280	valid
1.3s	622×	body	2560	valid
958.0ms	1922×	body	640	valid
352.0ms	829×	body	320	valid
109.0ms	353×	body	160	valid
92.0ms	1070×	body	80	valid