Details

sample96.0ms

Algorithm

intervals

Results

42.0ms	96×	body	1280	valid
21.0ms	22×	body	2560	valid
14.0ms	57×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	39×	body	80	valid
2.0ms	17×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize15.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ x eps))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `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:

28.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.3s

Counts

46 → 46

Iterations

Useful iterations: 3 (261.0ms)

Iter	Nodes	Cost
0	91	662
1	198	539
2	547	452
3	2289	388
done	5001	388

prune109.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

16.0ms	(+ (+ x eps) x)
16.0ms	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
21.0ms	(cos (/ (+ (+ x eps) x) 2))

series96.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
52.0ms	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
22.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.4s

Counts

60 → 60

Iterations

Useful iterations: 3 (337.0ms)

Iter	Nodes	Cost
0	99	768
1	234	695
2	717	615
3	2992	551
done	5000	551

prune225.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ (+ 0 eps) 2)) (log1p (expm1 (cos (/ (fma x 2 eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma x 2 eps) 2))))
0.4b	(expm1 (cos (/ (fma x 2 eps) 2)))
4.0b	(cos (/ (fma x 2 eps) 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

13.0ms	(* (sin (/ (+ 0 eps) 2)) (log1p (expm1 (cos (/ (fma x 2 eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma x 2 eps) 2))))
0.0ms	(expm1 (cos (/ (fma x 2 eps) 2)))
2.0ms	(cos (/ (fma x 2 eps) 2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin (/ (+ 0 eps) 2)) (log1p (expm1 (cos (/ (fma x 2 eps) 2)))))
55.0ms	(log1p (expm1 (cos (/ (fma x 2 eps) 2))))
54.0ms	(expm1 (cos (/ (fma x 2 eps) 2)))
28.0ms	(cos (/ (fma x 2 eps) 2))

simplify3.2s

Counts

63 → 63

Iterations

Useful iterations: 3 (232.0ms)

Iter	Nodes	Cost
0	95	903
1	196	763
2	565	667
3	2060	659
done	5001	659

prune265.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (cos (/ (fma x 2 eps) 2))))
0.3b	(* (sin (/ (+ 0 eps) 2)) (expm1 (log1p (cos (/ (fma x 2 eps) 2)))))
0.4b	(log1p (cos (/ (fma x 2 eps) 2)))
4.0b	(cos (/ (fma x 2 eps) 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (log1p (cos (/ (fma x 2 eps) 2))))
13.0ms	(* (sin (/ (+ 0 eps) 2)) (expm1 (log1p (cos (/ (fma x 2 eps) 2)))))
0.0ms	(log1p (cos (/ (fma x 2 eps) 2)))
2.0ms	(cos (/ (fma x 2 eps) 2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(expm1 (log1p (cos (/ (fma x 2 eps) 2))))
80.0ms	(* (sin (/ (+ 0 eps) 2)) (expm1 (log1p (cos (/ (fma x 2 eps) 2)))))
56.0ms	(log1p (cos (/ (fma x 2 eps) 2)))
28.0ms	(cos (/ (fma x 2 eps) 2))

simplify2.9s

Counts

63 → 63

Iterations

Useful iterations: 3 (231.0ms)

Iter	Nodes	Cost
0	91	898
1	179	762
2	507	660
3	1818	656
done	5000	656

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

regimes106.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch129.0ms

Steps

Iters	Range		Point
10	9.278264258908537e-20	9.143643357499823e-08	1.1905404803477009e-08
9	-1.0255030941766934e-06	-9.091202463712598e-16	-8.781839081277773e-09

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	50
1	35	37
done	35	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3282×	body	1280	valid
616.0ms	686×	body	2560	valid
464.0ms	1818×	body	640	valid
124.0ms	736×	body	320	valid
57.0ms	1121×	body	80	valid
39.0ms	357×	body	160	valid