Details

sample166.0ms

Algorithm

intervals

Results

62.0ms	98×	body	1280	valid
33.0ms	66×	body	640	valid
27.0ms	29×	body	320	valid
22.0ms	17×	body	2560	valid
3.0ms	34×	body	80	valid
2.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize18.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
4.1b	(sin (+ x eps))

rewrite120.0ms

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:

103.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series98.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify5.2s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.1s)

Iter	Nodes	Cost
0	91	662
1	194	539
2	450	452
3	1388	388
4	4919	374
done	5000	374

prune137.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.9b	(cos (/ (fma 2 x eps) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

21.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series121.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
41.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.9s

Counts

36 → 36

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	68	514
1	144	508
2	341	444
3	687	442
4	1340	431
5	2510	431
done	5001	430

prune182.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (fma 2 x eps) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
0.5b	(log (exp (cos (/ (fma 2 x eps) 2))))
3.9b	(cos (/ (fma 2 x eps) 2))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

11.0ms	(exp (cos (/ (fma 2 x eps) 2)))
56.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
16.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
8.0ms	(cos (/ (fma 2 x eps) 2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (cos (/ (fma 2 x eps) 2)))
72.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
44.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
45.0ms	(cos (/ (fma 2 x eps) 2))

simplify5.4s

Counts

81 → 81

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	112	1186
1	206	1079
2	483	949
3	952	942
4	1920	923
5	3589	923
done	5001	922

prune297.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (* (sqrt (exp (cos (/ (fma 2 x eps) 2)))) (sqrt (exp (cos (/ (fma 2 x eps) 2))))))
0.6b	(* (sqrt (exp (cos (/ (fma 2 x eps) 2)))) (sqrt (exp (cos (/ (fma 2 x eps) 2)))))
3.9b	(cos (/ (fma 2 x eps) 2))
3.9b	(cos (/ (fma 2 x eps) 2))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-pow1`
36×	`add-sqr-sqrt` `exp-prod`
35×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`log-pow`
18×	`sqrt-prod`
16×	`pow1/2` `pow-prod-up`
12×	`pow-prod-down` `pow-sqr`
9×	`add-exp-log`
8×	`swap-sqr`
6×	`associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus` `rem-log-exp` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 113

Calls

4 calls:

76.0ms	(log (* (sqrt (exp (cos (/ (fma 2 x eps) 2)))) (sqrt (exp (cos (/ (fma 2 x eps) 2))))))
49.0ms	(* (sqrt (exp (cos (/ (fma 2 x eps) 2)))) (sqrt (exp (cos (/ (fma 2 x eps) 2)))))
6.0ms	(cos (/ (fma 2 x eps) 2))
4.0ms	(cos (/ (fma 2 x eps) 2))

series152.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(log (* (sqrt (exp (cos (/ (fma 2 x eps) 2)))) (sqrt (exp (cos (/ (fma 2 x eps) 2))))))
58.0ms	(* (sqrt (exp (cos (/ (fma 2 x eps) 2)))) (sqrt (exp (cos (/ (fma 2 x eps) 2)))))
33.0ms	(cos (/ (fma 2 x eps) 2))
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.6s

Counts

125 → 125

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	113	2210
1	203	1432
2	468	1225
3	1082	1179
4	2805	1120
done	5001	1111

prune370.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes93.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.0b

bsearch135.0ms

Steps

Iters	Range		Point
11	8.666561730544872e-18	9556.682540875734	9.496762876577125e-09
7	-0.006495210018506858	-9.497075983896804e-05	-9.642672794131258e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	50
1	32	50
done	32	50

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3297×	body	1280	valid
1.2s	1868×	body	640	valid
674.0ms	598×	body	2560	valid
162.0ms	799×	body	320	valid
71.0ms	1091×	body	80	valid
47.0ms	347×	body	160	valid