Details

sample92.0ms

Algorithm

intervals

Results

39.0ms	97×	body	1280	valid
22.0ms	25×	body	2560	valid
14.0ms	61×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
2.3b	(sin (+ x eps))

rewrite66.0ms

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:

55.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series67.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify3.4s

Counts

46 → 46

Iterations

Useful iterations: 4 (2.1s)

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

prune100.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.5b	(cos (/ (fma 2 x eps) 2))

rewrite19.0ms

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:

14.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series81.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.2s

Counts

36 → 36

Iterations

Useful iterations: done (3.2s)

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

prune117.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
0.5b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
2.5b	(cos (/ (fma 2 x eps) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

22.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
3.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
2.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
4.0ms	(cos (/ (fma 2 x eps) 2))

series158.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
47.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
30.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.9s

Counts

105 → 105

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	122	1694
1	249	1400
2	717	1252
3	3873	1232
done	5000	1231

prune253.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

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))))
2.5b	(cos (/ (fma 2 x eps) 2))

rewrite44.0ms

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:

5.0ms	(exp (cos (/ (fma 2 x eps) 2)))
22.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
11.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
4.0ms	(cos (/ (fma 2 x eps) 2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (cos (/ (fma 2 x eps) 2)))
49.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
28.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.0s

Counts

81 → 81

Iterations

Useful iterations: done (4.0s)

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

prune229.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes89.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 14.5b

bsearch110.0ms

Steps

Iters	Range		Point
7	1.2981949479042878e-19	3.175736471147199e-18	3.144339914669044e-18
11	-2.8163082396285558e+17	-1.4864914298183363e-09	-8.131893915803983e-09

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	50
1	32	37
done	32	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3272×	body	1280	valid
632.0ms	678×	body	2560	valid
448.0ms	1845×	body	640	valid
114.0ms	736×	body	320	valid
54.0ms	1118×	body	80	valid
44.0ms	351×	body	160	valid