Details

sample228.0ms

Algorithm

intervals

Results

102.0ms	51×	body	2560	valid
58.0ms	73×	body	1280	valid
19.0ms	38×	body	640	valid
11.0ms	74×	body	80	valid
5.0ms	14×	body	320	valid
3.0ms	1×	body	5120	valid
1.0ms	5×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	1777
10	1777
9	1741
8	1551
7	1453
6	1243
5	902
4	507
3	233
2	101
1	44
0	23

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.6b

localize65.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (/ z 16.0) t) (fma 2.0 y 1.0))
3.6b	(* (* (/ b 16.0) t) (fma a 2.0 1.0))
32.6b	(cos (* (* (/ z 16.0) t) (fma 2.0 y 1.0)))
32.7b	(cos (* (* (/ b 16.0) t) (fma a 2.0 1.0)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
10×	`prod-exp` `cbrt-unprod`
8×	`fma-udef`
6×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `add-cube-cbrt`
4×	`distribute-rgt-in` `expm1-log1p-u` `cos-sum` `distribute-lft-in` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

25.0ms	(* (* (/ z 16.0) t) (fma 2.0 y 1.0))
24.0ms	(* (* (/ b 16.0) t) (fma a 2.0 1.0))
31.0ms	(cos (* (* (/ z 16.0) t) (fma 2.0 y 1.0)))
26.0ms	(cos (* (* (/ b 16.0) t) (fma a 2.0 1.0)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (* (/ z 16.0) t) (fma 2.0 y 1.0))
83.0ms	(* (* (/ b 16.0) t) (fma a 2.0 1.0))
31.0ms	(cos (* (* (/ z 16.0) t) (fma 2.0 y 1.0)))
38.0ms	(cos (* (* (/ b 16.0) t) (fma a 2.0 1.0)))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	2515
1	436
0	182

prune1.0s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 38.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos (* (* z t) 0.0625)) x) (cos (* (* (/ b 16.0) t) (fma a 2.0 1.0))))
3.6b	(* (* (/ b 16.0) t) (fma a 2.0 1.0))
25.0b	(cos (* (* z t) 0.0625))
32.7b	(cos (* (* (/ b 16.0) t) (fma a 2.0 1.0)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `add-cube-cbrt`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate-l` `associate-l/` `-commutative`
1×	`cbrt-undiv` `div-exp`

Counts

4 → 65

Calls

4 calls:

90.0ms	(* (* (cos (* (* z t) 0.0625)) x) (cos (* (* (/ b 16.0) t) (fma a 2.0 1.0))))
29.0ms	(* (* (/ b 16.0) t) (fma a 2.0 1.0))
12.0ms	(cos (* (* z t) 0.0625))
22.0ms	(cos (* (* (/ b 16.0) t) (fma a 2.0 1.0)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (* (cos (* (* z t) 0.0625)) x) (cos (* (* (/ b 16.0) t) (fma a 2.0 1.0))))
104.0ms	(* (* (/ b 16.0) t) (fma a 2.0 1.0))
20.0ms	(cos (* (* z t) 0.0625))
53.0ms	(cos (* (* (/ b 16.0) t) (fma a 2.0 1.0)))

simplify964.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	2142
1	354
0	149

prune1.1s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 37.3b

localize83.0ms

Local error

Found 4 expressions with local error:

25.9b	(sin (* (/ (* t b) 16.0) 1.0))
25.9b	(cos (* (/ (* t b) 16.0) 1.0))
26.7b	(sin (/ (* (* t b) (* a 2.0)) 16.0))
27.3b	(cos (/ (* (* t b) (* a 2.0)) 16.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

9.0ms	(sin (* (/ (* t b) 16.0) 1.0))
6.0ms	(cos (* (/ (* t b) 16.0) 1.0))
3.0ms	(sin (/ (* (* t b) (* a 2.0)) 16.0))
3.0ms	(cos (/ (* (* t b) (* a 2.0)) 16.0))

series111.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sin (* (/ (* t b) 16.0) 1.0))
20.0ms	(cos (* (/ (* t b) 16.0) 1.0))
30.0ms	(sin (/ (* (* t b) (* a 2.0)) 16.0))
31.0ms	(cos (/ (* (* t b) (* a 2.0)) 16.0))

simplify2.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
8	4683
7	1982
6	1257
5	842
4	525
3	320
2	168
1	93
0	64

prune1.1s

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 37.2b

localize92.0ms

Local error

Found 4 expressions with local error:

26.0b	(sin (* (/ 1.0 (/ 16.0 t)) b))
26.0b	(sin (* (/ 1.0 (/ 16.0 t)) b))
26.7b	(sin (/ (* (* t b) (* a 2.0)) 16.0))
27.3b	(cos (/ (* (* t b) (* a 2.0)) 16.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

6.0ms	(sin (* (/ 1.0 (/ 16.0 t)) b))
22.0ms	(sin (* (/ 1.0 (/ 16.0 t)) b))
6.0ms	(sin (/ (* (* t b) (* a 2.0)) 16.0))
6.0ms	(cos (/ (* (* t b) (* a 2.0)) 16.0))

series115.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sin (* (/ 1.0 (/ 16.0 t)) b))
31.0ms	(sin (* (/ 1.0 (/ 16.0 t)) b))
32.0ms	(sin (/ (* (* t b) (* a 2.0)) 16.0))
21.0ms	(cos (/ (* (* t b) (* a 2.0)) 16.0))

simplify2.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
8	3721
7	1641
6	1110
5	751
4	471
3	296
2	152
1	82
0	54

prune515.0ms

Pruning

43 alts after pruning (43 fresh and 0 done)

Merged error: 37.2b

regimes2.6s

Accuracy

11.9% (5.2b remaining)

Error of 44.4b against oracle of 39.2b and baseline of 45.1b

bsearch129.0ms

Steps

Iters	Range		Point
5	-1.875294936264292e+40	-8.077195036329744e+39	-1.179840817454973e+40

simplify4.0ms

Iterations

Iter	Nodes
done	44
1	44
0	33

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.4s	1761×	body	2560	valid
2.2s	2293×	body	1280	valid
813.0ms	1158×	body	640	valid
462.0ms	1958×	body	80	valid
170.0ms	525×	body	320	valid
91.0ms	34×	body	5120	valid
62.0ms	271×	body	160	valid