Details

sample325.0ms

Algorithm

intervals

Results

92.0ms	51×	body	2560	valid
79.0ms	73×	body	1280	valid
53.0ms	74×	body	80	valid
43.0ms	38×	body	640	valid
7.0ms	14×	body	320	valid
3.0ms	1×	body	5120	valid
2.0ms	5×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	1501
10	1501
9	1489
8	1336
7	1246
6	1065
5	802
4	460
3	223
2	98
1	42
0	23

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.6b

localize34.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ t (/ (/ 16.0 (+ (* 2.0 y) 1.0)) z))
3.6b	(* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))
32.5b	(cos (/ t (/ (/ 16.0 (+ (* 2.0 y) 1.0)) z)))
32.7b	(cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

435×	`times-frac`
203×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
49×	`associate-/r*`
25×	`associate-/r/`
22×	`add-cbrt-cube` `add-exp-log`
17×	`div-inv`
14×	`flip3-+` `flip-+`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-*l/` `add-log-exp`
3×	`associate-r` `pow-prod-down` `associate-/l*`
2×	`distribute-rgt-in` `frac-times` `cos-sum` `distribute-lft-in` `associate-*r/`
1×	`clear-num` `frac-2neg` `associate-l` `*-commutative`

Counts

4 → 259

Calls

4 calls:

39.0ms	(/ t (/ (/ 16.0 (+ (* 2.0 y) 1.0)) z))
29.0ms	(* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))
34.0ms	(cos (/ t (/ (/ 16.0 (+ (* 2.0 y) 1.0)) z)))
15.0ms	(cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ t (/ (/ 16.0 (+ (* 2.0 y) 1.0)) z))
106.0ms	(* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))
45.0ms	(cos (/ t (/ (/ 16.0 (+ (* 2.0 y) 1.0)) z)))
39.0ms	(cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a))))

simplify993.0ms

Counts

271 → 271

Iterations

Iter	Nodes
done	5000
1	1862
0	625

prune3.5s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 38.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* 1 x) (cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))))
3.6b	(* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))
32.7b	(cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
17×	`add-cbrt-cube`
13×	`pow1`
10×	`prod-exp`
8×	`cbrt-unprod`
6×	`associate-r` `pow-prod-down`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-*l/`
3×	`add-log-exp`
2×	`distribute-rgt-in` `frac-times` `cos-sum` `distribute-lft-in` `flip3-+` `associate-l` `associate-r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `1-exp` `div-exp`

Counts

3 → 55

Calls

3 calls:

49.0ms	(* (* 1 x) (cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))))
36.0ms	(* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))
29.0ms	(cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a))))

series251.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* (* 1 x) (cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))))
111.0ms	(* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a)))
39.0ms	(cos (* (* (/ t 16.0) b) (+ 1.0 (* 2.0 a))))

simplify1.3s

Counts

64 → 64

Iterations

Iter	Nodes
done	5002
2	2508
1	431
0	143

prune846.0ms

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 36.8b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune313.0ms

Pruning

42 alts after pruning (41 fresh and 1 done)

Merged error: 36.8b

localize34.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
16.3b	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
16.3b	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
32.4b	(cos (* (* (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0))) (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))) (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))))

rewrite574.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-div` `associate-*r/`
6×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
3×	`cbrt-prod` `pow1/3`

Counts

4 → 49

Calls

4 calls:

27.0ms	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
26.0ms	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
41.0ms	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
478.0ms	(cos (* (* (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0))) (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))) (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))))

series998.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
304.0ms	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
278.0ms	(cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))
104.0ms	(cos (* (* (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0))) (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))) (cbrt (* (* b (+ (* a 2.0) 1.0)) (/ t 16.0)))))

simplify815.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
2	1078
1	318
0	131

prune479.0ms

Pruning

48 alts after pruning (47 fresh and 1 done)

Merged error: 36.6b

regimes3.8s

Accuracy

1.8% (5.9b remaining)

Error of 44.7b against oracle of 38.8b and baseline of 44.8b

bsearch142.0ms

Steps

Iters	Range		Point
10	-1.0076512181867778e-305	4.3203036243623476e-301	8.22762172872154e-310

simplify4.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.0s	1761×	body	2560	valid
2.5s	2293×	body	1280	valid
906.0ms	1158×	body	640	valid
261.0ms	1958×	body	80	valid
234.0ms	525×	body	320	valid
117.0ms	34×	body	5120	valid
88.0ms	271×	body	160	valid