Details

sample246.0ms

Algorithm

intervals

Results

124.0ms	48×	body	2560	valid
73.0ms	97×	body	1280	valid
22.0ms	49×	body	640	valid
9.0ms	32×	body	320	valid
3.0ms	17×	body	160	valid
3.0ms	13×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

14.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
65.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	1941
2	596
1	240
0	106

prune392.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/240 (pow x 5)) (* x (+ 1/2 (* 1/24 (* x x)))))
0.0b	(* x (+ 1/2 (* 1/24 (* x x))))
0.0b	(* 1/240 (pow x 5))
0.2b	(* 1/24 (* x x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1` `associate-r`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
7×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp`

Counts

4 → 79

Calls

4 calls:

7.0ms	(+ (* 1/240 (pow x 5)) (* x (+ 1/2 (* 1/24 (* x x)))))
16.0ms	(* x (+ 1/2 (* 1/24 (* x x))))
23.0ms	(* 1/240 (pow x 5))
13.0ms	(* 1/24 (* x x))

series316.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* 1/240 (pow x 5)) (* x (+ 1/2 (* 1/24 (* x x)))))
122.0ms	(* x (+ 1/2 (* 1/24 (* x x))))
97.0ms	(* 1/240 (pow x 5))
34.0ms	(* 1/24 (* x x))

simplify1.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1546
1	422
0	141

prune443.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/240 (pow x 5)) (+ (* x 1/2) (* x (* 1/24 (* x x)))))
0.0b	(* 1/240 (pow x 5))
0.1b	(* x (* 1/24 (* x x)))
0.2b	(* 1/24 (* x x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`pow1`
15×	`add-sqr-sqrt`
12×	`prod-exp`
10×	`cbrt-unprod`
9×	`-un-lft-identity` `associate-r` `associate-l*` `pow-prod-down` `add-cube-cbrt` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `+-commutative` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 78

Calls

4 calls:

17.0ms	(+ (* 1/240 (pow x 5)) (+ (* x 1/2) (* x (* 1/24 (* x x)))))
9.0ms	(* 1/240 (pow x 5))
40.0ms	(* x (* 1/24 (* x x)))
17.0ms	(* 1/24 (* x x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* 1/240 (pow x 5)) (+ (* x 1/2) (* x (* 1/24 (* x x)))))
70.0ms	(* 1/240 (pow x 5))
53.0ms	(* x (* 1/24 (* x x)))
55.0ms	(* 1/24 (* x x))

simplify1.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1251
1	348
0	130

prune505.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(* (cos x) (cos x))
0.6b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.9b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
3×	`sqr-cos`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`difference-cubes` `+-commutative` `associate-+l+` `sum-log` `sub-neg` `flip3-+` `distribute-rgt-out` `flip3--` `diff-log` `cube-unmult` `pow3` `flip-+` `flip--`

Counts

4 → 80

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
8.0ms	(* (cos x) (cos x))
10.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
28.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (cos x) (cos x))
27.0ms	(* (cos x) (cos x))
48.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
54.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

simplify3.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	4007
2	1234
1	336
0	115

prune420.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

regimes322.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.1b

bsearch136.0ms

Steps

Iters	Range		Point
6	0.0022991053059264813	0.02586244036059231	0.015436630540337124
10	-733100.9210806559	-4.034181863829644e-08	-0.0230098474062637

simplify19.0ms

Iterations

Iter	Nodes
done	55
1	55
0	38

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.6s	1586×	body	2560	valid
2.8s	2748×	body	1280	valid
857.0ms	1855×	body	640	valid
327.0ms	945×	body	320	valid
92.0ms	495×	body	160	valid
39.0ms	7×	body	5120	valid
37.0ms	364×	body	80	valid