Details

sample179.0ms

Algorithm

intervals

Results

84.0ms	48×	body	2560	valid
51.0ms	89×	body	1280	valid
21.0ms	62×	body	640	valid
7.0ms	27×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	11×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:

16.0ms	(/ (- 1.0 (cos x)) (sin x))
10.0ms	(- 1.0 (cos x))

series472.0ms

Counts

2 → 6

Calls

2 calls:

435.0ms	(/ (- 1.0 (cos x)) (sin x))
36.0ms	(- 1.0 (cos x))

simplify808.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune401.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(* (cos x) (cos x))
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.9b	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

rewrite83.0ms

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`
5×	`sqr-cos`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`distribute-rgt-in` `difference-cubes` `+-commutative` `associate-+l+` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `distribute-rgt-out` `flip3--` `diff-log` `cube-unmult` `pow3` `flip-+` `flip--`

Counts

4 → 82

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
11.0ms	(* (cos x) (cos x))
19.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
42.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cos x) (cos x))
32.0ms	(* (cos x) (cos x))
52.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
67.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

simplify2.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	2710
1	357
0	121

prune606.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.5b	(log (exp (* (cos x) (cos x))))
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.9b	(- (* (* 1.0 1.0) 1.0) (* (cos x) (log (exp (* (cos x) (cos x))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`pow1` `log-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-log-exp`
8×	`associate--r+`
6×	`add-cbrt-cube` `add-exp-log`
5×	`sqr-cos`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`swap-sqr` `associate-r` `associate-l` `exp-sum` `log-pow`
1×	`pow2` `+-commutative` `associate-+l+` `exp-prod` `sum-log` `sub-neg` `flip3-+` `pow-plus` `distribute-rgt-out` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

12.0ms	(* (cos x) (cos x))
3.0ms	(log (exp (* (cos x) (cos x))))
10.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
21.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (log (exp (* (cos x) (cos x))))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (cos x) (cos x))
23.0ms	(log (exp (* (cos x) (cos x))))
62.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
88.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (log (exp (* (cos x) (cos x))))))

simplify2.7s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	2772
1	406
0	152

prune563.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
12×	`pow1`
11×	`add-cube-cbrt`
9×	`sqr-pow`
8×	`add-log-exp`
7×	`add-cbrt-cube` `add-exp-log`
5×	`distribute-lft-out--`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
1×	`pow2` `cube-mult` `pow-to-exp` `difference-cubes` `+-commutative` `sqr-cos` `sum-log` `sub-neg` `pow-pow` `flip3-+` `pow-plus` `flip3--` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
3.0ms	(pow (cos x) 3)
5.0ms	(+ (cos x) 1.0)
32.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series149.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cos x) (cos x))
36.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
71.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify4.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	3372
1	420
0	154

prune508.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.1b

regimes219.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.2b

bsearch177.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.021750215377787423
8	-0.9341403346610884	-0.003292329160956242	-0.02366290210440796

simplify10.0ms

Iterations

Iter	Nodes
done	58
1	58
0	43

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.5s	1619×	body	2560	valid
2.9s	2702×	body	1280	valid
909.0ms	1905×	body	640	valid
295.0ms	923×	body	320	valid
99.0ms	502×	body	160	valid
75.0ms	4×	body	5120	valid
38.0ms	345×	body	80	valid