Details

sample256.0ms

Algorithm

intervals

Results

131.0ms	59×	body	2560	valid
64.0ms	74×	body	1280	valid
28.0ms	60×	body	640	valid
13.0ms	36×	body	320	valid
3.0ms	12×	body	160	valid
2.0ms	15×	body	80	valid

simplify34.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize85.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite89.0ms

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--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 54

Calls

2 calls:

67.0ms	(/ (- 1.0 (cos x)) (sin x))
15.0ms	(- 1.0 (cos x))

series135.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- 1.0 (cos x)) (sin x))
53.0ms	(- 1.0 (cos x))

simplify3.8s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	1811
2	583
1	242
0	108

prune726.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize150.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* x x) 1/24) 1/2)
0.0b	(* (pow x 5) 1/240)
0.1b	(* x (+ (* (* x x) 1/24) 1/2))
0.4b	(* (* x x) 1/24)

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1` `associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
7×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `+-commutative` `sum-log` `distribute-lft-in` `pow-exp`

Counts

4 → 81

Calls

4 calls:

74.0ms	(+ (* (* x x) 1/24) 1/2)
45.0ms	(* (pow x 5) 1/240)
154.0ms	(* x (+ (* (* x x) 1/24) 1/2))
67.0ms	(* (* x x) 1/24)

series400.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (* (* x x) 1/24) 1/2)
90.0ms	(* (pow x 5) 1/240)
155.0ms	(* x (+ (* (* x x) 1/24) 1/2))
45.0ms	(* (* x x) 1/24)

simplify3.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1273
1	382
0	132

prune970.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize149.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (* (* x x) 1/24)) (* x 1/2))
0.0b	(* (pow x 5) 1/240)
0.1b	(* x (* (* x x) 1/24))
0.4b	(* (* x x) 1/24)

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`pow1`
15×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`associate-l`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `flip3-+` `pow-exp` `flip-+` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

155.0ms	(+ (* x (* (* x x) 1/24)) (* x 1/2))
42.0ms	(* (pow x 5) 1/240)
115.0ms	(* x (* (* x x) 1/24))
46.0ms	(* (* x x) 1/24)

series390.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(+ (* x (* (* x x) 1/24)) (* x 1/2))
109.0ms	(* (pow x 5) 1/240)
59.0ms	(* x (* (* x x) 1/24))
59.0ms	(* (* x x) 1/24)

simplify10.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	4879
2	1036
1	328
0	129

prune774.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize192.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.2b	(* (cos x) (cos x))
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.7b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

rewrite179.0ms

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`
4×	`insert-posit16`
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 → 84

Calls

4 calls:

36.0ms	(* (cos x) (cos x))
31.0ms	(* (cos x) (cos x))
39.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
69.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos x))
27.0ms	(* (cos x) (cos x))
90.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
96.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

simplify9.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	4376
2	1264
1	340
0	118

prune901.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes542.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 32.5b

bsearch5.0ms

simplify35.0ms

Iterations

Iter	Nodes
done	53
1	53
0	40

end0.0ms

sample9.8s

Algorithm

intervals

Results

4.1s	1531×	body	2560	valid
2.8s	2750×	body	1280	valid
1.6s	1947×	body	640	valid
868.0ms	906×	body	320	valid
128.0ms	498×	body	160	valid
50.0ms	364×	body	80	valid
19.0ms	4×	body	5120	valid