Details

sample216.0ms

Algorithm

intervals

Results

65.0ms	52×	body	640	valid
58.0ms	42×	body	2560	valid
23.0ms	44×	body	1280	valid
11.0ms	36×	body	320	valid
7.0ms	65×	body	80	valid
3.0ms	17×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize40.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
13.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite886.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

43.0ms	(- 1.0 (cos x))
797.0ms	(/ (- 1.0 (cos x)) (* x x))

series751.0ms

Counts

2 → 6

Calls

2 calls:

272.0ms	(- 1.0 (cos x))
469.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify7.5s

Counts

48 → 48

Iterations

Iter	Nodes
done	5007
3	2220
2	613
1	217
0	88

prune818.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

52.0ms	(/ (sqrt (- 1.0 (cos x))) x)
455.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
27.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

series829.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(/ (sqrt (- 1.0 (cos x))) x)
378.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
45.0ms	(- 1.0 (cos x))
53.0ms	(- 1.0 (cos x))

simplify10.9s

Counts

218 → 218

Iterations

Iter	Nodes
done	5001
2	2467
1	724
0	231

prune5.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.2b	(/ (- 1.0 (cos x)) x)
1.7b	(- 1.0 (cos x))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-l`
17×	`add-cbrt-cube`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

3 → 115

Calls

3 calls:

161.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
28.0ms	(/ (- 1.0 (cos x)) x)
103.0ms	(- 1.0 (cos x))

series579.0ms

Counts

3 → 9

Calls

3 calls:

366.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
156.0ms	(/ (- 1.0 (cos x)) x)
55.0ms	(- 1.0 (cos x))

simplify12.9s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1641
1	537
0	189

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize142.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(* (cos x) (cos x))
0.7b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.5b	(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

rewrite542.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

23.0ms	(* (cos x) (cos x))
33.0ms	(* (cos x) (cos x))
57.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
396.0ms	(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

series919.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos x))
303.0ms	(* (cos x) (cos x))
135.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
429.0ms	(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

simplify20.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5007
3	3942
2	1248
1	333
0	121

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes584.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.4b

bsearch472.0ms

Steps

Iters	Range		Point
9	2.490703692944805e-05	37.746059492850215	0.026958513149624132
9	-1.440408271564231	-1.963203309137196e-05	-0.033158298566556964

simplify20.0ms

Iterations

Iter	Nodes
done	53
1	53
0	36

end0.0ms

sample16.2s

Algorithm

intervals

Results

7.5s	1448×	body	640	valid
5.2s	1604×	body	2560	valid
1.9s	1219×	body	1280	valid
628.0ms	2290×	body	80	valid
448.0ms	950×	body	320	valid
169.0ms	489×	body	160	valid