Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	50×	body	2560	valid
10.0ms	45×	body	1280	valid
6.0ms	45×	body	640	valid
3.0ms	73×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	20×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize10.0ms

Local error

Found 2 expressions with local error:

3.4b	(- 1.0 (cos x))
15.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:

2.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series85.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(- 1.0 (cos x))
56.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

48 → 48

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	88	507
1	218	489
2	636	441
3	2189	441
done	5000	440

prune101.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.4b	(- 1.0 (cos x))
3.4b	(- 1.0 (cos x))

rewrite67.0ms

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:

10.0ms	(/ (sqrt (- 1.0 (cos x))) x)
39.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series167.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (sqrt (- 1.0 (cos x))) x)
45.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify838.0ms

Counts

218 → 218

Iterations

Useful iterations: 2 (305.0ms)

Iter	Nodes	Cost
0	231	4237
1	664	3612
2	2413	3070
done	5000	3070

prune378.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
3.4b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

14.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series105.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

156 → 156

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	229	2262
1	534	2156
2	1348	2046
3	3923	2024
done	5001	2024

prune268.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.2b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
3.6b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`add-log-exp`
4×	`times-frac` `associate-/l*`
3×	`swap-sqr` `associate-r` `associate-l` `difference-of-squares`
2×	`cbrt-undiv` `sqr-cos` `flip3--` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `div-inv` `distribute-lft-out` `associate--r+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

10.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
4.0ms	(* (cos x) (cos x))
3.0ms	(+ 1.0 (cos x))
3.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
16.0ms	(* (cos x) (cos x))
10.0ms	(+ 1.0 (cos x))
36.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify556.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (155.0ms)

Iter	Nodes	Cost
0	159	1249
1	417	1091
2	1628	954
done	5000	954

prune192.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch73.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.030256823677706827
10	-155084744.97222546	-0.0009113054925467739	-0.023582590462374556

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	50
1	40	50
done	40	50

end0.0ms

sample1.6s

Algorithm

intervals

Results

755.0ms	1655×	body	2560	valid
284.0ms	1208×	body	1280	valid
216.0ms	1464×	body	640	valid
102.0ms	951×	body	320	valid
69.0ms	2222×	body	80	valid
41.0ms	500×	body	160	valid