Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	50×	body	2560	valid
9.0ms	45×	body	1280	valid
6.0ms	45×	body	640	valid
2.0ms	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

localize6.0ms

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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify922.0ms

Counts

48 → 48

Iterations

Useful iterations: done (921.0ms)

Iter	Nodes	Cost
0	88	507
1	220	497
2	693	441
3	2556	441
done	5001	440

prune106.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

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))

rewrite66.0ms

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:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
42.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series173.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sqrt (- 1.0 (cos x))) x)
45.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

218 → 218

Iterations

Useful iterations: 2 (237.0ms)

Iter	Nodes	Cost
0	231	4237
1	671	3632
2	2891	3070
done	5000	3070

prune372.0ms

Pruning

10 alts after pruning (9 fresh and 1 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))

rewrite27.0ms

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:

11.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
22.0ms	(- 1.0 (cos x))

simplify703.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (154.0ms)

Iter	Nodes	Cost
0	229	2262
1	537	2160
2	1870	2046
done	5000	2046

prune255.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
3.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

47.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
1.0ms	(pow (cos x) 3)
3.0ms	(+ 1.0 (cos x))
18.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series216.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
33.0ms	(pow (cos x) 3)
9.0ms	(+ 1.0 (cos x))
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.0s

Counts

201 → 201

Iterations

Useful iterations: 2 (215.0ms)

Iter	Nodes	Cost
0	260	5407
1	623	5084
2	2559	4978
done	5000	4978

prune422.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.7b

bsearch64.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.030256823677706827
10	-155084744.97222546	-0.0009113054925467739	-0.029841445064018916

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	37
1	29	30
done	29	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

751.0ms	1655×	body	2560	valid
277.0ms	1208×	body	1280	valid
205.0ms	1464×	body	640	valid
94.0ms	951×	body	320	valid
71.0ms	2222×	body	80	valid
35.0ms	500×	body	160	valid