Details

sample64.0ms

Algorithm

intervals

Results

26.0ms	51×	body	2560	valid
12.0ms	40×	body	1280	valid
7.0ms	41×	body	640	valid
4.0ms	33×	body	320	valid
3.0ms	79×	body	80	valid
1.0ms	12×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize13.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

10.0ms	(- 1.0 (cos x))
58.0ms	(/ (- 1.0 (cos x)) (* x x))

series114.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- 1.0 (cos x))
80.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.1s

Counts

64 → 64

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	116	808
1	269	678
2	747	566
3	2669	526
done	5001	517

prune203.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 1/720 (pow x 4) 1/2)
13.6b	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/720 (pow x 4) 1/2)
0.0ms	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

series204.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(fma 1/720 (pow x 4) 1/2)
66.0ms	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

simplify2.3s

Counts

26 → 26

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	35	298
1	55	292
2	140	255
3	556	255
4	3220	255
done	5000	255

prune91.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

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))
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
156×	`times-frac`
104×	`sqrt-prod`
103×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
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 → 238

Calls

4 calls:

18.0ms	(/ (sqrt (- 1.0 (cos x))) x)
68.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
7.0ms	(- 1.0 (cos x))
8.0ms	(- 1.0 (cos x))

series189.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (sqrt (- 1.0 (cos x))) x)
51.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
20.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

250 → 250

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	261	4851
1	693	3988
2	2409	3318
done	5000	3078

prune551.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
1.7b	(- 1.0 (cos x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

29.0ms	(/ (- 1.0 (cos x)) x)
28.0ms	(/ (/ (- 1.0 (cos x)) x) x)
12.0ms	(- 1.0 (cos x))

series127.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- 1.0 (cos x)) x)
50.0ms	(/ (/ (- 1.0 (cos x)) x) x)
29.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	259	2577
1	583	2358
2	1473	2183
3	4779	2121
done	5000	2121

prune323.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.4b

bsearch68.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	0.028553554432783436
8	-45.38980787391071	-0.005411406272604966	-0.03306643978524941

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	43
1	30	30
done	30	30

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	1640×	body	2560	valid
615.0ms	1251×	body	1280	valid
358.0ms	1452×	body	640	valid
210.0ms	947×	body	320	valid
111.0ms	2232×	body	80	valid
57.0ms	478×	body	160	valid