Details

sample147.0ms

Algorithm

intervals

Results

81.0ms	59×	body	2560	valid
19.0ms	33×	body	1280	valid
16.0ms	47×	body	640	valid
8.0ms	84×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	182
1	13	182
2	21	182
3	26	182
4	28	182
done	28	182

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize20.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
16.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

5.0ms	(- 1.0 (cos x))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series129.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
108.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify3.5s

Counts

64 → 64

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	116	18950
1	290	16461
2	936	14423
3	4103	14248
done	5000	14223

prune266.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite145.0ms

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-cbrt-cube` `prod-diff` `add-exp-log` `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×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 238

Calls

4 calls:

24.0ms	(/ (sqrt (- 1.0 (cos x))) x)
82.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
11.0ms	(- 1.0 (cos x))
10.0ms	(- 1.0 (cos x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (sqrt (- 1.0 (cos x))) x)
63.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
20.0ms	(- 1.0 (cos x))
24.0ms	(- 1.0 (cos x))

simplify3.2s

Counts

250 → 250

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	261	96024
1	797	87093
2	2357	81929
done	5001	78834

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (- 1.0 (cos x))) (sqrt (sqrt (- 1.0 (cos x)))))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
28×	`sqrt-prod`
27×	`prod-diff`
18×	`sqrt-div`
15×	`pow1`
11×	`sqrt-pow1` `associate-r`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
8×	`associate-l`
7×	`pow1/2`
6×	`add-cbrt-cube` `add-exp-log` `pow-prod-up` `unswap-sqr`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `pow-prod-down`
2×	`pow3` `associate-l/` `associate-r/`
1×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 141

Calls

4 calls:

49.0ms	(* (sqrt (- 1.0 (cos x))) (sqrt (sqrt (- 1.0 (cos x)))))
10.0ms	(- 1.0 (cos x))
10.0ms	(- 1.0 (cos x))
11.0ms	(- 1.0 (cos x))

series309.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (sqrt (- 1.0 (cos x))) (sqrt (sqrt (- 1.0 (cos x)))))
34.0ms	(- 1.0 (cos x))
29.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

153 → 153

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	164	51183
1	346	42847
2	881	37188
3	2108	36344
done	5000	32004

prune704.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
2.0b	(log (exp (- 1.0 (cos x))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
9×	`fma-neg`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 115

Calls

4 calls:

6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))
38.0ms	(- 1.0 (cos x))
33.0ms	(log (exp (- 1.0 (cos x))))

simplify3.3s

Counts

127 → 127

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	124	45199
1	224	33765
2	442	26113
3	1094	25573
4	2985	19957
done	5000	19957

prune924.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes133.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.6b

bsearch92.0ms

Steps

Iters	Range		Point
9	5.312512837176874e-08	0.1909160003853501	0.036569739872455896
7	-0.18371106458419734	-0.0075399940621682995	-0.029664306942044347

simplify11.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	29	1097
1	31	1097
done	31	1097

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1561×	body	2560	valid
657.0ms	933×	body	320	valid
631.0ms	1275×	body	1280	valid
490.0ms	1482×	body	640	valid
130.0ms	2280×	body	80	valid
58.0ms	469×	body	160	valid