Details

sample112.0ms

Algorithm

intervals

Results

38.0ms	42×	body	2560	valid
23.0ms	44×	body	1280	valid
20.0ms	52×	body	640	valid
8.0ms	36×	body	320	valid
5.0ms	65×	body	80	valid
2.0ms	17×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

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:

13.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

series149.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- 1.0 (cos x))
109.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify4.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4026
2	919
1	290
0	116

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite136.0ms

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:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
35.0ms	(/ (- 1.0 (cos x)) x)
40.0ms	(- 1.0 (cos x))

series221.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (/ (- 1.0 (cos x)) x) x)
84.0ms	(/ (- 1.0 (cos x)) x)
44.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	1585
1	604
0	259

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))
12.8b	(sqrt (/ (/ (- 1.0 (cos x)) x) x))
12.8b	(sqrt (/ (/ (- 1.0 (cos x)) x) x))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
164×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
122×	`sqrt-prod`
112×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`div-inv` `add-log-exp`
6×	`pow1` `rem-sqrt-square` `fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `flip--`

Counts

4 → 208

Calls

4 calls:

20.0ms	(- 1.0 (cos x))
14.0ms	(- 1.0 (cos x))
34.0ms	(sqrt (/ (/ (- 1.0 (cos x)) x) x))
33.0ms	(sqrt (/ (/ (- 1.0 (cos x)) x) x))

series447.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (cos x))
35.0ms	(- 1.0 (cos x))
217.0ms	(sqrt (/ (/ (- 1.0 (cos x)) x) x))
161.0ms	(sqrt (/ (/ (- 1.0 (cos x)) x) x))

simplify4.5s

Counts

220 → 220

Iterations

Iter	Nodes
done	5002
3	4057
2	1290
1	586
0	312

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

1.7b	(- 1.0 (cos x))
1.9b	(log (exp (- 1.0 (cos x))))
12.8b	(sqrt (/ (/ (log (exp (- 1.0 (cos x)))) x) x))
12.8b	(sqrt (/ (/ (- 1.0 (cos x)) x) x))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

282×	`times-frac`
198×	`add-sqr-sqrt`
186×	`*-un-lft-identity`
158×	`sqrt-prod`
146×	`add-cube-cbrt`
60×	`log-pow`
50×	`exp-prod`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
16×	`pow1`
14×	`log-prod`
11×	`exp-sum`
8×	`div-inv`
6×	`rem-sqrt-square` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `sqrt-div`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 247

Calls

4 calls:

20.0ms	(- 1.0 (cos x))
37.0ms	(log (exp (- 1.0 (cos x))))
81.0ms	(sqrt (/ (/ (log (exp (- 1.0 (cos x)))) x) x))
52.0ms	(sqrt (/ (/ (- 1.0 (cos x)) x) x))

series466.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- 1.0 (cos x))
37.0ms	(log (exp (- 1.0 (cos x))))
228.0ms	(sqrt (/ (/ (log (exp (- 1.0 (cos x)))) x) x))
163.0ms	(sqrt (/ (/ (- 1.0 (cos x)) x) x))

simplify2.9s

Counts

259 → 259

Iterations

Iter	Nodes
done	5003
2	2073
1	1028
0	646

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes220.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.5b

bsearch167.0ms

Steps

Iters	Range		Point
9	2.490703692944805e-05	37.746059492850215	0.029466723206624044
9	-1.440408271564231	-1.963203309137196e-05	-0.02826034963706557

simplify15.0ms

Iterations

Iter	Nodes
done	45
1	45
0	38

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	1604×	body	2560	valid
936.0ms	2290×	body	80	valid
793.0ms	1219×	body	1280	valid
667.0ms	1448×	body	640	valid
235.0ms	950×	body	320	valid
78.0ms	489×	body	160	valid