Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
5.0ms	10×	body	1280	nan
4.0ms	22×	body	1280	valid
3.0ms	112×	body	80	nan
2.0ms	16×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	12×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	3×	body	160	nan

simplify99.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	58	12
5	63	12
6	71	12
7	86	12
8	114	12
9	127	12
10	129	12
done	129	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

24.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
12.0ms	(/ (- x y) (- 1.0 y))
30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
30.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
41.0ms	(/ (- x y) (- 1.0 y))
60.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
97.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.4s

Counts

239 → 239

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	390	8619
1	986	7647
2	2784	5892
done	5000	5877

prune518.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.8b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.8b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

278×	`add-sqr-sqrt`
266×	`*-un-lft-identity`
186×	`prod-diff`
154×	`times-frac`
138×	`add-cube-cbrt`
68×	`difference-of-squares`
64×	`distribute-lft-out--`
18×	`log-prod`
12×	`sqrt-prod` `associate-/r/`
10×	`flip3--` `flip--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg` `log-pow` `div-inv`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 276

Calls

4 calls:

28.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
31.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
21.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
20.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
142.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
151.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify1.1s

Counts

288 → 288

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	323	13254
1	776	12142
2	2122	9048
done	5000	9018

prune685.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 248

Calls

4 calls:

21.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
14.0ms	(/ (- x y) (- 1.0 y))
40.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
44.0ms	(/ (- x y) (- 1.0 y))
137.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
62.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.4s

Counts

260 → 260

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	432	8789
1	1072	8133
2	3011	6513
done	5000	6498

prune600.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.1b	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
0.1b	(/ (sqrt (exp 1.0)) (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

678×	`times-frac`
651×	`add-sqr-sqrt`
501×	`*-un-lft-identity`
317×	`add-cube-cbrt`
270×	`sqrt-prod`
142×	`difference-of-squares`
93×	`prod-diff`
92×	`distribute-lft-out--`
51×	`associate-/r*`
17×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube` `div-inv`
9×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `fma-neg` `div-sub` `clear-num`
1×	`sub-neg` `diff-log` `associate--r-`

Counts

4 → 536

Calls

4 calls:

12.0ms	(/ (- x y) (- 1.0 y))
80.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
56.0ms	(/ (sqrt (exp 1.0)) (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (- x y) (- 1.0 y))
223.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
147.0ms	(/ (sqrt (exp 1.0)) (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.2s

Counts

548 → 548

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	687	19389
1	1690	17990
done	5000	16770

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes211.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.7b

bsearch120.0ms

Steps

Iters	Range		Point
6	3568380.5266111037	20163573.119074974	19835852.98699539
8	-945895839911.4141	-309616365.81694436	-339938991.33710843

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	35	98
1	44	63
done	44	63

end0.0ms

sample991.0ms

Algorithm

intervals

Results

212.0ms	5643×	body	80	valid
159.0ms	836×	body	1280	valid
107.0ms	817×	body	640	valid
102.0ms	3821×	body	80	nan
58.0ms	376×	body	1280	nan
43.0ms	389×	body	640	nan
43.0ms	459×	body	320	valid
18.0ms	225×	body	320	nan
15.0ms	245×	body	160	valid
8.0ms	115×	body	160	nan