Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	133×	body	80	nan
3.0ms	26×	body	640	nan
3.0ms	22×	body	640	valid
2.0ms	11×	body	1280	nan
1.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.0b

Counts

2 → 1

localize8.0ms

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))
2.4b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.2b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite76.0ms

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:

17.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
21.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
80.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify99.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5003	3134

prune413.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	235	4	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	4	240

Merged error: 0.1b

Counts

240 → 4

localize12.0ms

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))))
3.2b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite76.0ms

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:

16.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
124.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify107.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1074	4812
1	3721	3718
2	5001	3710

prune607.0ms

Filtered

260 candidates to 157 candidates (60.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	259	5	264

Merged error: 0b

Counts

264 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.3b	(exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
2.4b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.2b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

186×	`add-sqr-sqrt`
181×	`*-un-lft-identity`
105×	`prod-diff`
102×	`times-frac`
90×	`add-cube-cbrt`
47×	`difference-of-squares`
46×	`distribute-lft-out--`
16×	`exp-sum`
9×	`pow1`
8×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
7×	`add-exp-log`
6×	`log-prod` `exp-prod` `add-cbrt-cube`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 221

Calls

4 calls:

9.0ms	(/ (- x y) (- 1.0 y))
6.0ms	(exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
19.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- x y) (- 1.0 y))
145.0ms	(exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify108.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1027	4633
1	3292	3391
2	5002	3083

prune472.0ms

Filtered

233 candidates to 118 candidates (50.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	233	5	238

Merged error: 0b

Counts

238 → 5

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (fma (exp (- 1.0 (log 1.0))) (- (* 1.0 x) (* 1.0 y)) (exp (- 1.0 (log 1.0)))))
0.2b	(fma (exp (- 1.0 (log 1.0))) (- (* 1.0 x) (* 1.0 y)) (exp (- 1.0 (log 1.0))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

1.0ms	(log (fma (exp (- 1.0 (log 1.0))) (- (* 1.0 x) (* 1.0 y)) (exp (- 1.0 (log 1.0)))))
1.0ms	(fma (exp (- 1.0 (log 1.0))) (- (* 1.0 x) (* 1.0 y)) (exp (- 1.0 (log 1.0))))

series493.0ms

Counts

2 → 6

Calls

2 calls:

298.0ms	(log (fma (exp (- 1.0 (log 1.0))) (- (* 1.0 x) (* 1.0 y)) (exp (- 1.0 (log 1.0)))))
195.0ms	(fma (exp (- 1.0 (log 1.0))) (- (* 1.0 x) (* 1.0 y)) (exp (- 1.0 (log 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	143	442
1	387	356
2	2012	322
3	5001	309

prune87.0ms

Filtered

30 candidates to 26 candidates (86.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	31	4	35

Merged error: 0b

Counts

35 → 4

regimes193.0ms

Accuracy

98.7% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 17.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	19
1	26	19

end0.0ms

sample1000.0ms

Algorithm

intervals

Results

223.0ms	5760×	body	80	valid
155.0ms	797×	body	1280	valid
111.0ms	769×	body	640	valid
104.0ms	3625×	body	80	nan
51.0ms	329×	body	1280	nan
47.0ms	382×	body	640	nan
43.0ms	438×	body	320	valid
19.0ms	220×	body	320	nan
18.0ms	236×	body	160	valid
6.0ms	105×	body	160	nan