Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	176×	body	80	valid
6.0ms	26×	body	1280	valid
5.0ms	27×	body	640	valid
4.0ms	21×	body	1280	nan
3.0ms	23×	body	640	nan
3.0ms	86×	body	80	nan
3.0ms	22×	body	320	valid
1.0ms	10×	body	320	nan
0.0ms	5×	body	160	valid
0.0ms	4×	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: 19.9b

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

rewrite72.0ms

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:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
81.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify104.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5001	3134

prune369.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	234	5	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	235	5	240

Merged error: 0.0b

Counts

240 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.3b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
3.8b	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
13.0b	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
33×	`cbrt-prod`
32×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`cbrt-div`
12×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `flip--`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3` `distribute-lft-out--`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-neg` `prod-diff`
2×	`log-div` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
11.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
5.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
3.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (- 1.0 y))
103.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
87.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
52.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	515	1426
1	1881	1292
2	5002	1221

prune303.0ms

Filtered

123 candidates to 92 candidates (74.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Merged error: 0.0b

Counts

128 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-sqr-sqrt`
140×	`*-un-lft-identity`
93×	`prod-diff`
79×	`times-frac`
72×	`add-cube-cbrt`
38×	`difference-of-squares`
34×	`distribute-lft-out--`
18×	`log-prod`
7×	`pow1` `add-exp-log` `flip3--` `flip--`
6×	`log-div` `associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `rem-log-exp` `log-pow` `div-inv`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 171

Calls

4 calls:

17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
21.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
82.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
85.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify80.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	743	4004
1	2323	2916
2	5001	2680

prune393.0ms

Filtered

183 candidates to 92 candidates (50.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	183	5	188

Merged error: 0.0b

Counts

188 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.9b	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite87.0ms

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×	`cbrt-prod` `associate-/r/`
10×	`flip3--` `flip--`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `fma-neg` `div-inv`
4×	`expm1-log1p-u` `log-div` `cbrt-div` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `pow1/3` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 274

Calls

4 calls:

17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
15.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
18.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
59.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
111.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
113.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	787	7334
1	2430	5114
2	5001	4638

prune580.0ms

Filtered

286 candidates to 118 candidates (41.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	286	5	291

Merged error: 0.0b

Counts

291 → 5

regimes182.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.5b

bsearch148.0ms

Steps

Iters	Range		Point
11	0.06291072096871789	3.278345425089741e+27	56269067.0291874
7	-79301947053416.23	-1073005218934.9313	-1086266281199.134

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample1.5s

Algorithm

intervals

Results

454.0ms	5599×	body	80	valid
208.0ms	866×	body	1280	valid
143.0ms	823×	body	640	valid
137.0ms	750×	body	1280	nan
106.0ms	742×	body	640	nan
102.0ms	2689×	body	80	nan
59.0ms	475×	body	320	valid
49.0ms	450×	body	320	nan
20.0ms	237×	body	160	valid
16.0ms	222×	body	160	nan