Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	178×	body	80	valid
7.0ms	32×	body	1280	valid
4.0ms	22×	body	640	valid
3.0ms	18×	body	1280	nan
3.0ms	23×	body	640	nan
2.0ms	75×	body	80	nan
2.0ms	14×	body	320	valid
2.0ms	16×	body	320	nan
1.0ms	10×	body	160	valid
1.0ms	9×	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: 19.2b

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))
2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms	(/ (- x y) (- 1.0 y))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
49.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify43.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune269.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 0.1b

Counts

121 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.1b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`log-prod`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
8×	`pow1` `add-cube-cbrt` `add-log-exp` `difference-of-squares`
6×	`add-exp-log` `log-pow`
4×	`log-div` `flip3--` `times-frac` `sqrt-div` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 76

Calls

4 calls:

14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
14.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
49.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
127.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
125.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	228	854
1	533	780
2	2128	776
3	5001	768

prune243.0ms

Filtered

88 candidates to 68 candidates (77.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 0.1b

Counts

94 → 5

localize10.0ms

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))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`times-frac`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
24×	`log-prod`
20×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
3×	`div-exp` `div-inv`
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 → 144

Calls

4 calls:

16.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
126.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify60.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	621	1546
1	1974	1467
2	5001	1448

prune339.0ms

Filtered

156 candidates to 118 candidates (75.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	156	5	161

Merged error: 0.1b

Counts

161 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`log-prod`
15×	`*-un-lft-identity`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 67

Calls

4 calls:

14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
14.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
86.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	194	742
1	481	673
2	1890	661
3	5002	661

prune254.0ms

Filtered

79 candidates to 63 candidates (79.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	79	5	84

Merged error: 0.1b

Counts

84 → 5

regimes186.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.3b

bsearch113.0ms

Steps

Iters	Range		Point
9	6.491467194793197	4145706647.39311	50023976.468255654
7	-986175827.5592324	-22146652.4131901	-251769243.5141435

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

265.0ms	5689×	body	80	valid
184.0ms	767×	body	1280	valid
136.0ms	803×	body	640	valid
128.0ms	734×	body	1280	nan
108.0ms	766×	body	640	nan
87.0ms	2583×	body	80	nan
58.0ms	486×	body	320	valid
42.0ms	421×	body	320	nan
20.0ms	255×	body	160	valid
16.0ms	239×	body	160	nan