Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	184×	body	80	valid
4.0ms	30×	body	640	valid
3.0ms	17×	body	1280	valid
3.0ms	113×	body	80	nan
2.0ms	17×	body	640	nan
2.0ms	16×	body	320	valid
2.0ms	10×	body	1280	nan
1.0ms	9×	body	160	valid
0.0ms	6×	body	160	nan
0.0ms	4×	body	320	nan

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (100.0%)

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: 17.8b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.6b	(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`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`diff-log` `associate--r-`
2×	`sub-neg` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 109

Calls

4 calls:

9.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (- x y) (- 1.0 y))
103.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
62.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
94.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify50.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	483	948
1	1374	900
2	5002	882

prune249.0ms

Filtered

121 candidates to 88 candidates (27.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Merged error: 0.1b

Counts

122 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
70×	`times-frac`
39×	`add-cube-cbrt`
30×	`difference-of-squares`
24×	`log-prod`
21×	`distribute-lft-out--`
17×	`associate-/r*`
13×	`add-exp-log`
12×	`log-div` `associate-/l*`
8×	`add-cbrt-cube`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `div-exp` `flip--`
4×	`clear-num`
3×	`frac-2neg` `rem-log-exp` `div-inv`
2×	`cbrt-undiv` `div-sub` `log-rec` `associate-/l/`
1×	`sub-neg` `diff-log` `log-pow` `associate--r-`

Counts

4 → 159

Calls

4 calls:

12.0ms	(/ (- x y) (- 1.0 y))
19.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
18.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
15.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (- x y) (- 1.0 y))
170.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
353.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
58.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify66.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	634	1694
1	2058	1593
2	5002	1582

prune357.0ms

Filtered

171 candidates to 127 candidates (25.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	172	5	177

Merged error: 0.0b

Counts

177 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (sqrt (exp 1.0))) (log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))))
0.0b	(log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
0.1b	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

183×	`add-sqr-sqrt`
130×	`times-frac`
122×	`*-un-lft-identity`
86×	`log-prod`
71×	`add-cube-cbrt`
66×	`sqrt-prod`
45×	`difference-of-squares`
40×	`associate--r+`
34×	`log-div`
27×	`distribute-lft-out--`
20×	`associate-/l*`
18×	`associate-/r*` `associate--r-`
10×	`add-log-exp`
9×	`pow1` `add-exp-log`
6×	`associate--l+` `add-cbrt-cube` `associate-/l/`
5×	`flip3--` `diff-log` `log-pow` `flip--`
4×	`clear-num`
3×	`frac-2neg` `log-rec` `div-inv`
2×	`sub-neg` `div-sub` `div-exp` `rem-log-exp`
1×	`cbrt-undiv`

Counts

4 → 232

Calls

4 calls:

35.0ms	(- (log (sqrt (exp 1.0))) (log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))))
21.0ms	(log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
21.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series883.0ms

Counts

4 → 12

Calls

4 calls:

334.0ms	(- (log (sqrt (exp 1.0))) (log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))))
251.0ms	(log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
235.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
63.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify87.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	764	3455
1	2122	3302
2	5002	3157

prune571.0ms

Filtered

244 candidates to 153 candidates (37.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	240	4	244
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	243	6	249

Merged error: 0b

Counts

249 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (exp 1.0)))
0.1b	(/ (sqrt (exp 1.0)) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-sqr-sqrt`
144×	`sqrt-prod`
124×	`times-frac`
104×	`*-un-lft-identity`
72×	`add-cube-cbrt`
32×	`difference-of-squares`
16×	`distribute-lft-out--`
15×	`associate-/r` `associate-/l`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `sqrt-div` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-undiv` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/` `associate--r-`

Counts

4 → 200

Calls

4 calls:

23.0ms	(/ (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (exp 1.0)))
24.0ms	(/ (sqrt (exp 1.0)) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series756.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (exp 1.0)))
336.0ms	(/ (sqrt (exp 1.0)) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
63.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify76.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	534	3123
1	1912	2949
2	5002	2878

prune550.0ms

Filtered

212 candidates to 124 candidates (41.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	213	5	218

Merged error: 0b

Counts

218 → 5

regimes185.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch156.0ms

Steps

Iters	Range		Point
11	6.07909688113224	1.5293703169856862e+22	292197028.9976399
8	-5154421704.732712	-137459.4213561049	-160923004.82383958

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	45
1	43	45

end0.0ms

sample1.0s

Algorithm

intervals

Results

216.0ms	5638×	body	80	valid
156.0ms	818×	body	1280	valid
109.0ms	809×	body	640	valid
107.0ms	3642×	body	80	nan
57.0ms	368×	body	1280	nan
49.0ms	432×	body	640	nan
43.0ms	456×	body	320	valid
20.0ms	279×	body	160	valid
17.0ms	199×	body	320	nan
6.0ms	106×	body	160	nan