Details

sample37.0ms

Algorithm

intervals

Results

6.0ms	168×	body	80	valid
6.0ms	33×	body	1280	valid
3.0ms	24×	body	640	valid
3.0ms	97×	body	80	nan
2.0ms	14×	body	1280	nan
2.0ms	20×	body	320	valid
2.0ms	15×	body	640	nan
1.0ms	11×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	7×	body	160	nan

simplify20.0ms

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: 21.9b

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))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.6b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite79.0ms

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:

18.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
88.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify105.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (67.0ms)

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

prune409.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	233	6	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	6	240

Merged error: 0.2b

Counts

240 → 6

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))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite73.0ms

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:

15.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
134.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify111.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (73.0ms)

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

prune771.0ms

Filtered

260 candidates to 156 candidates (60.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	255	5	260
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	260	6	266

Merged error: 0.1b

Counts

266 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1.0 y))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
0.2b	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
5.9b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
41×	`times-frac`
34×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`flip3--` `associate-/r/` `flip--` `associate-/l*` `add-log-exp`
5×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `prod-diff` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ 1 (- 1.0 y))
13.0ms	(* (- x y) (/ 1 (- 1.0 y)))
5.0ms	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
4.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series239.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (- 1.0 y))
36.0ms	(* (- x y) (/ 1 (- 1.0 y)))
122.0ms	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
54.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify68.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	579	1150
1	2526	1014
2	5001	953

prune397.0ms

Filtered

158 candidates to 109 candidates (69.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Merged error: 0.1b

Counts

164 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

326×	`add-sqr-sqrt`
296×	`*-un-lft-identity`
196×	`times-frac`
186×	`prod-diff`
156×	`add-cube-cbrt`
80×	`difference-of-squares`
70×	`distribute-lft-out--`
16×	`associate-/r/`
12×	`associate-/r*`
10×	`flip3--` `flip--`
8×	`add-cbrt-cube` `div-inv` `add-log-exp`
6×	`add-exp-log` `fma-neg` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `associate--r-`

Counts

4 → 314

Calls

4 calls:

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

series359.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
128.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify122.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	815	7800
1	2675	5688
2	5001	5264

prune741.0ms

Filtered

326 candidates to 152 candidates (46.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	326	6	332

Merged error: 0.1b

Counts

332 → 6

regimes191.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch124.0ms

Steps

Iters	Range		Point
9	4436625.583370406	1.11049414308367e+15	36362977.00338186
9	-21514814691.886383	-205992.06318510068	-411945099.21176857

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	33	26

end0.0ms

sample1.0s

Algorithm

intervals

Results

221.0ms	5700×	body	80	valid
161.0ms	822×	body	1280	valid
111.0ms	781×	body	640	valid
99.0ms	3769×	body	80	nan
58.0ms	359×	body	1280	nan
45.0ms	470×	body	320	valid
41.0ms	362×	body	640	nan
16.0ms	197×	body	320	nan
15.0ms	227×	body	160	valid
6.0ms	114×	body	160	nan