Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	184×	body	80	valid
6.0ms	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

simplify19.0ms

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 (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

localize8.0ms

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))))

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--` `add-log-exp`
8×	`associate-/r/`
7×	`add-exp-log`
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×	`diff-log` `associate--r-`
2×	`sub-neg` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 228

Calls

4 calls:

11.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
19.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- x y) (- 1.0 y))
94.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
89.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify110.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	981	4627
1	3211	3350
2	5001	3140

prune347.0ms

Filtered

240 candidates to 126 candidates (47.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	234	6	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	235	6	241

Merged error: 0.1b

Counts

241 → 6

localize10.0ms

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)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
207×	`*-un-lft-identity`
145×	`times-frac`
104×	`add-cube-cbrt`
93×	`prod-diff`
60×	`difference-of-squares`
51×	`distribute-lft-out--`
24×	`log-prod`
17×	`associate-/r*`
13×	`add-exp-log`
12×	`log-div` `associate-/r/` `associate-/l*`
8×	`flip3--` `add-cbrt-cube` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `clear-num` `log1p-expm1-u`
3×	`frac-2neg` `fma-neg` `rem-log-exp`
2×	`cbrt-undiv` `div-sub` `log-rec` `associate-/l/`
1×	`sub-neg` `diff-log` `log-pow` `associate--r-`

Counts

4 → 263

Calls

4 calls:

9.0ms	(/ (- x y) (- 1.0 y))
18.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (- x y) (- 1.0 y))
161.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
138.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify114.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1087	4960
1	3797	3844
2	5001	3832

prune481.0ms

Filtered

275 candidates to 166 candidates (39.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	272	3	275
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	276	5	281

Merged error: 0.0b

Counts

281 → 5

localize18.0ms

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)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

327×	`add-sqr-sqrt`
266×	`*-un-lft-identity`
205×	`times-frac`
155×	`add-cube-cbrt`
129×	`prod-diff`
86×	`log-prod`
75×	`difference-of-squares`
66×	`sqrt-prod`
57×	`distribute-lft-out--`
44×	`log-pow`
40×	`associate--r+`
34×	`log-div`
28×	`pow1`
20×	`sqrt-pow1` `associate-/l*`
18×	`associate-/r*` `associate--r-`
15×	`exp-prod`
12×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log`
8×	`flip3--` `flip--`
6×	`associate--l+` `associate-/r/` `add-cbrt-cube` `div-inv` `associate-/l/`
5×	`pow1/2` `diff-log`
4×	`expm1-log1p-u` `clear-num` `log1p-expm1-u`
3×	`frac-2neg` `log-rec`
2×	`sub-neg` `div-sub` `div-exp` `rem-log-exp`
1×	`cbrt-undiv`

Counts

4 → 381

Calls

4 calls:

33.0ms	(- (log (sqrt (exp 1.0))) (log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))))
20.0ms	(log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
25.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
18.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(- (log (sqrt (exp 1.0))) (log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))))
236.0ms	(log (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
219.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
62.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify151.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1418	8626
1	4552	6498
2	5001	6496

prune809.0ms

Filtered

393 candidates to 224 candidates (43.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	391	2	393
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	392	6	398

Merged error: 0.0b

Counts

398 → 6

localize20.0ms

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)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

402×	`add-sqr-sqrt`
354×	`*-un-lft-identity`
274×	`times-frac`
202×	`add-cube-cbrt`
186×	`prod-diff`
144×	`sqrt-prod`
92×	`difference-of-squares`
76×	`distribute-lft-out--`
15×	`associate-/r` `associate-/l`
14×	`associate-/r/`
10×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `sqrt-undiv` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `associate-/l/` `associate--r-`

Counts

4 → 400

Calls

4 calls:

23.0ms	(/ (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (exp 1.0)))
19.0ms	(/ (sqrt (exp 1.0)) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series722.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (exp 1.0)))
324.0ms	(/ (sqrt (exp 1.0)) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
61.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify162.0ms

Algorithm

egg-herbie

Counts

412 → 412

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1086	9623
1	3793	7420
2	5002	6941

prune786.0ms

Filtered

412 candidates to 178 candidates (56.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	411	1	412
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	413	5	418

Merged error: 0.0b

Counts

418 → 5

regimes168.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	23
1	28	23

end0.0ms

sample982.0ms

Algorithm

intervals

Results

212.0ms	5638×	body	80	valid
155.0ms	818×	body	1280	valid
109.0ms	809×	body	640	valid
101.0ms	3642×	body	80	nan
55.0ms	368×	body	1280	nan
51.0ms	432×	body	640	nan
43.0ms	456×	body	320	valid
18.0ms	279×	body	160	valid
16.0ms	199×	body	320	nan
6.0ms	106×	body	160	nan