Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
13.0ms	45×	body	640	valid
9.0ms	159×	body	80	valid
5.0ms	26×	body	320	valid
4.0ms	110×	body	80	nan
2.0ms	15×	body	160	valid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (/ x (+ x y)) x) x)
6.1b	(pow (/ x (+ x y)) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

5.0ms	(/ x (+ x y))
10.0ms	(/ (pow (/ x (+ x y)) x) x)
6.0ms	(pow (/ x (+ x y)) x)

series526.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ x (+ x y))
172.0ms	(/ (pow (/ x (+ x y)) x) x)
299.0ms	(pow (/ x (+ x y)) x)

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	537	1436
1	2640	1406
2	5001	1406

prune976.0ms

Filtered

181 candidates to 131 candidates (27.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	4	182

Merged error: 0.3b

Counts

182 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.0b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
53×	`cbrt-prod`
52×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
18×	`cbrt-div`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`distribute-lft-out`
7×	`pow-exp`
6×	`pow1` `pow-unpow`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
18.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (+ x y))
160.0ms	(cbrt (+ x y))
337.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
350.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	728	1428
1	2246	1356
2	5001	1325

prune1.2s

Filtered

134 candidates to 92 candidates (31.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	135	3	138

Merged error: 0.0b

Counts

138 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.6b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cbrt-prod`
89×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `log-prod`
14×	`distribute-lft-out`
10×	`add-exp-log`
8×	`cbrt-div`
6×	`pow1`
4×	`flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow-unpow`
2×	`pow1/3` `div-exp` `rem-log-exp` `pow-exp` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 150

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (+ x y))
162.0ms	(cbrt (+ x y))
336.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
91.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify64.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	636	1629
1	2009	1593
2	5001	1523

prune2.0s

Filtered

162 candidates to 108 candidates (33.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	162	3	165

Merged error: 0.0b

Counts

165 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (pow (/ x (+ x y)) x))
0.0b	(/ x (+ x y))
6.1b	(pow (/ x (+ x y)) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`associate-/r*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+` `associate-/l*`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

10.0ms	(/ x (pow (/ x (+ x y)) x))
5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series684.0ms

Counts

3 → 9

Calls

3 calls:

324.0ms	(/ x (pow (/ x (+ x y)) x))
55.0ms	(/ x (+ x y))
304.0ms	(pow (/ x (+ x y)) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	543	1458
1	2498	1428
2	5002	1428

prune1.6s

Filtered

181 candidates to 129 candidates (28.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	181	3	184

Merged error: 0.0b

Counts

184 → 3

regimes103.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.8b

bsearch134.0ms

Steps

Iters	Range		Point
9	1.5972903132525599e-06	28.700163284045342	7.732105221395109
10	-2.373313349971615e+16	-27.465585783021098	-5349815.209025494

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	37	19

end0.0ms

sample2.1s

Algorithm

intervals

Results

728.0ms	1487×	body	1280	valid
430.0ms	1431×	body	640	valid
262.0ms	4892×	body	80	valid
167.0ms	854×	body	320	valid
121.0ms	3085×	body	80	nan
61.0ms	474×	body	160	valid

Details

sample75.0ms

simplify116.0ms

prune8.0ms

localize6.0ms

rewrite29.0ms

series526.0ms

simplify73.0ms

prune976.0ms

localize17.0ms

rewrite40.0ms

series1.0s

simplify70.0ms

prune1.2s

localize16.0ms

rewrite31.0ms

series751.0ms

simplify64.0ms

prune2.0s

localize8.0ms

rewrite30.0ms

series684.0ms

simplify72.0ms

prune1.6s

regimes103.0ms

bsearch134.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling