Details

sample56.0ms

Algorithm

intervals

Results

17.0ms	41×	body	1280	valid
14.0ms	57×	body	640	valid
8.0ms	156×	body	80	valid
3.0ms	18×	body	320	valid
3.0ms	86×	body	80	nan
1.0ms	12×	body	160	valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4133	4
7	5001	4

prune4.0ms

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: 8.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
4.0b	(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`
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:

11.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series426.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(/ (pow (/ x (+ x y)) x) x)
43.0ms	(/ x (+ x y))
242.0ms	(pow (/ x (+ x y)) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	536	1438
1	2634	1406
2	5002	1406

prune296.0ms

Filtered

181 candidates to 131 candidates (27.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0.3b

Counts

182 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.8b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

1211×	`cbrt-prod`
1039×	`add-sqr-sqrt`
957×	`*-un-lft-identity`
924×	`unpow-prod-down`
906×	`times-frac`
567×	`add-cube-cbrt`
435×	`swap-sqr`
381×	`associate-r` `associate-l`
236×	`unswap-sqr`
168×	`distribute-lft-out`
59×	`*-commutative`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
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 → 979

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
95.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series935.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
177.0ms	(cbrt x)
279.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
300.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify234.0ms

Algorithm

egg-herbie

Counts

991 → 991

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	4248	18743
1	5001	18716

prune2.1s

Filtered

991 candidates to 453 candidates (54.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	990	1	991
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	992	2	994

Merged error: 0.0b

Counts

994 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

12006×	`cbrt-prod`
8900×	`add-sqr-sqrt`
4987×	`associate-r`
4165×	`unpow-prod-down`
4129×	`times-frac`
4104×	`unswap-sqr`
2718×	`*-un-lft-identity`
1716×	`add-cube-cbrt`
1671×	`associate-l`
1478×	`swap-sqr`
514×	`*-commutative`
439×	`distribute-lft-out`
100×	`cbrt-div`
34×	`flip3-+` `flip-+`
32×	`frac-times`
28×	`associate-/r/`
20×	`add-exp-log`
16×	`associate-*r/`
10×	`associate-*l/`
7×	`pow-exp`
6×	`pow1` `pow-unpow`
5×	`div-exp`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `div-inv` `sqr-pow`

Counts

4 → 4281

Calls

4 calls:

7.0ms	(cbrt (* (cbrt x) (cbrt x)))
12.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
383.0ms	(pow (/ (* (cbrt x) (cbrt (* (cbrt x) (cbrt x)))) (* (cbrt (+ x y)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))) x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt (* (cbrt x) (cbrt x)))
273.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
326.0ms	(pow (/ (* (cbrt x) (cbrt (* (cbrt x) (cbrt x)))) (* (cbrt (+ x y)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))) x)
285.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify1.2s

Algorithm

egg-herbie

Counts

4293 → 4293

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	7263	140136

prune18.5s

Filtered

4293 candidates to 2582 candidates (39.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	4293	0	4293
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	4293	2	4295

Merged error: 0.0b

Counts

4295 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
4×	`add-exp-log`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`div-exp`
1×	`pow1` `cbrt-undiv` `exp-neg` `frac-2neg` `mul-1-neg` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

7.0ms

(/ (exp (* -1 y)) x)

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(/ (exp (* -1 y)) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	115	188
1	307	175
2	1448	173
3	5001	173

prune44.0ms

Filtered

32 candidates to 23 candidates (28.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	32	2	34

Merged error: 0b

Counts

34 → 2

regimes48.0ms

Accuracy

97.7% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 5.9b

bsearch99.0ms

Steps

Iters	Range		Point
9	5.128716274992958e-16	1.0035131970971057e-07	9.874893663935251e-08
7	-631.316943717255	-15.967116801913882	-503.5755048876667

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	46	36

end0.0ms

sample1.7s

Algorithm

intervals

Results

628.0ms	1493×	body	1280	valid
352.0ms	1424×	body	640	valid
208.0ms	4873×	body	80	valid
139.0ms	873×	body	320	valid
88.0ms	2969×	body	80	nan
46.0ms	471×	body	160	valid