Details

sample79.0ms

Algorithm

intervals

Results

30.0ms	60×	body	1280	valid
14.0ms	47×	body	640	valid
8.0ms	143×	body	80	valid
7.0ms	35×	body	320	valid
7.0ms	102×	body	80	nan
2.0ms	16×	body	160	valid

simplify111.0ms

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	4142	4
7	5001	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 11.6b

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))
6.4b	(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)

series404.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(/ (pow (/ x (+ x y)) x) x)
43.0ms	(/ x (+ x y))
229.0ms	(pow (/ x (+ x y)) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (15.0ms)

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

prune353.0ms

Filtered

181 candidates to 131 candidates (72.4%)

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: 0.6b

Counts

182 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`unpow-prod-down`
12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `pow-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series828.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
180.0ms	(cbrt x)
187.0ms	(cbrt x)
278.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify155.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	367	613
1	1117	573
2	4414	551
3	5001	551

prune221.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Merged error: 0.1b

Counts

80 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

55×	`cbrt-prod`
48×	`log-prod` `*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `rem-log-exp` `associate-/r/` `flip-+`
1×	`log-div` `div-exp` `log-pow` `div-inv`

Counts

4 → 95

Calls

4 calls:

3.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ x y))
193.0ms	(cbrt x)
186.0ms	(cbrt x)
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify136.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	360	861
1	982	830
2	4123	810
3	5001	810

prune383.0ms

Filtered

107 candidates to 88 candidates (82.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	107	4	111

Merged error: 0.1b

Counts

111 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

4.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify49.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1465	170
3	5003	170

prune51.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	30	5	35

Merged error: 0.1b

Counts

35 → 5

regimes70.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.9b

bsearch115.0ms

Steps

Iters	Range		Point
9	5.08584384811324e-07	108.10498260228141	27.519261333115796
9	-8.211399685419546e+34	-1.3726129525153165e+29	-5.167592364684384e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

766.0ms	1547×	body	1280	valid
469.0ms	1566×	body	640	valid
262.0ms	4785×	body	80	valid
162.0ms	813×	body	320	valid
128.0ms	3009×	body	80	nan
53.0ms	428×	body	160	valid