Details

sample99.0ms

Algorithm

intervals

Results

34.0ms	50×	body	1280	valid
21.0ms	47×	body	640	valid
14.0ms	152×	body	80	valid
8.0ms	30×	body	320	valid
5.0ms	91×	body	80	nan
2.0ms	9×	body	160	valid

simplify145.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

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

prune4.0ms

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: 12.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.3b	(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:

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

series395.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(/ (pow (/ x (+ x y)) x) x)
41.0ms	(/ x (+ x y))
226.0ms	(pow (/ x (+ x y)) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	537	1436
1	2640	1406
2	5002	1406

prune333.0ms

Filtered

181 candidates to 131 candidates (72.4%)

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: 0.5b

Counts

182 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.9b	(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)

series800.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
173.0ms	(cbrt x)
175.0ms	(cbrt x)
271.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify138.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	367	612
1	1118	572
2	4404	551
3	5001	551

prune207.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 0.0b

Counts

79 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
2.8b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite16.0ms

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)
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (+ x y))
175.0ms	(cbrt x)
172.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify143.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (32.0ms)

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

prune378.0ms

Filtered

107 candidates to 88 candidates (82.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	107	3	110

Merged error: 0.0b

Counts

110 → 3

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)

simplify47.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1435	169
3	5001	169

prune58.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	30	4	34

Merged error: 0b

Counts

34 → 4

Details

sample99.0ms

simplify145.0ms

prune4.0ms

localize7.0ms

rewrite29.0ms

series395.0ms

simplify71.0ms

prune333.0ms

localize16.0ms

rewrite21.0ms

series800.0ms

simplify138.0ms

prune207.0ms

localize15.0ms

rewrite16.0ms

series551.0ms

simplify143.0ms

prune378.0ms

localize5.0ms

rewrite5.0ms

series19.0ms

simplify47.0ms

prune58.0ms

regimes61.0ms

bsearch2.0ms

Profiling