Details

sample57.0ms

Algorithm

intervals

Results

17.0ms	41×	body	1280	valid
15.0ms	57×	body	640	valid
7.0ms	156×	body	80	valid
3.0ms	18×	body	320	valid
3.0ms	86×	body	80	nan
1.0ms	12×	body	160	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (13.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4183	4
7	5001	4

prune7.0ms

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)

rewrite33.0ms

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×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

12.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series424.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(/ (pow (/ x (+ x y)) x) x)
44.0ms	(/ x (+ x y))
240.0ms	(pow (/ x (+ x y)) x)

simplify83.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	553	1458
1	2719	1426
2	5002	1426

prune316.0ms

Filtered

187 candidates to 137 candidates (26.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	3	188

Merged error: 0.3b

Counts

188 → 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)

rewrite237.0ms

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×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 987

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
98.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series936.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
178.0ms	(cbrt x)
281.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
296.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify258.0ms

Algorithm

egg-herbie

Counts

999 → 999

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	4265	18779
1	5002	18750

prune2.0s

Filtered

999 candidates to 461 candidates (53.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	998	1	999
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	1000	2	1002

Merged error: 0.0b

Counts

1002 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod`
113×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
62×	`cbrt-div`
59×	`add-cube-cbrt`
48×	`unpow-prod-down`
42×	`times-frac`
27×	`swap-sqr`
24×	`distribute-lft-out`
21×	`associate-r` `associate-l`
19×	`flip3-+` `flip-+`
12×	`frac-times` `unswap-sqr`
7×	`add-exp-log`
6×	`associate-r/` `associate-l/`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3` `*-commutative`
2×	`pow-exp` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `div-exp` `div-inv` `sqr-pow`

Counts

4 → 215

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
269.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
268.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
280.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify80.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	597	2593
1	2000	2547
2	5002	2382

prune795.0ms

Filtered

227 candidates to 143 candidates (37.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	227	2	229

Merged error: 0.0b

Counts

229 → 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` `expm1-log1p-u` `frac-2neg` `mul-1-neg` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

7.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	119	196
1	317	182
2	1495	180
3	5002	180

prune47.0ms

Filtered

34 candidates to 25 candidates (26.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	34	2	36

Merged error: 0b

Counts

36 → 2

regimes46.0ms

Accuracy

97.7% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 5.9b

bsearch95.0ms

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	42	48
1	42	48

end0.0ms

sample1.8s

Algorithm

intervals

Results

655.0ms	1493×	body	1280	valid
368.0ms	1424×	body	640	valid
213.0ms	4873×	body	80	valid
143.0ms	873×	body	320	valid
93.0ms	2969×	body	80	nan
48.0ms	471×	body	160	valid