Details

sample64.0ms

Algorithm

intervals

Results

25.0ms	55×	body	1280	valid
14.0ms	56×	body	640	valid
6.0ms	137×	body	80	valid
4.0ms	25×	body	320	valid
3.0ms	90×	body	80	nan
2.0ms	15×	body	160	valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	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: 11.2b

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))
5.1b	(pow (/ x (+ x y)) x)

rewrite35.0ms

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:

13.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
8.0ms	(pow (/ x (+ x y)) x)

series418.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(/ (pow (/ x (+ x y)) x) x)
40.0ms	(/ x (+ x y))
235.0ms	(pow (/ x (+ x y)) x)

simplify79.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	554	1456
1	2725	1426
2	5001	1426

prune407.0ms

Filtered

187 candidates to 137 candidates (73.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	4	188

Merged error: 0.0b

Counts

188 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.7b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

1213×	`cbrt-prod`
1039×	`add-sqr-sqrt`
961×	`*-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`
170×	`distribute-lft-out`
59×	`*-commutative`
20×	`add-exp-log`
18×	`cbrt-div`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
7×	`pow-exp`
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 → 993

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
128.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series798.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (+ x y))
131.0ms	(cbrt (+ x y))
262.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
276.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify226.0ms

Algorithm

egg-herbie

Counts

1005 → 1005

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	4304	18879
1	5001	18844

prune2.3s

Filtered

1005 candidates to 467 candidates (46.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1004	1	1005
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	1007	2	1009

Merged error: 0.0b

Counts

1009 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
0.7b	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
0.7b	(pow (/ (* (cbrt x) (cbrt (* (cbrt x) (cbrt x)))) (* (cbrt (+ x y)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))) x)
0.7b	(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

12152×	`cbrt-prod`
8942×	`add-sqr-sqrt`
4981×	`associate-r`
4261×	`unpow-prod-down`
4219×	`times-frac`
4100×	`unswap-sqr`
2786×	`*-un-lft-identity`
1766×	`add-cube-cbrt`
1665×	`associate-l`
1472×	`swap-sqr`
513×	`*-commutative`
448×	`distribute-lft-out`
104×	`cbrt-div`
35×	`flip3-+` `flip-+`
32×	`frac-times`
30×	`associate-/r/`
23×	`add-exp-log`
16×	`associate-*r/`
10×	`associate-*l/`
9×	`pow-unpow` `pow-exp`
7×	`pow1`
6×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 4365

Calls

4 calls:

11.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
20.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
529.0ms	(pow (/ (* (cbrt x) (cbrt (* (cbrt x) (cbrt x)))) (* (cbrt (+ x y)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))) x)
13.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

260.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
264.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
305.0ms	(pow (/ (* (cbrt x) (cbrt (* (cbrt x) (cbrt x)))) (* (cbrt (+ x y)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))) x)
529.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify1.2s

Algorithm

egg-herbie

Counts

4377 → 4377

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	7452	141759

prune20.1s

Filtered

4377 candidates to 2660 candidates (60.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	4377	0	4377
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	4377	2	4379

Merged error: 0.0b

Counts

4379 → 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)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify56.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	119	196
1	317	182
2	1504	180
3	5001	180

prune68.0ms

Filtered

34 candidates to 25 candidates (73.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	33	3	36

Merged error: 0b

Counts

36 → 3

regimes54.0ms

Accuracy

88% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 5.3b

bsearch121.0ms

Steps

Iters	Range		Point
7	3.798938191215488e-08	6.341782789262252e-06	6.231696762840839e-06
8	-3.088210918579413e+152	-1.010047755036718e+149	-1.0215350936667226e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	39
1	48	39

end0.0ms

sample1.8s

Algorithm

intervals

Results

683.0ms	1554×	body	1280	valid
360.0ms	1435×	body	640	valid
210.0ms	4828×	body	80	valid
144.0ms	859×	body	320	valid
95.0ms	3046×	body	80	nan
48.0ms	428×	body	160	valid