Details

analyze574.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample67.0ms

Algorithm

intervals

Results

25.0ms	48×	body	1280	valid
10.0ms	145×	body	80	valid
9.0ms	31×	body	640	valid
5.0ms	24×	body	320	valid
2.0ms	8×	body	640	invalid
2.0ms	4×	body	1280	invalid
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	invalid
1.0ms	10×	body	80	invalid
0.0ms	9×	body	80	nan
0.0ms	2×	body	160	invalid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4985	9
1	4985	9

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: 10.5b

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))
4.6b	(pow (/ x (+ x y)) x)

rewrite31.0ms

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))
7.0ms	(pow (/ x (+ x y)) x)

series47.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
21.0ms	(pow (/ x (+ x y)) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5011	2849

prune188.0ms

Filtered

134 candidates to 181 candidates (-35.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	175	6	181
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	175	7	182

Merged error: 0.4b

Counts

182 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
4.6b	(pow (/ x (+ x y)) x)
4.6b	(pow (/ x (+ x y)) x)
4.6b	(pow (/ x (+ x y)) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

54×	`unpow-prod-down`
50×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
9×	`pow-unpow` `distribute-lft-out`
7×	`pow1`
6×	`pow-exp` `associate-/r/`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-pow` `flip3-+` `div-exp` `flip-+` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 110

Calls

4 calls:

1.0ms	(cbrt x)
7.0ms	(pow (/ x (+ x y)) x)
7.0ms	(pow (/ x (+ x y)) x)
7.0ms	(pow (/ x (+ x y)) x)

series76.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
17.0ms	(pow (/ x (+ x y)) x)
20.0ms	(pow (/ x (+ x y)) x)
17.0ms	(pow (/ x (+ x y)) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4995	1774
1	4995	1774

prune147.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	122	7	129

Merged error: 0.4b

Counts

129 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (/ x (+ x y))) x)
0.7b	(pow (sqrt (/ x (+ x y))) x)
4.2b	(sqrt (/ x (+ x y)))
4.2b	(sqrt (/ x (+ x y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
64×	`*-un-lft-identity`
50×	`times-frac`
46×	`add-sqr-sqrt`
42×	`unpow-prod-down`
40×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
8×	`associate-/r/`
6×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 136

Calls

4 calls:

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sqrt (/ x (+ x y))) x)
32.0ms	(pow (sqrt (/ x (+ x y))) x)
12.0ms	(sqrt (/ x (+ x y)))
8.0ms	(sqrt (/ x (+ x y)))

simplify43.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5551	2408

prune176.0ms

Filtered

108 candidates to 148 candidates (-37.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	148	7	155

Merged error: 0.4b

Counts

155 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.2b	(pow (/ (sqrt x) (sqrt (+ x y))) x)
0.2b	(pow (/ (sqrt x) (sqrt (+ x y))) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-prod`
172×	`*-un-lft-identity`
168×	`times-frac`
120×	`add-sqr-sqrt` `add-cube-cbrt`
96×	`unpow-prod-down`
26×	`distribute-lft-out`
14×	`add-exp-log` `associate-/r*`
12×	`associate-/l*`
8×	`sqrt-div` `associate-/r/` `add-cbrt-cube`
6×	`pow1` `pow-unpow`
4×	`sqrt-undiv` `flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqrt-pow2` `sqr-pow`

Counts

4 → 268

Calls

4 calls:

7.0ms	(/ (sqrt x) (sqrt (+ x y)))
8.0ms	(/ (sqrt x) (sqrt (+ x y)))
11.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)
11.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)

series93.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (sqrt x) (sqrt (+ x y)))
16.0ms	(/ (sqrt x) (sqrt (+ x y)))
32.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)
33.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5006	4636

prune183.0ms

Filtered

144 candidates to 280 candidates (-94.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	280	7	287

Merged error: 0.4b

Counts

287 → 7

regimes137.0ms

Accuracy

50.1% (5.1b remaining)

Error of 6.4b against oracle of 1.3b and baseline of 11.4b

bsearch182.0ms

Steps

Iters	Range	Point
8	9.054833061604537e+165	1.4388267308427828e+170	2.7087781073527612e+166
7	2.2651685303319043e+17	8.271617558349033e+18	2.5297358828475472e+17
10	-1.1729940684378226e+138	-5.882276064991604e+125	-5.949766666727802e+125

Iters

Range

Point

9.054833061604537e+165

1.4388267308427828e+170

2.7087781073527612e+166

2.2651685303319043e+17

8.271617558349033e+18

2.5297358828475472e+17

-1.1729940684378226e+138

-5.882276064991604e+125

-5.949766666727802e+125

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	71
1	32	71

end0.0ms

sample1.9s

Algorithm

intervals

Results

707.0ms	1444×	body	1280	valid
355.0ms	1192×	body	640	valid
240.0ms	4388×	body	80	valid
129.0ms	662×	body	320	valid
78.0ms	278×	body	640	invalid
49.0ms	107×	body	1280	invalid
39.0ms	314×	body	160	valid
36.0ms	179×	body	320	invalid
12.0ms	106×	body	160	invalid
8.0ms	137×	body	80	invalid
7.0ms	179×	body	80	nan

Details

analyze574.0ms

sample67.0ms

simplify37.0ms

prune7.0ms

localize7.0ms

rewrite31.0ms

series47.0ms

simplify65.0ms

prune188.0ms

localize14.0ms

rewrite25.0ms

series76.0ms

simplify56.0ms

prune147.0ms

localize13.0ms

rewrite31.0ms

series85.0ms

simplify43.0ms

prune176.0ms

localize9.0ms

rewrite53.0ms

series93.0ms

simplify57.0ms

prune183.0ms

regimes137.0ms

bsearch182.0ms

simplify1.0ms

end0.0ms

sample1.9s

Profiling