Details

sample6.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 2.124023%

Guaranteed chance to sample good point: 23.00449%

Results

20.0ms	193×	body	80	valid
13.0ms	29×	body	640	valid
11.0ms	10×	body	1280	invalid
8.0ms	11×	body	1280	valid
7.0ms	75×	body	80	invalid
6.0ms	13×	body	640	invalid
5.0ms	14×	body	320	valid
2.0ms	9×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	5×	body	160	invalid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	17
1	71	17
2	241	17
3	747	17
4	2196	17
5	5001	17

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 42.6b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
39.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

13.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
137.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune243.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	5	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Merged error: 27.3b

Counts

148 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
40.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
40.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`cbrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 168

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
17.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
176.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
180.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify85.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1313	6856
1	5001	6776

prune512.0ms

Filtered

100 candidates to 180 candidates (-80.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	180	6	186

Merged error: 27.3b

Counts

186 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
6.3b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
39.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`log-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

4 → 179

Calls

4 calls:

4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
131.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
135.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify95.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1513	6939
1	5002	6823

prune364.0ms

Filtered

98 candidates to 191 candidates (-94.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	187	10	197

Merged error: 27.3b

Counts

197 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
6.4b	(pow (exp 1/2) (log (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))))
40.8b	(log (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`log-div`
128×	`frac-times` `frac-add`
66×	`pow-sub`
64×	`associate-*r/`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod`
5×	`add-exp-log`
4×	`pow-unpow` `pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-up` `unpow-prod-down` `exp-prod`
2×	`flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 182

Calls

4 calls:

4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(pow (exp 1/2) (log (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))))
19.0ms	(log (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
170.0ms	(pow (exp 1/2) (log (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))))
111.0ms	(log (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify93.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1835	7407
1	5003	7340

prune391.0ms

Filtered

105 candidates to 194 candidates (-84.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	187	7	194
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	189	15	204

Merged error: 21.1b

Counts

204 → 15

regimes1.6s

Accuracy

49.3% (10.9b remaining)

Error of 28.7b against oracle of 17.8b and baseline of 39.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms

sample10.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 2.124023%

Guaranteed chance to sample good point: 23.00449%

Results

631.0ms	5992×	body	80	valid
394.0ms	821×	body	640	valid
346.0ms	493×	body	1280	valid
231.0ms	2250×	body	80	invalid
215.0ms	458×	body	640	invalid
200.0ms	300×	body	1280	invalid
167.0ms	444×	body	320	valid
94.0ms	247×	body	320	invalid
60.0ms	250×	body	160	valid
23.0ms	103×	body	160	invalid

Details

sample6.9s

simplify54.0ms

prune5.0ms

localize18.0ms

rewrite56.0ms

series179.0ms

simplify62.0ms

prune243.0ms

localize22.0ms

rewrite64.0ms

series365.0ms

simplify85.0ms

prune512.0ms

localize21.0ms

rewrite71.0ms

series276.0ms

simplify95.0ms

prune364.0ms

localize28.0ms

rewrite74.0ms

series290.0ms

simplify93.0ms

prune391.0ms

regimes1.6s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample10.0s

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