Details

analyze6.6s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 4.481588%

Guaranteed chance to sample good point: 16.407445%

sample97.0ms

Algorithm

intervals

Results

24.0ms	187×	body	80	valid
11.0ms	16×	body	1280	valid
10.0ms	22×	body	640	valid
9.0ms	20×	body	640	invalid
8.0ms	25×	body	320	valid
6.0ms	59×	body	80	invalid
5.0ms	7×	body	1280	invalid
3.0ms	8×	body	320	invalid
1.0ms	6×	body	160	valid
0.0ms	2×	body	160	invalid

simplify50.0ms

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: 40.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite78.0ms

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:

21.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
288.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune260.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	7	148

Merged error: 26.5b

Counts

148 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*l/`
74×	`associate-*r/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `rem-sqrt-square` `sqr-cos` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

5.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
158.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify97.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2471	7439
1	5001	7337

prune372.0ms

Filtered

102 candidates to 204 candidates (-100.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	204	7	211

Merged error: 26.5b

Counts

211 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
143.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify77.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1266	6778
1	5001	6662

prune467.0ms

Filtered

100 candidates to 184 candidates (-84.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	184	7	191

Merged error: 26.5b

Counts

191 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
6.1b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite78.0ms

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:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(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))))))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
138.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
138.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify86.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1513	6939
1	5002	6823

prune335.0ms

Filtered

98 candidates to 191 candidates (-94.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	188	10	198

Merged error: 26.5b

Counts

198 → 10

regimes1.3s

Accuracy

72.3% (3.7b remaining)

Error of 29.5b against oracle of 25.8b and baseline of 39.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	53
1	42	53

end0.0ms

analyze6.5s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 4.481588%

Guaranteed chance to sample good point: 16.407445%

sample2.8s

Algorithm

intervals

Results

616.0ms	5900×	body	80	valid
391.0ms	830×	body	640	valid
336.0ms	485×	body	1280	valid
227.0ms	459×	body	640	invalid
209.0ms	285×	body	1280	invalid
187.0ms	520×	body	320	valid
186.0ms	1891×	body	80	invalid
75.0ms	217×	body	320	invalid
66.0ms	265×	body	160	valid
23.0ms	101×	body	160	invalid

Details

analyze6.6s

sample97.0ms

simplify50.0ms

prune5.0ms

localize16.0ms

rewrite78.0ms

series332.0ms

simplify58.0ms

prune260.0ms

localize17.0ms

rewrite63.0ms

series178.0ms

simplify97.0ms

prune372.0ms

localize20.0ms

rewrite68.0ms

series293.0ms

simplify77.0ms

prune467.0ms

localize22.0ms

rewrite78.0ms

series286.0ms

simplify86.0ms

prune335.0ms

regimes1.3s

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze6.5s

sample2.8s

Profiling