Details

sample97.0ms

Algorithm

intervals

Results

25.0ms	264×	body	80	valid
20.0ms	24×	body	1280	valid
16.0ms	36×	body	640	valid
6.0ms	19×	body	320	valid
4.0ms	18×	body	160	valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5091	32

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 36.5b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
33.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite51.0ms

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:

12.0ms	(* (* (- 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))
19.0ms	(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))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
139.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5172	6821

prune258.0ms

Filtered

78 candidates to 147 candidates (-88.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	140	9	149

Merged error: 23.6b

Counts

149 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
33.9b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite65.0ms

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))
25.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series153.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
136.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify133.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4962	11780
1	4962	11780

prune338.0ms

Filtered

107 candidates to 204 candidates (-90.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	204	9	213

Merged error: 23.6b

Counts

213 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b	(cos (/ (+ phi1 phi2) 2.0))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
33.9b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 4) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `associate-*l/` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 4) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
136.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 4) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5273	6537

prune280.0ms

Filtered

67 candidates to 112 candidates (-67.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	111	10	121

Merged error: 23.6b

Counts

121 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b	(cos (/ (+ phi1 phi2) 2.0))
1.5b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 5) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
34.9b	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 5) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
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))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 5) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
23.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 5) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
183.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 5) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
191.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 5) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify74.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5025	11646

prune577.0ms

Filtered

100 candidates to 180 candidates (-80.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	180	10	190

Merged error: 23.6b

Counts

190 → 10

regimes1.1s

Accuracy

70.3% (4.2b remaining)

Error of 28.7b against oracle of 24.4b and baseline of 38.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	69
1	53	69

end0.0ms

sample3.0s

Algorithm

intervals

Results

827.0ms	8392×	body	80	valid
609.0ms	1319×	body	640	valid
559.0ms	832×	body	1280	valid
224.0ms	698×	body	320	valid
83.0ms	364×	body	160	valid

Details

sample97.0ms

simplify102.0ms

prune15.0ms

localize19.0ms

rewrite51.0ms

series179.0ms

simplify48.0ms

prune258.0ms

localize19.0ms

rewrite65.0ms

series153.0ms

simplify133.0ms

prune338.0ms

localize22.0ms

rewrite52.0ms

series152.0ms

simplify46.0ms

prune280.0ms

localize26.0ms

rewrite71.0ms

series384.0ms

simplify74.0ms

prune577.0ms

regimes1.1s

bsearch1.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling