Details

sample71.0ms

Algorithm

intervals

Results

23.0ms	279×	body	80	valid
12.0ms	40×	body	640	valid
12.0ms	27×	body	1280	valid
5.0ms	22×	body	320	valid
1.0ms	7×	body	160	valid

simplify52.0ms

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

prune3.0ms

Filtered

1 candidates to 0 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: 40.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

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

series531.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
393.0ms	(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

127 → 127

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune394.0ms

Filtered

127 candidates to 77 candidates (60.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	7	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Merged error: 27.6b

Counts

128 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
405.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1349	3745
1	5002	3672

prune429.0ms

Filtered

128 candidates to 69 candidates (53.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	129	7	136

Merged error: 27.6b

Counts

136 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
13×	`log-pow`
12×	`exp-prod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `log-prod` `cube-prod` `sqrt-prod`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `rem-log-exp` `flip-+` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

4.0ms	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
404.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1360	3931
1	5002	3837

prune484.0ms

Filtered

129 candidates to 74 candidates (57.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	129	7	136

Merged error: 27.6b

Counts

136 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
6.2b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite76.0ms

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))
27.0ms	(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))))

series894.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
420.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
416.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify88.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1513	6939
1	5002	6823

prune599.0ms

Filtered

191 candidates to 100 candidates (52.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	188	10	198

Merged error: 27.6b

Counts

198 → 10

regimes596.0ms

Accuracy

72.6% (3.7b remaining)

Error of 29.2b against oracle of 25.5b and baseline of 39.2b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	36
1	36	36

end0.0ms

sample2.0s

Algorithm

intervals

Results

623.0ms	8351×	body	80	valid
419.0ms	1264×	body	640	valid
352.0ms	766×	body	1280	valid
178.0ms	735×	body	320	valid
55.0ms	342×	body	160	valid

Details

sample71.0ms

simplify52.0ms

prune3.0ms

localize16.0ms

rewrite43.0ms

series531.0ms

simplify58.0ms

prune394.0ms

localize25.0ms

rewrite42.0ms

series511.0ms

simplify60.0ms

prune429.0ms

localize25.0ms

rewrite45.0ms

series512.0ms

simplify66.0ms

prune484.0ms

localize21.0ms

rewrite76.0ms

series894.0ms

simplify88.0ms

prune599.0ms

regimes596.0ms

bsearch3.0ms

simplify1.0ms

end0.0ms

sample2.0s

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