Details

sample102.0ms

Algorithm

intervals

Results

25.0ms	261×	body	80	valid
21.0ms	26×	body	1280	valid
19.0ms	43×	body	640	valid
8.0ms	23×	body	320	valid
3.0ms	15×	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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 37.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.1b	(cos (/ (+ phi1 phi2) 2.0))
3.1b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

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:

6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(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))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
134.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify55.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune263.0ms

Filtered

127 candidates to 77 candidates (39.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	7	128

Merged error: 23.2b

Counts

128 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ phi1 phi2) 2.0))
3.1b	(cos (/ (+ phi1 phi2) 2.0))
3.1b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `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))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series150.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
134.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1278	4428
1	5001	4345

prune414.0ms

Filtered

112 candidates to 80 candidates (28.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Merged error: 23.2b

Counts

119 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ phi1 phi2) 2.0))
3.1b	(cos (/ (+ phi1 phi2) 2.0))
34.6b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
34.6b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite81.0ms

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))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
28.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
178.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
187.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify100.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1325	8770
1	5001	8646

prune1.3s

Filtered

180 candidates to 130 candidates (27.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	179	10	189

Merged error: 23.2b

Counts

189 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ phi1 phi2) 2.0))
5.2b	(exp (log (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))))
34.6b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
34.6b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
198×	`cbrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
66×	`log-div` `exp-diff`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod` `exp-sum`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`log-pow`
1×	`rem-exp-log`

Counts

4 → 246

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
36.0ms	(exp (log (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))))
24.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
26.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
181.0ms	(exp (log (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))))
180.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
183.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify142.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1567	13310
1	5003	13138

prune2.2s

Filtered

258 candidates to 179 candidates (30.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	258	10	268

Merged error: 23.2b

Counts

268 → 10

regimes1.7s

Accuracy

72.8% (3.8b remaining)

Error of 29.2b against oracle of 25.3b and baseline of 39.4b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms

sample2.8s

Algorithm

intervals

Results

816.0ms	8460×	body	80	valid
575.0ms	1281×	body	640	valid
489.0ms	735×	body	1280	valid
228.0ms	680×	body	320	valid
84.0ms	381×	body	160	valid

Details

sample102.0ms

simplify52.0ms

prune5.0ms

localize16.0ms

rewrite44.0ms

series165.0ms

simplify55.0ms

prune263.0ms

localize22.0ms

rewrite49.0ms

series150.0ms

simplify63.0ms

prune414.0ms

localize29.0ms

rewrite81.0ms

series376.0ms

simplify100.0ms

prune1.3s

localize31.0ms

rewrite121.0ms

series548.0ms

simplify142.0ms

prune2.2s

regimes1.7s

bsearch2.0ms

simplify1.0ms

end0.0ms

sample2.8s

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