Details

sample95.0ms

Algorithm

intervals

Results

24.0ms	261×	body	80	valid
22.0ms	44×	body	640	valid
15.0ms	23×	body	1280	valid
7.0ms	23×	body	320	valid
2.0ms	10×	body	160	valid

simplify51.0ms

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: 41.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
38.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite46.0ms

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)))
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) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
142.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune233.0ms

Filtered

127 candidates to 77 candidates (39.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	6	128

Merged error: 26.7b

Counts

128 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
31.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
14.0ms	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
15.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
109.0ms	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
122.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

simplify78.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1371	6075
1	5002	5955

prune302.0ms

Filtered

203 candidates to 108 candidates (46.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	199	10	209

Merged error: 26.4b

Counts

209 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
5.2b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))))
31.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

288×	`flip3--` `flip--`
240×	`associate-*l/`
192×	`frac-times` `frac-add`
132×	`sqrt-div`
96×	`associate-*r/`
66×	`log-div` `exp-diff`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `distribute-rgt-in` `sub-neg` `associate-+l+` `associate-+r+` `distribute-lft-in` `add-cbrt-cube`
3×	`flip3-+` `log-pow` `flip-+`
2×	`sqrt-pow1` `pow1/2`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `rem-exp-log`

Counts

4 → 255

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2.0))
15.0ms	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
21.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))))
15.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
110.0ms	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
122.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))))
128.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

simplify107.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1563	9019
1	5002	8885

prune449.0ms

Filtered

267 candidates to 132 candidates (50.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	261	6	267
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	262	15	277

Merged error: 26.4b

Counts

277 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

5.1b	(pow (exp (* (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))) (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))))) (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))))
31.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
31.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
31.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

288×	`flip3--` `flip--`
240×	`associate-*l/`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
13×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod`
5×	`add-log-exp`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
3×	`unpow-prod-down` `rem-sqrt-square` `pow-pow` `flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 262

Calls

4 calls:

4.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))) (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))))) (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))))
16.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
16.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
16.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.2s	(pow (exp (* (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))) (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))))) (cbrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))))))
122.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
123.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
124.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

simplify120.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1366	10350
1	5002	10054

prune963.0ms

Filtered

274 candidates to 140 candidates (48.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	270	4	274
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	272	17	289

Merged error: 24.0b

Counts

289 → 17

regimes1.6s

Accuracy

59% (7.1b remaining)

Error of 29.1b against oracle of 22.0b 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

sample2.8s

Algorithm

intervals

Results

769.0ms	8296×	body	80	valid
573.0ms	1311×	body	640	valid
496.0ms	769×	body	1280	valid
233.0ms	751×	body	320	valid
74.0ms	348×	body	160	valid

Details

sample95.0ms

simplify51.0ms

prune5.0ms

localize16.0ms

rewrite46.0ms

series172.0ms

simplify56.0ms

prune233.0ms

localize16.0ms

rewrite61.0ms

series259.0ms

simplify78.0ms

prune302.0ms

localize20.0ms

rewrite87.0ms

series366.0ms

simplify107.0ms

prune449.0ms

localize33.0ms

rewrite84.0ms

series1.5s

simplify120.0ms

prune963.0ms

regimes1.6s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.8s

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