Details

sample100.0ms

Algorithm

intervals

Results

25.0ms	275×	body	80	valid
22.0ms	44×	body	640	valid
16.0ms	25×	body	1280	valid
8.0ms	26×	body	320	valid
2.0ms	8×	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

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: 42.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
38.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite52.0ms

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:

15.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(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))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* (- 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))
138.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune288.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	137	10	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	10	148

Merged error: 26.1b

Counts

148 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
38.6b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite61.0ms

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:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series154.0ms

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))
137.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify106.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2471	7439
1	5001	7337

prune371.0ms

Filtered

102 candidates to 204 candidates (-100.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	204	10	214

Merged error: 26.1b

Counts

214 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
0.8b	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
4.0b	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
38.6b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

356×	`frac-times`
318×	`flip3--` `flip--`
210×	`sqrt-div`
208×	`frac-add`
178×	`associate-*l/`
124×	`associate-*r/`
83×	`flip3-+` `flip-+`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `sum-log` `*-commutative` `cos-2` `unswap-sqr`

Counts

4 → 289

Calls

4 calls:

13.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
3.0ms	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
2.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
26.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
7.0ms	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
5.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
444.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify197.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3823	15164
1	5003	15050

prune1.1s

Filtered

155 candidates to 301 candidates (-94.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	296	5	301
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	300	11	311

Merged error: 26.1b

Counts

311 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
4.0b	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
4.0b	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
38.6b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (/ (+ 1/8 (pow (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) 3)) (+ (* (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) (- (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) 1/2)) 1/4))) (* (- 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/`
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` `cos-2`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 175

Calls

4 calls:

2.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
2.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
2.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
33.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (/ (+ 1/8 (pow (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) 3)) (+ (* (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) (- (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) 1/2)) 1/4))) (* (- phi1 phi2) (- phi1 phi2))))

series4.2s

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
4.2s	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (/ (+ 1/8 (pow (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) 3)) (+ (* (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) (- (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))) 1/2)) 1/4))) (* (- phi1 phi2) (- phi1 phi2))))

simplify144.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2673	10778
1	5001	10685

prune677.0ms

Filtered

100 candidates to 187 candidates (-87.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	186	12	198

Merged error: 26.1b

Counts

198 → 12

regimes2.0s

Accuracy

75.9% (3.3b remaining)

Error of 28.6b against oracle of 25.3b and baseline of 38.9b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	48
1	51	48

end0.0ms

sample2.9s

Algorithm

intervals

Results

800.0ms	8415×	body	80	valid
585.0ms	1318×	body	640	valid
533.0ms	809×	body	1280	valid
235.0ms	748×	body	320	valid
77.0ms	346×	body	160	valid

Details

sample100.0ms

simplify51.0ms

prune5.0ms

localize17.0ms

rewrite52.0ms

series179.0ms

simplify60.0ms

prune288.0ms

localize18.0ms

rewrite61.0ms

series154.0ms

simplify106.0ms

prune371.0ms

localize20.0ms

rewrite82.0ms

series486.0ms

simplify197.0ms

prune1.1s

localize29.0ms

rewrite63.0ms

series4.2s

simplify144.0ms

prune677.0ms

regimes2.0s

bsearch3.0ms

simplify2.0ms

end0.0ms

sample2.9s

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