Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	273×	body	80	valid
18.0ms	37×	body	640	valid
14.0ms	20×	body	1280	valid
7.0ms	20×	body	320	valid
3.0ms	13×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	17
1	71	17
2	241	17
3	747	17
4	2196	17
5	5001	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

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))))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
34.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite200.0ms

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:

68.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
99.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))
378.0ms	(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 (28.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 25.4b

localize24.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
35.1b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.1b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite164.0ms

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:

10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
61.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
61.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series956.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))
453.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
455.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify88.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1301	6834
1	5001	6754

prune4.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 25.4b

localize29.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
35.1b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.2b	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) 1/3)

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`cbrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow`
1×	`pow-to-exp` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

11.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
61.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
102.0ms	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) 1/3)

series941.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))
446.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
447.0ms	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) 1/3)

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1349	3859
1	5001	3741

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 25.4b

localize39.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
6.6b	(pow (pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
35.1b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.1b	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3)))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

10.0ms	(cos (/ (+ phi1 phi2) 2.0))
176.0ms	(pow (pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
61.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
104.0ms	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3)))

series2.3s

Counts

4 → 12

Calls

4 calls:

30.0ms	(cos (/ (+ phi1 phi2) 2.0))
854.0ms	(pow (pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
455.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
969.0ms	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3)))

simplify68.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1511	4673
1	5002	4585

prune3.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.4b

regimes1.2s

Accuracy

72.6% (3.8b remaining)

Error of 29.2b against oracle of 25.5b and baseline of 39.1b

bsearch5.0ms

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

880.0ms	8376×	body	80	valid
618.0ms	1283×	body	640	valid
586.0ms	821×	body	1280	valid
252.0ms	733×	body	320	valid
83.0ms	363×	body	160	valid