Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	267×	body	80	valid
11.0ms	26×	body	1280	valid
9.0ms	33×	body	640	valid
4.0ms	18×	body	320	valid
2.0ms	13×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
33.8b	(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:

13.0ms	(* (* (- 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))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
406.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune454.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
33.8b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite52.0ms

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

series481.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
399.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (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

prune553.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 26.3b

localize27.0ms

Local error

Found 4 expressions with local error:

3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
6.0b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
33.8b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite94.0ms

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))
36.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
25.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series855.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
399.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
399.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify99.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1525	8908
1	5002	8770

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 26.3b

localize32.0ms

Local error

Found 4 expressions with local error:

3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
6.4b	(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
33.8b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `pow-sub`
64×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`unpow-prod-up` `pow-unpow` `log-prod` `sqrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `log-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `sqr-pow`

Counts

4 → 186

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
34.0ms	(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
28.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series967.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
514.0ms	(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
400.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify119.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1919	9540
1	5002	9432

prune1.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 18.6b

regimes911.0ms

Accuracy

26.7% (13.5b remaining)

Error of 34.1b against oracle of 20.6b and baseline of 39.0b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	37
1	48	37

end0.0ms

sample1.8s

Algorithm

intervals

Results

524.0ms	8294×	body	80	valid
368.0ms	1333×	body	640	valid
298.0ms	761×	body	1280	valid
133.0ms	673×	body	320	valid
50.0ms	358×	body	160	valid