Details

sample95.0ms

Algorithm

intervals

Results

25.0ms	251×	body	80	valid
21.0ms	48×	body	640	valid
20.0ms	34×	body	1280	valid
10.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify50.0ms

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: 40.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite94.0ms

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:

28.0ms	(* (* (- 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))
45.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
397.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune463.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

146×	`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:

10.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
106.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
405.0ms	(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

127 → 127

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1309	3623
1	5002	3539

prune439.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 27.4b

localize22.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
6.0b	(exp (log (sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))))
37.2b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

288×	`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))
77.0ms	(exp (log (sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))))
106.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

series859.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
396.0ms	(exp (log (sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))))
405.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

simplify86.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1504	6939
1	5002	6823

prune693.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 27.4b

localize32.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
6.4b	(pow E (log (sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))))
37.2b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

288×	`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))
78.0ms	(pow E (log (sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))))
106.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
695.0ms	(pow E (log (sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))))
398.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

simplify94.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1898	7439
1	5003	7353

prune710.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 22.5b

regimes727.0ms

Accuracy

25.5% (13.7b remaining)

Error of 34.2b against oracle of 20.5b and baseline of 38.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	58
1	60	58

end0.0ms

sample2.6s

Algorithm

intervals

Results

868.0ms	8276×	body	80	valid
591.0ms	1328×	body	640	valid
464.0ms	777×	body	1280	valid
246.0ms	746×	body	320	valid
78.0ms	350×	body	160	valid