Details

sample72.0ms

Algorithm

intervals

Results

22.0ms	284×	body	80	valid
14.0ms	40×	body	640	valid
10.0ms	22×	body	1280	valid
5.0ms	20×	body	320	valid
2.0ms	11×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 40.5b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
37.5b	(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))
18.0ms	(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))))
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))))

simplify64.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune425.0ms

Filtered

147 candidates to 77 candidates (52.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Merged error: 25.6b

Counts

148 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
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) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
411.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1349	3745
1	5002	3672

prune440.0ms

Filtered

128 candidates to 69 candidates (53.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	128	7	135

Merged error: 25.6b

Counts

135 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
38.7b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
38.7b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite70.0ms

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:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

27.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
493.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
494.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify94.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1301	6834
1	5001	6754

prune815.0ms

Filtered

180 candidates to 100 candidates (55.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	179	8	187

Merged error: 25.6b

Counts

187 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- phi1 phi2) (- phi1 phi2))
0.0b	(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
2.8b	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
37.5b	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

47×	`flip3--` `flip--`
36×	`sqrt-div`
32×	`frac-add`
28×	`associate-*r/`
27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`frac-times`
14×	`pow1`
12×	`add-cube-cbrt`
11×	`associate-r`
10×	`associate-*l/`
9×	`add-log-exp`
8×	`add-exp-log` `associate-l` `add-cbrt-cube`
7×	`swap-sqr` `sqrt-prod`
6×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`sub-neg` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate--l+` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 130

Calls

4 calls:

9.0ms	(* (- phi1 phi2) (- phi1 phi2))
19.0ms	(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
10.0ms	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
15.0ms	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- phi1 phi2) (- phi1 phi2))
213.0ms	(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
30.0ms	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
156.0ms	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

simplify108.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	725	2598
1	3675	2543
2	5001	2539

prune445.0ms

Filtered

142 candidates to 89 candidates (62.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	139	11	150

Merged error: 24.9b

Counts

150 → 11

regimes557.0ms

Accuracy

70.3% (4.3b remaining)

Error of 28.8b against oracle of 24.5b and baseline of 38.9b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	36
1	36	36

end0.0ms

sample2.1s

Algorithm

intervals

Results

657.0ms	8375×	body	80	valid
429.0ms	1265×	body	640	valid
350.0ms	744×	body	1280	valid
181.0ms	709×	body	320	valid
58.0ms	348×	body	160	valid