Details

Time bar (total: 4.6s)

sample64.0ms

Algorithm
intervals
Results
17.0ms280×body80valid
11.0ms28×body1280valid
9.0ms35×body640valid
5.0ms27×body320valid
2.0ms12×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 3.2b

Counts
2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
2×associate-*l/ *-commutative
1×flip3-- flip--
Counts
3 → 4
Calls
3 calls:
2.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
5.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms
(cos (/ (+ phi1 phi2) 2.0))

series585.0ms

Counts
3 → 9
Calls
3 calls:
466.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
91.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
016292
149278
2204172
3500169

prune54.0ms

Filtered
13 candidates to 11 candidates (84.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New10313
Fresh000
Picked011
Done000
Total10414

Merged error: 3.1b

Counts
14 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot (- lambda1 lambda2) (- phi1 phi2))
0.0b
(* (hypot (- lambda1 lambda2) (- phi1 phi2)) R)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
1×hypot-udef *-commutative
Counts
2 → 2
Calls
2 calls:
1.0ms
(hypot (- lambda1 lambda2) (- phi1 phi2))
2.0ms
(* (hypot (- lambda1 lambda2) (- phi1 phi2)) R)

series310.0ms

Counts
2 → 6
Calls
2 calls:
146.0ms
(hypot (- lambda1 lambda2) (- phi1 phi2))
164.0ms
(* (hypot (- lambda1 lambda2) (- phi1 phi2)) R)

simplify116.0ms

Algorithm
egg-herbie
Counts
8 → 8
Iterations

Useful iterations: 4 (114.0ms)

IterNodesCost
010246
128045
291341
3423836
4500135

prune30.0ms

Filtered
8 candidates to 8 candidates (100.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New808
Fresh022
Picked011
Done011
Total8412

Merged error: 3.1b

Counts
12 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))
1.4b
(- (* lambda1 lambda1) (* lambda2 lambda2))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
25.9b
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×*-commutative
12×difference-of-squares
8×associate-*l*
6×associate-/l*
4×prod-diff associate-*l/
3×flip3-- flip--
2×fma-neg associate-/r/ associate-/l/
1×sub-neg frac-2neg flip3-+ clear-num flip-+ div-inv
Counts
4 → 34
Calls
4 calls:
8.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(- (* lambda1 lambda1) (* lambda2 lambda2))
4.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))

series289.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms
(- (* lambda1 lambda1) (* lambda2 lambda2))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
121.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))

simplify66.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0193262
1664243
22349223
35001209

prune123.0ms

Filtered
46 candidates to 25 candidates (54.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New43346
Fresh011
Picked011
Done112
Total44650

Merged error: 3.1b

Counts
50 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
0.2b
(/ (+ lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
0.2b
(/ (+ lambda1 lambda2) (/ (+ lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
3.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
11×associate-/r/
7×associate-/r*
6×associate-*l/ associate-/l/
3×flip3-- frac-2neg flip3-+ clear-num *-commutative flip-- flip-+ div-inv
Counts
4 → 27
Calls
4 calls:
5.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
7.0ms
(/ (+ lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
9.0ms
(/ (+ lambda1 lambda2) (/ (+ lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
4.0ms
(cos (/ (+ phi1 phi2) 2.0))

series383.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
173.0ms
(/ (+ lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
91.0ms
(/ (+ lambda1 lambda2) (/ (+ lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify137.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0172221
1574190
24066184
35002184

prune140.0ms

Filtered
39 candidates to 29 candidates (74.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New36339
Fresh123
Picked101
Done112
Total39645

Merged error: 3.1b

Counts
45 → 6

regimes229.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02513
12513

end0.0ms

sample1.8s

Algorithm
intervals
Results
552.0ms8520×body80valid
365.0ms1332×body640valid
310.0ms774×body1280valid
150.0ms700×body320valid
52.0ms358×body160valid