Details

Time bar (total: 5.5s)

sample62.0ms

Algorithm
intervals
Results
16.0ms261×body80valid
12.0ms45×body640valid
10.0ms27×body1280valid
4.0ms19×body320valid
2.0ms16×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

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)))
4.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
7.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series571.0ms

Counts
3 → 9
Calls
3 calls:
460.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
85.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify98.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0290525
11003448
24763442
35001440

prune236.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* 1 (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
4.0ms
(* (hypot (* 1 (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
7.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series564.0ms

Counts
3 → 9
Calls
3 calls:
448.0ms
(* (hypot (* 1 (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
89.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0293550
11047469
25001463

prune261.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
4.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
26×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt associate-*r*
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×associate-*l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3
2×associate-*l/
1×pow-to-exp flip3-- pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out-- rem-cube-cbrt difference-of-squares
Counts
4 → 97
Calls
4 calls:
10.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
2.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series196.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
27.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
53.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0273715
11100668
25002655

prune387.0ms

Filtered
109 candidates to 68 candidates (62.4%)
Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 40
Calls
4 calls:
1.0ms
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series192.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify177.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (49.0ms)

IterNodesCost
088284
1165254
2433252
31255252
44860243
55001243

prune238.0ms

Filtered
52 candidates to 46 candidates (88.5%)
Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 4.6b

regimes459.0ms

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.4b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0229
1249
2249

end0.0ms

sample1.8s

Algorithm
intervals
Results
546.0ms8490×body80valid
361.0ms1279×body640valid
311.0ms744×body1280valid
155.0ms780×body320valid
54.0ms371×body160valid