Details

Time bar (total: 5.3s)

sample72.0ms

Algorithm
intervals
Results
22.0ms284×body80valid
13.0ms40×body640valid
10.0ms22×body1280valid
5.0ms20×body320valid
2.0ms11×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: 2.2b

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)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.9b
(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:
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))

series560.0ms

Counts
3 → 9
Calls
3 calls:
446.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
87.0ms
(* (- 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

prune220.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New491362
Fresh000
Picked101
Done000
Total501363

Merged error: 2.1b

Counts
63 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×associate-*l* log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 55
Calls
4 calls:
7.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series254.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
54.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
57.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0206431
1601364
22665364
35001364

prune227.0ms

Filtered
67 candidates to 54 candidates (80.6%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New67067
Fresh01212
Picked011
Done000
Total671380

Merged error: 2.1b

Counts
80 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(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))

series189.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify172.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (49.0ms)

IterNodesCost
088284
1165254
2433252
31255252
44860243
55001243

prune224.0ms

Filtered
52 candidates to 46 candidates (88.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New51152
Fresh11011
Picked101
Done011
Total531265

Merged error: 2.1b

Counts
65 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (cbrt (cos (/ (+ phi1 phi2) 2.0))))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
1×expm1-log1p expm1-udef
Counts
4 → 38
Calls
4 calls:
1.0ms
(expm1 (cbrt (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
8.0ms
(cos (/ (+ phi1 phi2) 2.0))

series319.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(expm1 (cbrt (cos (/ (+ phi1 phi2) 2.0))))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 4 (69.0ms)

IterNodesCost
0109273
1233241
2654241
31850241
45001234

prune209.0ms

Filtered
50 candidates to 44 candidates (88.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New50050
Fresh01010
Picked011
Done011
Total501262

Merged error: 2.1b

Counts
62 → 12

regimes345.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01910
11910

end0.0ms

sample2.1s

Algorithm
intervals
Results
647.0ms8375×body80valid
438.0ms1265×body640valid
358.0ms744×body1280valid
175.0ms709×body320valid
57.0ms348×body160valid