Details

Time bar (total: 6.3s)

sample58.0ms

Algorithm
intervals
Results
16.0ms260×body80valid
11.0ms41×body640valid
6.0ms15×body1280valid
4.0ms20×body320valid
2.0ms19×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0b
(cos (/ (+ phi1 phi2) 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
1.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
6.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms
(cos (/ (+ phi1 phi2) 2.0))

series954.0ms

Counts
4 → 12
Calls
4 calls:
381.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
457.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
90.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0328677
11130579
25001569

prune267.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(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))

series204.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(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

prune249.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 36
Calls
4 calls:
5.0ms
(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))

series114.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify100.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 4 (27.0ms)

IterNodesCost
054240
197212
2247212
3653212
42375204
55001204

prune286.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
11×pow1 add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
7×sqrt-prod
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative unswap-sqr
Counts
4 → 65
Calls
4 calls:
5.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
6.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
666.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
465.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0318932
11240780
25002773

prune276.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 2.9b

regimes343.0ms

Accuracy

0% (0.1b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0178
1178

end0.0ms

sample1.8s

Algorithm
intervals
Results
543.0ms8432×body80valid
380.0ms1336×body640valid
314.0ms747×body1280valid
145.0ms696×body320valid
54.0ms399×body160valid