Details

Time bar (total: 29.5s)

sample127.0ms

Algorithm
intervals
Results
38.0ms25×body1280valid
26.0ms248×body80valid
20.0ms45×body640valid
9.0ms28×body320valid
2.0ms12×body160valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01732
13416
27616
325716
482616
5235516
done500016

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize18.0ms

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)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite95.0ms

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))
15.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
53.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
498.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
714.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
172.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
53.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.6s

Counts
75 → 75
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01391279
13271271
29601077
331941060
done50001059

prune443.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.6b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite54.0ms

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×expm1-log1p-u associate-*l*
4×log1p-expm1-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:
40.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
82.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
87.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
40.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify4.3s

Counts
67 → 67
Iterations

Useful iterations: 4 (2.9s)

IterNodesCost
098808
1191718
2473622
31375619
44671616
done5000616

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
0.6b
(log1p (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log expm1-log1p-u add-cbrt-cube
4×log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp log1p-udef pow-pow pow1/3 log1p-expm1 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
5.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
6.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
1.0ms
(log1p (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))

series245.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
76.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
79.0ms
(log1p (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
60.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.6s

Counts
80 → 80
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0961019
1190813
2443728
32282716
done5001712

prune484.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.4b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite96.0ms

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:
18.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
30.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
758.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))
51.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify3.8s

Counts
77 → 77
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01241946
13181509
210621299
349141269
done50001269

prune426.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.0b

regimes625.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01921
12221
done2221

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.2s8351×body80valid
976.0ms1268×body640valid
760.0ms798×body1280valid
367.0ms719×body320valid
102.0ms365×body160valid