Details

Time bar (total: 20.2s)

sample135.0ms

Algorithm
intervals
Results
49.0ms44×body640valid
28.0ms244×body80valid
14.0ms23×body1280valid
11.0ms28×body320valid
3.0ms11×body160valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01732
13416
27616
325716
482616
5235516
done500016

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize26.0ms

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)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite54.0ms

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:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
8.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
32.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
524.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
716.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
159.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
45.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts
75 → 75
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01391279
13271271
29601077
331941060
done50001059

prune489.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
11×pow1 add-sqr-sqrt add-cbrt-cube
9×*-un-lft-identity
7×add-cube-cbrt
6×associate-*r* associate-*l* prod-exp
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
2×associate-*l/ *-commutative
1×hypot-udef flip3-- 1-exp flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 64
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
22.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
28.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
630.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
691.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
122.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts
76 → 76
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01501364
13461301
29891075
332061058
done50001057

prune431.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi1 phi2) 2.0)))
0.1b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-exp-log add-cbrt-cube
5×associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×distribute-rgt-in distribute-lft-in
2×associate-*l/
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod rem-exp-log distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 73
Calls
4 calls:
24.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
51.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
57.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
20.0ms
(cos (/ (+ phi1 phi2) 2.0))

series346.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
156.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
38.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
54.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.7s

Counts
85 → 85
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01201104
1221993
2581873
31674868
done5000865

prune553.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(pow E (cos (/ (+ phi1 phi2) 2.0)))
0.5b
(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
21×log-prod
18×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
12×unpow-prod-down
9×add-exp-log
7×pow1 distribute-rgt-in distribute-lft-in
6×add-cbrt-cube
5×associate-*l*
4×expm1-log1p-u rem-log-exp associate-*r* pow-exp log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow
2×pow-to-exp e-exp-1 associate-*l/ log-pow
1×flip3-- pow-pow pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 89
Calls
4 calls:
38.0ms
(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
24.0ms
(pow E (cos (/ (+ phi1 phi2) 2.0)))
23.0ms
(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))

series395.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
106.0ms
(pow E (cos (/ (+ phi1 phi2) 2.0)))
86.0ms
(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
40.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts
101 → 101
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01431538
12761303
27851167
325271147
done50001132

prune516.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 3.9b

regimes17.0ms