Details

Time bar (total: 15.8s)

sample71.0ms

Algorithm
intervals
Results
20.0ms251×body80valid
13.0ms44×body640valid
11.0ms26×body1280valid
6.0ms25×body320valid
2.0ms14×body160valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01732
13416
27616
319516
449116
5138616
6495016
done500016

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize14.0ms

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)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

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))
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series961.0ms

Counts
4 → 12
Calls
4 calls:
390.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
455.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
89.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.6s

Counts
75 → 75
Iterations

Useful iterations: 3 (655.0ms)

IterNodesCost
01391279
13141271
29691077
335791060
done50001060

prune277.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

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))
3.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
8.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
390.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
526.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
88.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.5s

Counts
75 → 75
Iterations

Useful iterations: 3 (587.0ms)

IterNodesCost
01381279
13141271
29231077
334311060
done50001060

prune279.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize19.0ms

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))))
0.4b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

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:
10.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series277.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
60.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
63.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.0s

Counts
67 → 67
Iterations

Useful iterations: 4 (1.0s)

IterNodesCost
0101813
1208719
2525626
31562621
43746618
done5000618

prune274.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))
2.8b
(cos (/ (+ phi1 phi2) 2.0))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

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))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series195.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(cbrt (cos (/ (+ phi1 phi2) 2.0)))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.7s

Counts
52 → 52
Iterations

Useful iterations: 4 (170.0ms)

IterNodesCost
048501
189494
2161444
3317437
4817433
51924433
done5000433

prune235.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

regimes309.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01618
11918
done1918

end0.0ms

sample1.9s

Algorithm
intervals
Results
567.0ms8414×body80valid
381.0ms1290×body640valid
351.0ms818×body1280valid
160.0ms738×body320valid
53.0ms382×body160valid