Details

Time bar (total: 16.6s)

sample192.0ms

Algorithm
intervals
Results
66.0ms42×body640valid
42.0ms272×body80valid
24.0ms25×body1280valid
12.0ms25×body320valid
5.0ms14×body160valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
01732
13416
27616
325916
4105516
done500116

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize41.0ms

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)))
2.3b
(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)
25.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
19.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
620.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
779.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
156.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
53.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify828.0ms

Counts
75 → 75
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
01391279
13351271
214311079
done50021069

prune459.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize24.0ms

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)))
2.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite78.0ms

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)
46.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
597.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
785.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
170.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
38.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify830.0ms

Counts
75 → 75
Iterations

Useful iterations: done (826.0ms)

IterNodesCost
01391279
13351271
214311079
done50021069

prune522.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- 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)))
2.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite63.0ms

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:
39.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))

series382.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
86.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
81.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
39.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify671.0ms

Counts
67 → 67
Iterations

Useful iterations: done (668.0ms)

IterNodesCost
0101813
1218719
2686629
done5000624

prune395.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.2b
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
0.4b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
2.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
6×log1p-expm1-u
5×expm1-log1p-u
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×expm1-log1p expm1-udef
1×log1p-udef log1p-expm1
Counts
4 → 42
Calls
4 calls:
0.0ms
(expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
0.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
18.0ms
(cos (/ (+ phi1 phi2) 2.0))

series477.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
152.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
80.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.2s

Counts
54 → 54
Iterations

Useful iterations: done (1.2s)

IterNodesCost
081589
1169518
2417464
31545456
done5001443

prune352.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.4b

regimes515.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01820
12418
22518
done2518

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.3s8396×body80valid
1.3s1291×body640valid
1.1s754×body1280valid
414.0ms710×body320valid
93.0ms381×body160valid