Details

Time bar (total: 52.7s)

sample193.0ms

Algorithm
intervals
Results
61.0ms25×body1280valid
36.0ms259×body80valid
24.0ms39×body640valid
7.0ms17×body320valid
3.0ms9×body160valid

simplify4.5s

Counts
1 → 1
Iterations
IterNodes
done5003
51878
4761
3231
272
134
017

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
3.3b
(cos (/ (+ phi2 phi1) 2.0))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×expm1-log1p-u insert-posit16 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 → 67
Calls
4 calls:
1.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
14.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
48.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
20.0ms
(cos (/ (+ phi2 phi1) 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
815.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
1.2s
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
180.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
43.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify5.1s

Counts
79 → 79
Iterations
IterNodes
done5000
34278
21073
1363
0146

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.7b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
0.4b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
3.3b
(cos (/ (+ phi2 phi1) 2.0))
3.3b
(cos (/ (+ phi2 phi1) 2.0))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
11×pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
7×sqrt-prod
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative unswap-sqr
Counts
4 → 69
Calls
4 calls:
27.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
39.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
25.0ms
(cos (/ (+ phi2 phi1) 2.0))
30.0ms
(cos (/ (+ phi2 phi1) 2.0))

series3.7s

Counts
4 → 12
Calls
4 calls:
2.3s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
1.4s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
56.0ms
(cos (/ (+ phi2 phi1) 2.0))
50.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify2.7s

Counts
81 → 81
Iterations
IterNodes
done5001
21187
1337
0130

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize176.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
0.4b
(expm1 (cos (/ (+ phi2 phi1) 2.0)))
3.3b
(cos (/ (+ phi2 phi1) 2.0))
3.3b
(cos (/ (+ phi2 phi1) 2.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×expm1-log1p associate-*r* *-commutative expm1-udef
Counts
4 → 56
Calls
4 calls:
43.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
1.0ms
(expm1 (cos (/ (+ phi2 phi1) 2.0)))
15.0ms
(cos (/ (+ phi2 phi1) 2.0))
16.0ms
(cos (/ (+ phi2 phi1) 2.0))

series3.1s

Counts
4 → 12
Calls
4 calls:
2.8s
(* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
163.0ms
(expm1 (cos (/ (+ phi2 phi1) 2.0)))
66.0ms
(cos (/ (+ phi2 phi1) 2.0))
68.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify5.1s

Counts
68 → 68
Iterations
IterNodes
done5007
33120
2883
1306
0125

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.7b

localize251.0ms

Local error

Found 4 expressions with local error:

0.4b
(expm1 (expm1 (log1p (cos (/ (+ phi2 phi1) 2.0)))))
0.4b
(log1p (cos (/ (+ phi2 phi1) 2.0)))
3.3b
(cos (/ (+ phi2 phi1) 2.0))
3.3b
(cos (/ (+ phi2 phi1) 2.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u log1p-expm1-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 44
Calls
4 calls:
1.0ms
(expm1 (expm1 (log1p (cos (/ (+ phi2 phi1) 2.0)))))
1.0ms
(log1p (cos (/ (+ phi2 phi1) 2.0)))
16.0ms
(cos (/ (+ phi2 phi1) 2.0))
27.0ms
(cos (/ (+ phi2 phi1) 2.0))

series522.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(expm1 (expm1 (log1p (cos (/ (+ phi2 phi1) 2.0)))))
142.0ms
(log1p (cos (/ (+ phi2 phi1) 2.0)))
65.0ms
(cos (/ (+ phi2 phi1) 2.0))
66.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify10.3s

Counts
56 → 56
Iterations
IterNodes
done5000
64102
52456
41185
3530
2252
1138
071

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.6b

regimes3.0s

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done17
117
014

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.3s1299×body640valid
1.2s8247×body80valid
944.0ms735×body320valid
879.0ms841×body1280valid
147.0ms374×body160valid