Details

Time bar (total: 20.7s)

sample206.0ms

Algorithm
intervals
Results
63.0ms41×body640valid
54.0ms254×body80valid
36.0ms31×body1280valid
21.0ms30×body320valid
5.0ms14×body160valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done2013
62013
51878
4761
3231
272
134
017

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
3.5b
(cos (/ (+ phi2 phi1) 2))

rewrite46.0ms

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:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
19.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
20.0ms
(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
570.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
619.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
106.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.2s

Counts
79 → 79
Iterations
IterNodes
done2005
32005
21076
1360
0144

prune633.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.3b
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.4b
(expm1 (cos (/ (+ phi2 phi1) 2)))
3.5b
(cos (/ (+ phi2 phi1) 2))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
5×associate-*l* log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
34.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
1.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
13.0ms
(cos (/ (+ phi2 phi1) 2))

series389.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
87.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
89.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.5s

Counts
71 → 71
Iterations
IterNodes
done2000
42000
31782
2532
1221
0103

prune536.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi1 phi2) 2)))
0.2b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2)))))
0.4b
(log (exp (cos (/ (+ phi1 phi2) 2))))
3.5b
(cos (/ (+ phi1 phi2) 2))

rewrite94.0ms

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-cbrt-cube add-exp-log
5×associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in
2×associate-*l/
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- difference-of-squares unswap-sqr rem-exp-log
Counts
4 → 77
Calls
4 calls:
17.0ms
(exp (cos (/ (+ phi1 phi2) 2)))
39.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2)))))
21.0ms
(log (exp (cos (/ (+ phi1 phi2) 2))))
16.0ms
(cos (/ (+ phi1 phi2) 2))

series243.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(exp (cos (/ (+ phi1 phi2) 2)))
114.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2)))))
25.0ms
(log (exp (cos (/ (+ phi1 phi2) 2))))
30.0ms
(cos (/ (+ phi1 phi2) 2))

simplify1.0s

Counts
89 → 89
Iterations
IterNodes
done2000
32000
2605
1247
0121

prune766.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 4.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))

rewrite57.0ms

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:
8.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
21.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
18.0ms
(cos (/ (+ phi2 phi1) 2))
9.0ms
(cos (/ (+ phi2 phi1) 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
925.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
570.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
40.0ms
(cos (/ (+ phi2 phi1) 2))
36.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.2s

Counts
81 → 81
Iterations
IterNodes
done2029
32029
21160
1334
0127

prune566.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 4.9b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.6s8169×body80valid
1.8s1324×body640valid
1.2s803×body1280valid
559.0ms754×body320valid
188.0ms358×body160valid