Details

Time bar (total: 25.5s)

sample143.0ms

Algorithm
intervals
Results
38.0ms255×body80valid
27.0ms42×body640valid
25.0ms30×body1280valid
8.0ms17×body320valid
4.0ms13×body160valid

simplify967.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
41037
3259
276
134
017

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize41.0ms

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

rewrite73.0ms

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 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 (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
10.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
43.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
17.0ms
(cos (/ (+ phi2 phi1) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
614.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
783.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
141.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
36.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify848.0ms

Counts
75 → 75
Iterations
IterNodes
done5001
21577
1359
0142

prune696.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
11×add-sqr-sqrt pow1 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 (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
20.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
41.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
17.0ms
(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
560.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
798.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
119.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
36.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify871.0ms

Counts
76 → 76
Iterations
IterNodes
done5000
21733
1401
0153

prune631.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.0b
(cos (/ (+ phi1 phi2) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
26×add-sqr-sqrt
17×*-un-lft-identity
15×associate-*r* add-cube-cbrt
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×associate-*l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3
2×associate-*l/
1×pow-to-exp pow-pow flip3-- pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod flip-- distribute-lft-out-- rem-cube-cbrt difference-of-squares
Counts
4 → 97
Calls
4 calls:
25.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
2.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
9.0ms
(cos (/ (+ phi1 phi2) 2.0))

series295.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
43.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
69.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
31.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.6s

Counts
109 → 109
Iterations
IterNodes
done5001
21961
1324
0130

prune809.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.7b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×*-un-lft-identity add-cube-cbrt
11×pow1
6×pow1/3 swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 69
Calls
4 calls:
10.0ms
(* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))
16.0ms
(cos (/ (+ phi2 phi1) 2.0))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))

series675.0ms

Counts
4 → 12
Calls
4 calls:
570.0ms
(* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))
29.0ms
(cos (/ (+ phi2 phi1) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify6.7s

Counts
81 → 81
Iterations
IterNodes
done5001
34408
2656
1192
089

prune788.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 3.7b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done23
223
122
016

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.4s8252×body80valid
1.1s1308×body640valid
902.0ms827×body1280valid
360.0ms715×body320valid
149.0ms391×body160valid