Details

Time bar (total: 25.2s)

sample129.0ms

Algorithm
intervals
Results
30.0ms269×body80valid
29.0ms26×body320valid
22.0ms46×body640valid
17.0ms24×body1280valid
2.0ms11×body160valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
323832
474232
5197232
6448632
done500132

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
35.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
68×frac-times
66×sqrt-div
64×frac-add
44×pow1
34×associate-*r/
17×pow-prod-down
16×add-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow-sqr pow-prod-up add-log-exp
3×sqrt-prod
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 135
Calls
4 calls:
135.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))
144.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series915.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
40.0ms
(cos (/ (+ phi1 phi2) 2.0))
48.0ms
(cos (/ (+ phi1 phi2) 2.0))
710.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify788.0ms

Counts
147 → 147
Iterations

Useful iterations: done (777.0ms)

IterNodesCost
04557854
113207209
done50006835

prune763.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
35.9b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
97×flip3-- flip--
82×associate-*r/ associate-*l/
66×sqrt-div
64×frac-times frac-add
10×pow1
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* *-commutative flip-+
Counts
4 → 113
Calls
4 calls:
53.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
218.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series932.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
41.0ms
(cos (/ (+ phi1 phi2) 2.0))
39.0ms
(cos (/ (+ phi1 phi2) 2.0))
600.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify725.0ms

Counts
125 → 125
Iterations

Useful iterations: done (718.0ms)

IterNodesCost
04467253
112826792
done50006540

prune840.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
35.9b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
96×flip3-- flip--
80×associate-*r/ associate-*l/
66×sqrt-div
64×frac-times frac-add
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1
4×add-exp-log log-pow add-cbrt-cube add-log-exp
3×log-prod exp-prod sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 108
Calls
4 calls:
31.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
15.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
228.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
53.0ms
(cos (/ (+ phi1 phi2) 2.0))
697.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify848.0ms

Counts
120 → 120
Iterations

Useful iterations: done (841.0ms)

IterNodesCost
04417125
112396462
done50006307

prune742.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.2b

localize59.0ms

Local error

Found 4 expressions with local error:

2.9b
(cos (/ (+ phi1 phi2) 2.0))
35.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite569.0ms

Algorithm
rewrite-expression-head
Rules
384×associate-*l/
288×flip3-- flip--
198×sqrt-div
192×frac-times frac-add
96×associate-*r/
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 244
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
149.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
139.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
194.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.0s

Counts
4 → 12
Calls
4 calls:
33.0ms
(cos (/ (+ phi1 phi2) 2.0))
675.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
638.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
672.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify896.0ms

Counts
256 → 256
Iterations

Useful iterations: done (865.0ms)

IterNodesCost
041719757
1122318383
done500017888

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.2b

regimes898.0ms

Accuracy

71.5% (3.9b remaining)

Error of 29.0b against oracle of 25.1b and baseline of 38.8b

bsearch10.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02569
13369
done3369

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.5s1319×body640valid
1.4s8426×body80valid
1.4s778×body1280valid
377.0ms713×body320valid
158.0ms355×body160valid