Details

Time bar (total: 4.6m)

sample252.0ms

Algorithm
intervals
Results
115.0ms253×body80valid
40.0ms56×body640valid
28.0ms24×body1280valid
17.0ms33×body320valid
7.0ms21×body160valid

simplify4.9s

Counts
1 → 1
Iterations
IterNodes
done5000
52127
4788
3225
266
132
017

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.4b
(cos (/ (+ phi1 phi2) 2.0))
4.4b
(cos (/ (+ phi1 phi2) 2.0))
34.8b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite421.0ms

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:
138.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
16.0ms
(cos (/ (+ phi1 phi2) 2.0))
215.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
192.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
55.0ms
(cos (/ (+ phi1 phi2) 2.0))
941.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.8s

Counts
147 → 147
Iterations
IterNodes
done5001
11335
0455

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.5b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.4b
(cos (/ (+ phi1 phi2) 2.0))
4.4b
(cos (/ (+ phi1 phi2) 2.0))
34.8b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite438.0ms

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:
80.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
282.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts
4 → 12
Calls
4 calls:
299.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
57.0ms
(cos (/ (+ phi1 phi2) 2.0))
72.0ms
(cos (/ (+ phi1 phi2) 2.0))
922.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.2s

Counts
125 → 125
Iterations
IterNodes
done5014
11289
0446

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.1b

localize130.0ms

Local error

Found 4 expressions with local error:

4.4b
(cos (/ (+ phi1 phi2) 2.0))
4.4b
(cos (/ (+ phi1 phi2) 2.0))
4.4b
(cos (/ (+ phi1 phi2) 2.0))
34.8b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
96×flip3-- flip--
80×associate-*r/ associate-*l/
66×sqrt-div
64×frac-times frac-add
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
2.3s
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series984.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
43.0ms
(cos (/ (+ phi1 phi2) 2.0))
43.0ms
(cos (/ (+ phi1 phi2) 2.0))
845.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.2s

Counts
112 → 112
Iterations
IterNodes
done5002
11232
0421

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.1b

localize256.0ms

Local error

Found 4 expressions with local error:

19.6b
(sqrt (* (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))))
35.9b
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite5.6s

Algorithm
rewrite-expression-head
Rules
13152×flip3-- flip--
13124×frac-times
11026×associate-*r/ associate-*l/
9042×cbrt-div
8768×frac-add
4488×sqrt-div
137×flip3-+ flip-+
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 4738
Calls
4 calls:
1.2s
(sqrt (* (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))))
170.0ms
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
164.0ms
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
199.0ms
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series4.2s

Counts
4 → 12
Calls
4 calls:
1.1s
(sqrt (* (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))))
1.0s
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
1.0s
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
1.1s
(cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify45.3s

Counts
4750 → 4750
Iterations
IterNodes
done12343
012343

prune3.1m

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 26.1b

regimes1.7s

Accuracy

33.8% (9.5b remaining)

Error of 34.4b against oracle of 24.9b and baseline of 39.3b

bsearch121.0ms

Steps
ItersRangePoint
5
6.4087912878512355e+53
1.3877468741025902e+54
9.379999870736137e+53

simplify10.0ms

Iterations
IterNodes
done30
130
023

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.0s8281×body80valid
1.5s1342×body640valid
1.4s805×body1280valid
414.0ms697×body320valid
110.0ms336×body160valid