Details

Time bar (total: 26.1s)

sample154.0ms

Algorithm
intervals
Results
33.0ms248×body80valid
30.0ms28×body320valid
29.0ms45×body640valid
21.0ms25×body1280valid
3.0ms12×body160valid

simplify4.4s

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: 38.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite319.0ms

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:
120.0ms
(* (* (- lambda1 lambda2) (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))
160.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series889.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
45.0ms
(cos (/ (+ phi1 phi2) 2.0))
648.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify711.0ms

Counts
147 → 147
Iterations

Useful iterations: done (703.0ms)

IterNodesCost
04557854
113207209
done50006835

prune810.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 26.8b

localize73.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
35.1b
(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))))

rewrite792.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
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:
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
15.0ms
(cos (/ (+ phi1 phi2) 2.0))
730.0ms
(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))))

series842.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
36.0ms
(cos (/ (+ phi1 phi2) 2.0))
56.0ms
(cos (/ (+ phi1 phi2) 2.0))
720.0ms
(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))))

simplify702.0ms

Counts
112 → 112
Iterations

Useful iterations: done (687.0ms)

IterNodesCost
04218318
112437826
done50016485

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 26.8b

localize54.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
6.0b
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
66×log-div exp-diff
64×associate-*r/
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×log-prod exp-prod exp-sum sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×log-pow
2×sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-sqrt-square rem-exp-log
Counts
4 → 179
Calls
4 calls:
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
20.0ms
(cos (/ (+ phi1 phi2) 2.0))
160.0ms
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
202.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
37.0ms
(cos (/ (+ phi1 phi2) 2.0))
50.0ms
(cos (/ (+ phi1 phi2) 2.0))
671.0ms
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
639.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify817.0ms

Counts
191 → 191
Iterations

Useful iterations: done (797.0ms)

IterNodesCost
065613899
1146812673
done500112243

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 26.8b

localize55.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
6.4b
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
66×log-div pow-sub
64×associate-*r/
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1
6×unpow-prod-up pow-unpow log-prod sqrt-prod
5×add-exp-log
4×add-cbrt-cube add-log-exp
3×unpow-prod-down log-pow
2×sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+
1×pow-to-exp rem-sqrt-square e-exp-1 pow-pow sqr-pow
Counts
4 → 186
Calls
4 calls:
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
178.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
167.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.5s

Counts
4 → 12
Calls
4 calls:
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))
816.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
635.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.0s

Counts
198 → 198
Iterations

Useful iterations: done (978.0ms)

IterNodesCost
067914417
1186313443
done500013126

prune1.2s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 16.3b

regimes1.6s

Accuracy

27.6% (15.5b remaining)

Error of 32.6b against oracle of 17.1b and baseline of 38.5b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03568
14368
done4368

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.8s8351×body80valid
1.4s1268×body640valid
879.0ms798×body1280valid
374.0ms719×body320valid
147.0ms365×body160valid