Details

Time bar (total: 24.8s)

sample148.0ms

Algorithm
intervals
Results
57.0ms269×body80valid
25.0ms46×body640valid
18.0ms24×body1280valid
11.0ms26×body320valid
3.0ms11×body160valid

simplify4.7s

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

localize24.0ms

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))))

rewrite276.0ms

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:
79.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
156.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series862.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
620.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify680.0ms

Counts
147 → 147
Iterations

Useful iterations: done (669.0ms)

IterNodesCost
04557854
113207209
done50006835

prune728.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.2b

localize39.0ms

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))))

rewrite345.0ms

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:
61.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
19.0ms
(cos (/ (+ phi1 phi2) 2.0))
227.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
260.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))
48.0ms
(cos (/ (+ phi1 phi2) 2.0))
714.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify687.0ms

Counts
125 → 125
Iterations

Useful iterations: done (677.0ms)

IterNodesCost
04467253
112826792
done50006540

prune831.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.2b

localize51.0ms

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) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
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:
40.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))
162.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series808.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
57.0ms
(cos (/ (+ phi1 phi2) 2.0))
45.0ms
(cos (/ (+ phi1 phi2) 2.0))
656.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify721.0ms

Counts
120 → 120
Iterations

Useful iterations: done (712.0ms)

IterNodesCost
04417125
112306462
done50006258

prune754.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.2b

localize40.0ms

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))))

rewrite465.0ms

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:
16.0ms
(cos (/ (+ phi1 phi2) 2.0))
123.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
137.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
145.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.2s

Counts
4 → 12
Calls
4 calls:
58.0ms
(cos (/ (+ phi1 phi2) 2.0))
740.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
713.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
709.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify728.0ms

Counts
256 → 256
Iterations

Useful iterations: done (697.0ms)

IterNodesCost
041719757
1122318383
done500017888

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.2b

regimes793.0ms

Accuracy

71.5% (3.9b remaining)

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

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02569
13369
done3369

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.7s8426×body80valid
1.5s1319×body640valid
1.2s778×body1280valid
364.0ms713×body320valid
104.0ms355×body160valid