Details

Time bar (total: 27.6s)

sample155.0ms

Algorithm
intervals
Results
48.0ms275×body80valid
26.0ms44×body640valid
24.0ms26×body1280valid
11.0ms25×body320valid
2.0ms8×body160valid

simplify4.0s

Counts
1 → 1
Iterations
IterNodes
done5001
54415
4917
3240
269
132
017

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0)))
2.7b
(cos (/ (+ phi2 phi1) 2.0))
2.7b
(cos (/ (+ phi2 phi1) 2.0))
39.6b
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0))))))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
132×associate-*l/
97×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
10×pow1
9×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×add-log-exp
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-+
Counts
4 → 113
Calls
4 calls:
63.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0)))
16.0ms
(cos (/ (+ phi2 phi1) 2.0))
8.0ms
(cos (/ (+ phi2 phi1) 2.0))
71.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
164.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0)))
52.0ms
(cos (/ (+ phi2 phi1) 2.0))
46.0ms
(cos (/ (+ phi2 phi1) 2.0))
995.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0))))))

simplify1.1s

Counts
125 → 125
Iterations
IterNodes
done5000
11330
0444

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.0b

localize54.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2.0))
2.7b
(cos (/ (+ phi2 phi1) 2.0))
27.9b
(/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2))
39.6b
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2)))))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
49×flip3-- flip--
42×sqrt-div
40×frac-times frac-add
36×associate-*r/
28×associate-*l/
18×add-cbrt-cube add-exp-log
11×*-un-lft-identity
8×add-sqr-sqrt associate-/l/
7×add-cube-cbrt
6×prod-exp cbrt-unprod
5×pow1 flip3-+ flip-+
4×cbrt-undiv associate-/r* times-frac div-exp add-log-exp
3×sqrt-prod
2×associate-/r/ distribute-lft-out
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-inv associate-/l*
Counts
4 → 106
Calls
4 calls:
8.0ms
(cos (/ (+ phi2 phi1) 2.0))
13.0ms
(cos (/ (+ phi2 phi1) 2.0))
175.0ms
(/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2))
30.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
36.0ms
(cos (/ (+ phi2 phi1) 2.0))
33.0ms
(cos (/ (+ phi2 phi1) 2.0))
234.0ms
(/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2))
926.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2)))))

simplify536.0ms

Counts
118 → 118
Iterations
IterNodes
done5001
11269
0388

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.8b

localize66.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2.0))
2.7b
(cos (/ (+ phi2 phi1) 2.0))
27.9b
(/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2))
39.6b
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2)))))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
49×flip3-- flip--
42×sqrt-div
40×frac-times frac-add
36×associate-*r/
28×associate-*l/
18×add-cbrt-cube add-exp-log
11×*-un-lft-identity
8×add-sqr-sqrt associate-/l/
7×add-cube-cbrt
6×prod-exp cbrt-unprod
5×pow1 flip3-+ flip-+
4×cbrt-undiv associate-/r* times-frac div-exp add-log-exp
3×sqrt-prod
2×associate-/r/ distribute-lft-out
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-inv associate-/l*
Counts
4 → 106
Calls
4 calls:
14.0ms
(cos (/ (+ phi2 phi1) 2.0))
9.0ms
(cos (/ (+ phi2 phi1) 2.0))
176.0ms
(/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2))
41.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
49.0ms
(cos (/ (+ phi2 phi1) 2.0))
46.0ms
(cos (/ (+ phi2 phi1) 2.0))
266.0ms
(/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2))
942.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi2 phi1) 2.0)) (* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (* (+ lambda2 lambda1) (- lambda1 lambda2)))) (+ lambda1 lambda2)))))

simplify625.0ms

Counts
118 → 118
Iterations
IterNodes
done5001
11280
0392

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 32.8b

localize67.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2.0))
8.4b
(/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))
20.2b
(* (/ (cos (/ (+ phi2 phi1) 2.0)) (* (cbrt (+ lambda2 lambda1)) (cbrt (+ lambda2 lambda1)))) (/ (cos (/ (+ phi2 phi1) 2.0)) (/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))))
39.6b
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (/ (cos (/ (+ phi2 phi1) 2.0)) (* (cbrt (+ lambda2 lambda1)) (cbrt (+ lambda2 lambda1)))) (/ (cos (/ (+ phi2 phi1) 2.0)) (/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2))))))))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
137×frac-times
110×flip3-- flip--
92×times-frac
90×sqrt-div
88×frac-add
81×associate-*r/
73×associate-*l/
63×add-exp-log
62×associate-*r*
51×add-sqr-sqrt
50×*-un-lft-identity
47×add-cbrt-cube
41×associate-/r/
40×add-cube-cbrt
25×cbrt-undiv div-exp
20×cbrt-prod flip3-+ prod-exp cbrt-unprod flip-+
15×associate-*l*
14×cbrt-div
7×pow1 associate-/l*
6×div-inv
5×distribute-lft-out
4×add-log-exp unswap-sqr
3×sqrt-prod
2×associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 266
Calls
4 calls:
17.0ms
(cos (/ (+ phi2 phi1) 2.0))
39.0ms
(/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))
165.0ms
(* (/ (cos (/ (+ phi2 phi1) 2.0)) (* (cbrt (+ lambda2 lambda1)) (cbrt (+ lambda2 lambda1)))) (/ (cos (/ (+ phi2 phi1) 2.0)) (/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))))
34.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (/ (cos (/ (+ phi2 phi1) 2.0)) (* (cbrt (+ lambda2 lambda1)) (cbrt (+ lambda2 lambda1)))) (/ (cos (/ (+ phi2 phi1) 2.0)) (/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2))))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
33.0ms
(cos (/ (+ phi2 phi1) 2.0))
224.0ms
(/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))
335.0ms
(* (/ (cos (/ (+ phi2 phi1) 2.0)) (* (cbrt (+ lambda2 lambda1)) (cbrt (+ lambda2 lambda1)))) (/ (cos (/ (+ phi2 phi1) 2.0)) (/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2)))))
1.0s
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (/ (cos (/ (+ phi2 phi1) 2.0)) (* (cbrt (+ lambda2 lambda1)) (cbrt (+ lambda2 lambda1)))) (/ (cos (/ (+ phi2 phi1) 2.0)) (/ (cbrt (+ lambda2 lambda1)) (* (+ lambda2 lambda1) (- lambda1 lambda2))))))))

simplify1.0s

Counts
278 → 278
Iterations
IterNodes
done5000
12755
0882

prune2.8s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 31.8b

regimes958.0ms

Accuracy

19.6% (9.4b remaining)

Error of 37.3b against oracle of 27.9b and baseline of 39.6b

bsearch158.0ms

Steps
ItersRangePoint
8
-6.289866861227281e+127
-1.3119232040995741e+125
-6.214547549450306e+127

simplify3.0ms

Iterations
IterNodes
done37
137
029

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.3s8426×body80valid
1.1s1292×body640valid
964.0ms761×body1280valid
323.0ms753×body320valid
171.0ms375×body160valid