Details

Time bar (total: 31.8s)

sample167.0ms

Algorithm
intervals
Results
40.0ms244×body80valid
33.0ms44×body640valid
26.0ms28×body320valid
23.0ms23×body1280valid
4.0ms11×body160valid

simplify5.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
14332
221232
3392232
done500132

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize58.0ms

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))
39.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite355.0ms

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:
129.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
187.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series972.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))
41.0ms
(cos (/ (+ phi1 phi2) 2.0))
725.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts
147 → 147
Iterations

Useful iterations: done (1.8s)

IterNodesCost
04557854
126567180
done50026873

prune762.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
39.2b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
198×flip3-- flip--
196×frac-times
138×sqrt-div
136×frac-add
130×associate-*l/
74×associate-*r/
73×cos-mult
12×pow1 add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
4×add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqr-cos sqrt-pow1 flip3-+ pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 192
Calls
4 calls:
18.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
161.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series829.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
45.0ms
(cos (/ (+ phi1 phi2) 2.0))
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
688.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify858.0ms

Counts
204 → 204
Iterations

Useful iterations: done (836.0ms)

IterNodesCost
080914625
done500012667

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 27.8b

localize69.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
39.2b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
39.2b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite459.0ms

Algorithm
rewrite-expression-head
Rules
396×flip3-- flip--
392×frac-times
276×sqrt-div
272×frac-add
260×associate-*l/
148×associate-*r/
144×cos-mult
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 316
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
195.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
154.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.5s

Counts
4 → 12
Calls
4 calls:
117.0ms
(cos (/ (+ phi1 phi2) 2.0))
48.0ms
(cos (/ (+ phi1 phi2) 2.0))
649.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
640.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.7s

Counts
328 → 328
Iterations

Useful iterations: done (2.7s)

IterNodesCost
078128082
1435324186
done500023884

prune2.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 27.8b

localize65.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
40.3b
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
40.3b
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×cbrt-div
128×frac-times frac-add
64×associate-*r/
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
2×flip3-+ pow1/3 flip-+
Counts
4 → 168
Calls
4 calls:
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
18.0ms
(cos (/ (+ phi1 phi2) 2.0))
105.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
130.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.8s

Counts
4 → 12
Calls
4 calls:
58.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
815.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
862.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.5s

Counts
180 → 180
Iterations

Useful iterations: done (1.5s)

IterNodesCost
043413262
1247112440
done500012198

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 27.8b

regimes1.1s

Accuracy

74.6% (3.6b remaining)

Error of 28.7b against oracle of 25.1b and baseline of 39.3b

bsearch6.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02669
13369
done3369

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.5s8470×body80valid
1.4s1295×body640valid
1.4s776×body1280valid
315.0ms693×body320valid
137.0ms336×body160valid