Details

Time bar (total: 23.7s)

sample160.0ms

Algorithm
intervals
Results
70.0ms274×body80valid
20.0ms29×body1280valid
19.0ms40×body640valid
7.0ms23×body320valid
4.0ms18×body160valid

simplify4.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
323832
474232
5197232
6448632
done500132

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(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:
133.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
152.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series911.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
41.0ms
(cos (/ (+ phi1 phi2) 2.0))
47.0ms
(cos (/ (+ phi1 phi2) 2.0))
664.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify753.0ms

Counts
147 → 147
Iterations

Useful iterations: done (746.0ms)

IterNodesCost
04557854
113207209
done50006835

prune649.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite211.0ms

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:
19.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
133.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series674.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
564.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts
204 → 204
Iterations

Useful iterations: done (1.1s)

IterNodesCost
080914625
1235512593
done500112377

prune933.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.5b

localize36.0ms

Local error

Found 4 expressions with local error:

3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite718.0ms

Algorithm
rewrite-expression-head
Rules
96×flip3-- associate-*l/ 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:
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
20.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
647.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(cos (/ (+ phi1 phi2) 2.0))
41.0ms
(cos (/ (+ phi1 phi2) 2.0))
51.0ms
(cos (/ (+ phi1 phi2) 2.0))
562.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify629.0ms

Counts
112 → 112
Iterations

Useful iterations: done (619.0ms)

IterNodesCost
04258318
112117826
done50007661

prune596.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 25.5b

localize56.0ms

Local error

Found 4 expressions with local error:

3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite390.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
64×associate-*r/
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 → 172
Calls
4 calls:
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(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))))
122.0ms
(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:
50.0ms
(cos (/ (+ phi1 phi2) 2.0))
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
684.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
638.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify848.0ms

Counts
184 → 184
Iterations

Useful iterations: done (816.0ms)

IterNodesCost
041713298
1122312382
done500012036

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.5b

regimes867.0ms

Accuracy

70.6% (4.1b remaining)

Error of 29.5b against oracle of 25.4b and baseline of 39.2b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02669
13369
done3369

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.8s8362×body80valid
1.1s790×body1280valid
1.1s1335×body640valid
455.0ms743×body320valid
89.0ms333×body160valid