Details

Time bar (total: 33.1s)

sample102.0ms

Algorithm
intervals
Results
29.0ms262×body80valid
21.0ms44×body640valid
12.0ms18×body1280valid
8.0ms22×body320valid
2.0ms10×body160valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
017466
132466
269466
3240466
4917466
54415466
done5001466

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite222.0ms

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-cbrt-cube add-exp-log
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
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:
75.0ms
(* (* (- 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))
109.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series660.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
480.0ms
(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
0458154057
11387114437
done5000113797

prune820.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.8b

localize95.0ms

Local error

Found 4 expressions with local error:

2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.6b
(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))))

rewrite605.0ms

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 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
9.0ms
(cos (/ (+ phi1 phi2) 2.0))
9.0ms
(cos (/ (+ phi1 phi2) 2.0))
559.0ms
(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))))

series739.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))
36.0ms
(cos (/ (+ phi1 phi2) 2.0))
626.0ms
(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))))

simplify2.8s

Counts
112 → 112
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0424153398
11283117786
done5001117626

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.8b

localize115.0ms

Local error

Found 4 expressions with local error:

2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (* (* (cbrt (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))))

rewrite715.0ms

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 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
659.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (* (* (cbrt (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))))

series738.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(cos (/ (+ phi1 phi2) 2.0))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
628.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (* (* (cbrt (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))))

simplify3.3s

Counts
112 → 112
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0427166198
11292130586
done5000130426

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.8b

localize104.0ms

Local error

Found 4 expressions with local error:

2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite306.0ms

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 *-un-lft-identity add-cube-cbrt sqrt-prod
4×add-cbrt-cube add-exp-log add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 172
Calls
4 calls:
18.0ms
(cos (/ (+ phi1 phi2) 2.0))
15.0ms
(cos (/ (+ phi1 phi2) 2.0))
142.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
108.0ms
(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:
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
48.0ms
(cos (/ (+ phi1 phi2) 2.0))
654.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
663.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.2s

Counts
184 → 184
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0420269824
11271198964
done5001198644

prune1.7s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 23.8b

regimes2.2s

Accuracy

68.1% (4.8b remaining)

Error of 29.7b against oracle of 24.9b and baseline of 39.9b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
022677
127677
done27677

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.7s8366×body80valid
806.0ms1309×body640valid
722.0ms782×body1280valid
560.0ms398×body160valid
315.0ms768×body320valid