Details

sample124.0ms

Algorithm

intervals

Results

40.0ms	265×	body	80	valid
30.0ms	46×	body	640	valid
18.0ms	22×	body	1280	valid
13.0ms	17×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2141
4	757
3	225
2	66
1	32
0	17

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

29.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
8.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
127.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series761.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
24.0ms	(cos (/ (+ phi1 phi2) 2))
35.0ms	(cos (/ (+ phi1 phi2) 2))
574.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
1	1296
0	446

prune895.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2))))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite174.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `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 → 112

Calls

4 calls:

22.0ms	(log (exp (cos (/ (+ phi1 phi2) 2))))
16.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
124.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(log (exp (cos (/ (+ phi1 phi2) 2))))
39.0ms	(cos (/ (+ phi1 phi2) 2))
37.0ms	(cos (/ (+ phi1 phi2) 2))
539.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.4s

Counts

124 → 124

Iterations

Iter	Nodes
done	5003
1	1324
0	446

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.0b

localize88.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite684.0ms

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` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 104

Calls

4 calls:

8.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
9.0ms	(cos (/ (+ phi1 phi2) 2))
655.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series684.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cos (/ (+ phi1 phi2) 2))
38.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))
569.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
1	1273
0	428

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.0b

localize85.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite378.0ms

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` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 248

Calls

4 calls:

16.0ms	(cos (/ (+ phi1 phi2) 2))
128.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
101.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
114.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.8s

Counts

4 → 12

Calls

4 calls:

36.0ms	(cos (/ (+ phi1 phi2) 2))
585.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
608.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
565.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
1	1298
0	425

prune2.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.0b

regimes949.0ms

Accuracy

33.1% (8.8b remaining)

Error of 32.8b against oracle of 23.9b and baseline of 37.1b

bsearch162.0ms

Steps

Iters	Range		Point
9	5.0875015420834634e-30	1.4423693549975343e-20	1.400742996618376e-20

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.3s	8345×	body	80	valid
2.0s	783×	body	1280	valid
1.5s	1197×	body	640	valid
540.0ms	687×	body	320	valid
154.0ms	343×	body	160	valid