Details

sample441.0ms

Algorithm

intervals

Results

247.0ms	115×	body	1280	valid
144.0ms	85×	body	640	valid
20.0ms	21×	body	320	valid
6.0ms	26×	body	80	valid
5.0ms	9×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.4b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
18×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`associate-+r+` `sub-neg` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `associate-l` `sin-diff` `flip-+`

Counts

4 → 75

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
36.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
166.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
3	1948
2	723
1	376
0	195

prune928.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.9b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.4b	(cos (- lambda1 lambda2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`cos-diff` `fma-def` `associate-r`
2×	`associate-+r+` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

29.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
33.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
156.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
3	2765
2	894
1	405
0	198

prune989.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-+r+` `insert-posit16` `log1p-expm1-u`
3×	`+-commutative` `fma-def`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`sum-log` `flip3-+` `flip-+` `sin-mult`

Counts

4 → 76

Calls

4 calls:

24.0ms	(* (cos lambda1) (sin lambda2))
28.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
404.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos lambda1) (sin lambda2))
62.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
316.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4269
2	1064
1	356
0	148

prune963.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))))))
0.4b	(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))))
0.4b	(* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))
1.3b	(- (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-sqr-sqrt`
171×	`pow1`
110×	`associate-r`
80×	`associate-l`
77×	`pow-prod-down` `unswap-sqr`
68×	`*-un-lft-identity`
57×	`add-cbrt-cube` `add-exp-log`
56×	`add-cube-cbrt`
39×	`prod-exp` `cbrt-unprod`
36×	`prod-diff`
34×	`pow-prod-up`
32×	`swap-sqr`
19×	`*-commutative`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`fma-udef`
12×	`fma-neg` `pow-sqr`
6×	`pow-plus` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow2`
2×	`cube-unmult` `associate--l+` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 310

Calls

4 calls:

296.0ms	(* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))))))
0.0ms	(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))))
75.0ms	(* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))
57.0ms	(- (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))

series1.9s

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))))))
1.0s	(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))))
258.0ms	(* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))
335.0ms	(- (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))

simplify2.7s

Counts

322 → 322

Iterations

Iter	Nodes
done	5000
1	1275
0	367

prune2.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample14.7s

Algorithm

intervals

Results

9.4s	3541×	body	1280	valid
3.4s	2316×	body	640	valid
997.0ms	985×	body	320	valid
388.0ms	416×	body	160	valid
218.0ms	742×	body	80	valid