Details

sample1.1s

Algorithm

intervals

Results

686.0ms	172×	body	1280	valid
103.0ms	50×	body	640	valid
31.0ms	23×	body	320	valid
4.0ms	5×	body	160	valid
3.0ms	6×	body	80	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
3	39
2	38
1	27
0	17

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b	(cos (- lambda1 lambda2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 76

Calls

4 calls:

24.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
11.0ms	(cos (- lambda1 lambda2))

series154.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin phi1) (sin phi2))
50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
33.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2006
4	2006
3	1335
2	624
1	339
0	191

prune853.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.6b

localize124.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 84

Calls

4 calls:

92.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
22.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
73.0ms	(* (sin phi1) (sin phi2))
79.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.6s

Counts

96 → 96

Iterations

Iter	Nodes
done	2009
3	2009
2	1947
1	535
0	195

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.5b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))
0.3b	(* R (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
1.1b	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/` `cos-mult` `sin-mult`

Counts

4 → 78

Calls

4 calls:

23.0ms	(* (sin lambda2) (sin lambda1))
35.0ms	(* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))
6.0ms	(* R (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin lambda2) (sin lambda1))
302.0ms	(* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))
29.0ms	(* R (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
15.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	2016
3	2016
2	1062
1	366
0	165

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.5b

localize214.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cos-mult`
82×	`pow1`
81×	`sin-mult`
50×	`associate-/r/`
49×	`associate-*r/`
48×	`associate-*l/` `frac-add`
42×	`frac-times`
37×	`add-cbrt-cube` `add-exp-log`
34×	`pow-prod-down`
27×	`frac-sub`
19×	`prod-exp` `cbrt-unprod`
15×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow-plus` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `flip3--` `div-exp` `flip--`
2×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`acos-asin` `clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `associate-/l*` `associate-/l/`

Counts

4 → 168

Calls

4 calls:

299.0ms	(/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
56.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
52.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

818.0ms	(/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
82.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
95.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
50.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify1.8s

Counts

180 → 180

Iterations

Iter	Nodes
done	2002
2	2002
1	1391
0	434

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.5b

regimes2.2s

Accuracy

0% (0.4b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample22.6s

Algorithm

intervals

Results

16.2s	4784×	body	1280	valid
4.6s	2129×	body	640	valid
979.0ms	698×	body	320	valid
334.0ms	262×	body	160	valid
52.0ms	9×	body	2560	valid
43.0ms	120×	body	80	valid