Details

sample366.0ms

Algorithm

intervals

Results

235.0ms	111×	body	1280	valid
75.0ms	80×	body	640	valid
14.0ms	22×	body	320	valid
7.0ms	31×	body	80	valid
4.0ms	12×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize480.0ms

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))))
1.4b	(cos (- lambda1 lambda2))
1.5b	(sin (- lambda1 lambda2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`cos-diff`
2×	`cos-sum` `associate-+r+` `sub-neg` `sin-sum`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 44

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
20.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))
15.0ms	(sin (- lambda1 lambda2))

series404.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
261.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
41.0ms	(cos (- lambda1 lambda2))
44.0ms	(sin (- lambda1 lambda2))

simplify5.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
4	2554
3	1169
2	479
1	210
0	101

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.1b

localize176.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))))
1.4b	(cos (- lambda1 lambda2))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

92.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

series722.0ms

Counts

4 → 12

Calls

4 calls:

398.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
67.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
222.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms	(cos (- lambda1 lambda2))

simplify6.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5002
3	3580
2	926
1	312
0	128

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize174.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`insert-posit16`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `flip-+` `flip--` `sin-mult`

Counts

4 → 65

Calls

4 calls:

18.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
128.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
26.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series925.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (sin lambda1) (sin lambda2))
112.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
359.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
316.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify7.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	4507
2	1145
1	371
0	144

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize408.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2))))
0.3b	(/ (+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (* (cos phi1) (cos phi1)) (cos phi1))) (+ (* (* (cos phi2) (* (cos lambda2) (cos lambda1))) (- (* (cos phi2) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.4b	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
1.4b	(- (* (cos phi2) (* (cos lambda2) (cos lambda1))) (cos phi1))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

655×	`pow1`
390×	`pow-prod-down`
213×	`add-cbrt-cube` `add-exp-log`
168×	`prod-exp` `cbrt-unprod`
102×	`pow-prod-up`
43×	`associate-*l/` `cos-mult`
36×	`pow-sqr`
16×	`associate-*r/`
13×	`add-sqr-sqrt` `frac-times` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `pow-plus` `frac-add`
9×	`associate-/l/`
7×	`associate-/r/`
6×	`add-log-exp`
5×	`cube-unmult`
4×	`pow2` `pow3` `sum-cubes` `insert-posit16` `associate-/l*`
3×	`associate-/r*` `flip3--` `flip--`
2×	`flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `swap-sqr` `div-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

780.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2))))
2.1s	(/ (+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (* (cos phi1) (cos phi1)) (cos phi1))) (+ (* (* (cos phi2) (* (cos lambda2) (cos lambda1))) (- (* (cos phi2) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (cos phi1) (cos phi1))))
278.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
75.0ms	(- (* (cos phi2) (* (cos lambda2) (cos lambda1))) (cos phi1))

series3.1s

Counts

4 → 12

Calls

4 calls:

348.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2))))
2.2s	(/ (+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (* (cos phi1) (cos phi1)) (cos phi1))) (+ (* (* (cos phi2) (* (cos lambda2) (cos lambda1))) (- (* (cos phi2) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (cos phi1) (cos phi1))))
301.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
262.0ms	(- (* (cos phi2) (* (cos lambda2) (cos lambda1))) (cos phi1))

simplify2.9s

Counts

312 → 312

Iterations

Iter	Nodes
done	5004
1	1017
0	338

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes2.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify22.0ms

Iterations

Iter	Nodes
done	34
1	34
0	24

end0.0ms

sample10.9s

Algorithm

intervals

Results

7.0s	3624×	body	1280	valid
2.5s	2363×	body	640	valid
645.0ms	937×	body	320	valid
180.0ms	407×	body	160	valid
159.0ms	669×	body	80	valid