Details

sample306.0ms

Algorithm

intervals

Results

213.0ms	153×	body	1280	valid
59.0ms	71×	body	640	valid
11.0ms	23×	body	320	valid
3.0ms	6×	body	160	valid
1.0ms	3×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
done	33	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b	(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series115.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (sin phi2))
46.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

67 → 67

Iterations

Useful iterations: 3 (322.0ms)

Iter	Nodes	Cost
0	111	1035
1	199	1027
2	435	889
3	826	887
4	1180	887
5	2201	887
done	5001	887

prune302.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 65

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin lambda1) (sin (- lambda2)))
46.0ms	(* (sin phi1) (sin phi2))
72.0ms	(* (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)))))))

simplify2.7s

Counts

77 → 77

Iterations

Useful iterations: 3 (367.0ms)

Iter	Nodes	Cost
0	143	1487
1	281	1473
2	726	1270
3	1619	1200
4	2867	1200
done	5001	1200

prune432.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (exp (log (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))) R)
0.6b	(log (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))
0.9b	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-prod`
6×	`associate-r`
4×	`exp-sum` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`acos-asin` `rem-log-exp` `log-pow` `sin-mult`

Counts

4 → 61

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
10.0ms	(* (exp (log (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(log (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
71.0ms	(* (exp (log (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))) R)
48.0ms	(log (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))
16.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))

simplify2.3s

Counts

73 → 73

Iterations

Useful iterations: 4 (426.0ms)

Iter	Nodes	Cost
0	128	1973
1	231	1910
2	498	1615
3	888	1615
4	1164	1586
5	1845	1586
6	3801	1586
done	5000	1586

prune424.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))) R)
0.3b	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))
0.8b	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))))
0.9b	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))
2.0ms	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))) R)
43.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2)))))
18.0ms	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))))
16.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (sin phi1) (sin phi2))))

simplify2.6s

Counts

70 → 70

Iterations

Useful iterations: 5 (469.0ms)

Iter	Nodes	Cost
0	107	2374
1	183	2277
2	355	2025
3	533	2025
4	728	1929
5	1389	1927
6	4388	1927
done	5000	1927

prune302.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

regimes626.0ms

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	34	38
done	34	38

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.0s	4821×	body	1280	valid
1.5s	2132×	body	640	valid
297.0ms	628×	body	320	valid
97.0ms	304×	body	160	valid
46.0ms	13×	body	2560	valid
24.0ms	104×	body	80	valid