Details

sample247.0ms

Algorithm

intervals

Results

167.0ms	151×	body	1280	valid
49.0ms	69×	body	640	valid
8.0ms	20×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	5×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12
done	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize24.0ms

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)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite39.0ms

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:

12.0ms	(* (sin phi1) (sin phi2))
8.0ms	(* (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)))))
16.0ms	(cos (- lambda1 lambda2))

series127.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
20.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569
done	5001	569

prune306.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize35.0ms

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)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`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 → 72

Calls

4 calls:

56.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
12.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
46.0ms	(* (sin phi1) (sin phi2))
74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify64.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	486	1308
1	2165	1097
2	5001	1096
done	5001	1096

prune441.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b	(/ (* (* (cos phi1) (cos phi2)) (- (* (* (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)))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
59×	`cos-mult`
42×	`sin-mult`
38×	`associate-*r/`
37×	`add-exp-log` `add-cbrt-cube`
34×	`frac-times` `pow-prod-down`
33×	`associate-/l/`
23×	`associate-*l/`
19×	`prod-exp` `frac-sub` `cbrt-unprod`
11×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `times-frac` `div-exp` `associate-/r*` `flip--`
2×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`acos-asin` `frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 142

Calls

4 calls:

46.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
249.0ms	(/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
43.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
502.0ms	(/ (* (* (cos phi1) (cos phi2)) (- (* (* (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)))
48.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify107.0ms

Counts

154 → 154

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	698	2314
1	3886	1836
2	5002	1832
done	5002	1832

prune847.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (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)))
0.7b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`add-log-exp`
4×	`pow-sqr` `log-pow` `cos-mult` `pow-prod-up`
3×	`acos-asin` `log-prod`
2×	`pow-plus` `exp-diff`
1×	`pow2` `frac-times` `log-div` `associate-r/` `swap-sqr` `rem-log-exp` `associate-r` `associate-l` `associate-l/` `*-commutative` `rem-exp-log`

Counts

4 → 73

Calls

4 calls:

3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
40.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
58.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
44.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
46.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify123.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	284	2141
1	1006	1841
2	4545	1831
3	5003	1831
done	5003	1831

prune366.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.2b

regimes779.0ms

Accuracy

0% (0.4b remaining)

Error of 3.4b against oracle of 3.0b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	35
1	35	35
done	35	35

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.6s	4783×	body	1280	valid
1.4s	2147×	body	640	valid
277.0ms	641×	body	320	valid
76.0ms	285×	body	160	valid
41.0ms	11×	body	2560	valid
20.0ms	137×	body	80	valid