Details

sample709.0ms

Algorithm

intervals

Results

439.0ms	151×	body	1280	valid
154.0ms	69×	body	640	valid
20.0ms	22×	body	320	valid
6.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	43	18
done	43	18

prune72.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize48.0ms

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)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.2b	(cos (- lambda1 lambda2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `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 → 72

Calls

4 calls:

33.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (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))

series183.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin phi1) (sin phi2))
62.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
41.0ms	(cos (- lambda1 lambda2))

simplify4.7s

Counts

84 → 84

Iterations

Useful iterations: 5 (1.6s)

Iter	Nodes	Cost
0	187	1607
1	316	1393
2	597	1170
3	942	1127
4	1247	1054
5	1907	990
6	3847	990
done	5001	990

prune575.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite63.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

Calls

4 calls:

26.0ms	(* (sin phi1) (sin phi2))
25.0ms	(* (sin lambda1) (sin lambda2))
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))))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin phi1) (sin phi2))
62.0ms	(* (sin lambda1) (sin lambda2))
108.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
45.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.2s

Counts

84 → 84

Iterations

Useful iterations: 2 (192.0ms)

Iter	Nodes	Cost
0	141	1538
1	271	1441
2	698	1225
3	1348	1225
4	1818	1225
5	2750	1225
done	5001	1225

prune740.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
0.9b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))))
1.4b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))

rewrite43.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 66

Calls

4 calls:

34.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
3.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))) R)
51.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
14.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))))
16.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))

simplify5.9s

Counts

78 → 78

Iterations

Useful iterations: 5 (1.0s)

Iter	Nodes	Cost
0	98	2330
1	148	2225
2	290	1971
3	515	1971
4	828	1971
5	1697	1969
6	4944	1969
done	5000	1969

prune708.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.4b	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite46.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (sin lambda2))
80.0ms	(* (sin phi1) (sin phi2))
121.0ms	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
33.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.1s

Counts

84 → 84

Iterations

Useful iterations: 2 (171.0ms)

Iter	Nodes	Cost
0	142	1626
1	271	1479
2	699	1225
3	1321	1225
4	1791	1225
5	2733	1225
done	5001	1225

prune613.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.4b

regimes944.0ms

Accuracy

0% (0.3b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	32	28
done	32	28

end0.0ms

sample18.6s

Algorithm

intervals

Results

12.8s	4725×	body	1280	valid
4.1s	2150×	body	640	valid
729.0ms	715×	body	320	valid
137.0ms	271×	body	160	valid
90.0ms	130×	body	80	valid
57.0ms	11×	body	2560	valid