Details

sample263.0ms

Algorithm

intervals

Results

191.0ms	145×	body	1280	valid
41.0ms	58×	body	640	valid
10.0ms	21×	body	320	valid
4.0ms	26×	body	80	valid
2.0ms	6×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	71	24
4	74	24
done	74	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series178.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: 3 (383.0ms)

Iter	Nodes	Cost
0	128	709
1	291	697
2	1000	601
3	3149	599
done	5000	599

prune309.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite27.0ms

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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 67

Calls

4 calls:

7.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series199.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos lambda1) (sin lambda2))
43.0ms	(* (cos phi1) (sin phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

79 → 79

Iterations

Useful iterations: 3 (448.0ms)

Iter	Nodes	Cost
0	145	773
1	338	760
2	1173	652
3	3482	650
done	5000	650

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 82

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin lambda2) (sin lambda1))
18.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
44.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (sin lambda2) (sin lambda1))
168.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))

simplify759.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (161.0ms)

Iter	Nodes	Cost
0	193	1246
1	524	1212
2	2145	1056
done	5000	1056

prune492.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

89×	`pow1`
41×	`sin-mult`
40×	`cos-mult`
38×	`associate-*r/` `pow-prod-down`
35×	`add-exp-log` `add-cbrt-cube`
34×	`frac-times`
23×	`associate-*l/`
20×	`prod-exp` `cbrt-unprod`
18×	`frac-sub`
17×	`sin-cos-mult`
10×	`sub-div`
9×	`add-sqr-sqrt` `associate-r`
8×	`pow-sqr` `pow-prod-up`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`pow-plus` `*-commutative` `add-log-exp`
2×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `swap-sqr` `flip--`
1×	`difference-of-squares` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

4.0ms	(* (sin lambda2) (sin lambda1))
15.0ms	(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
95.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))))
14.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda2) (sin lambda1))
53.0ms	(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
213.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))))
56.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify61.0ms

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	253	3732