Details

sample631.0ms

Algorithm

intervals

Results

423.0ms	148×	body	1280	valid
84.0ms	60×	body	640	valid
67.0ms	26×	body	80	valid
15.0ms	17×	body	320	valid
4.0ms	5×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	744
1	27	744
2	45	744
3	69	744
4	73	744
done	73	744

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize404.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

19.0ms	(* (sin phi1) (cos phi2))
28.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

series257.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin phi1) (cos phi2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(sin (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))

simplify4.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	114	19922
1	268	18796
2	794	18716
3	3276	18396
done	5001	18396

prune727.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

16.0ms	(* (cos phi1) (sin phi2))
17.0ms	(* (sin phi1) (cos phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

series316.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cos phi1) (sin phi2))
60.0ms	(* (sin phi1) (cos phi2))
156.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify3.6s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	134	22084
1	318	20756
2	886	20596
3	3094	20236
done	5000	20236

prune960.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`*-commutative` `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 → 83

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
18.0ms	(* (sin phi1) (cos phi2))
19.0ms	(* (sin lambda1) (sin lambda2))
87.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos phi1) (sin phi2))
56.0ms	(* (sin phi1) (cos phi2))
65.0ms	(* (sin lambda1) (sin lambda2))
252.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify131.0ms

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	182	34558