Details

sample534.0ms

Algorithm

intervals

Results

405.0ms	148×	body	1280	valid
79.0ms	60×	body	640	valid
16.0ms	17×	body	320	valid
7.0ms	26×	body	80	valid
3.0ms	5×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	744
1	28	744
2	47	744
3	77	744
4	80	744
done	80	744

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize65.0ms

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))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* (sin phi1) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(sin (- lambda1 lambda2))
36.0ms	(cos (- lambda1 lambda2))

series251.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin phi1) (cos phi2))
113.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
40.0ms	(sin (- lambda1 lambda2))
38.0ms	(cos (- lambda1 lambda2))

simplify4.1s

Counts

98 → 98

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	208	39874
1	427	35483
2	962	31577
3	3253	31537
done	5008	29589

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.9b

localize80.0ms

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))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin phi1) (cos phi2))
53.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series314.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos phi1) (sin phi2))
57.0ms	(* (sin phi1) (cos phi2))
157.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

simplify4.2s

Counts

97 → 97

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	210	33170
1	446	30172
2	1123	28305
3	3828	27930
done	5001	26905

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize114.0ms

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))))

rewrite112.0ms

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×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `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 → 91

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
14.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
71.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi1) (sin phi2))
58.0ms	(* (sin phi1) (cos phi2))
69.0ms	(* (sin lambda1) (sin lambda2))
283.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify183.0ms

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	190	37298