Details

sample68.0ms

Algorithm

intervals

Results

17.0ms	268×	body	80	valid
10.0ms	26×	body	1280	valid
10.0ms	36×	body	640	valid
9.0ms	19×	body	320	valid
2.0ms	13×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	179	32
4	422	32
5	1040	32
6	3365	32
done	5000	32

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
35.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

27.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
48.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
403.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify405.0ms

Counts

147 → 147

Iterations

Useful iterations: done (398.0ms)

Iter	Nodes	Cost
0	455	7854
1	1212	7209
done	5001	7047

prune449.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.6b	(cos (* 0.5 (+ phi2 phi1)))
3.6b	(cos (* 0.5 (+ phi2 phi1)))
35.6b	(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

21×	`flip3--` `flip--`
18×	`sqrt-div`
16×	`frac-add`
8×	`frac-times`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `cos-sum` `associate-r/` `associate-l/` `add-cbrt-cube`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`associate--l+`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 63

Calls

4 calls:

40.0ms	(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.0ms	(cos (* 0.5 (+ phi2 phi1)))
3.0ms	(cos (* 0.5 (+ phi2 phi1)))
103.0ms	(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series902.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
26.0ms	(cos (* 0.5 (+ phi2 phi1)))
31.0ms	(cos (* 0.5 (+ phi2 phi1)))
577.0ms	(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify714.0ms

Counts

75 → 75

Iterations

Useful iterations: done (709.0ms)

Iter	Nodes	Cost
0	227	5490
1	567	4982
2	2525	4684
done	5000	4570

prune416.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
1.8b	(- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.6b	(cos (* 0.5 (+ phi2 phi1)))
35.6b	(sqrt (+ (- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

21×	`flip3--` `flip--`
18×	`sqrt-div`
16×	`frac-add`
8×	`add-sqr-sqrt` `frac-times`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-log-exp`
5×	`add-exp-log`
4×	`associate-r/` `associate-l/` `add-cbrt-cube`
3×	`unpow-prod-down` `pow-unpow` `sqrt-prod`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate--l+`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-exp` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

13.0ms	(pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
77.0ms	(- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.0ms	(cos (* 0.5 (+ phi2 phi1)))
156.0ms	(sqrt (+ (- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.4s

Counts

4 → 12

Calls

4 calls:

130.0ms	(pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
954.0ms	(- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
27.0ms	(cos (* 0.5 (+ phi2 phi1)))
1.3s	(sqrt (+ (- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify251.0ms

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	311	7871
1	810	6698