Details

sample161.0ms

Algorithm

intervals

Results

44.0ms	44×	body	640	valid
41.0ms	244×	body	80	valid
23.0ms	23×	body	1280	valid
15.0ms	28×	body	320	valid
4.0ms	11×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	238	32
4	742	32
5	1972	32
6	4486	32
done	5001	32

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
39.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite411.0ms

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:

149.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
19.0ms	(cos (/ (+ phi1 phi2) 2.0))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
205.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series869.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
36.0ms	(cos (/ (+ phi1 phi2) 2.0))
659.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify826.0ms

Counts

147 → 147

Iterations

Useful iterations: done (819.0ms)

Iter	Nodes	Cost
0	455	7854
1	1320	7209
done	5000	6835

prune730.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 28.2b

localize49.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
4.6b	(cos (* 0.5 (+ phi2 phi1)))
4.6b	(cos (* 0.5 (+ phi2 phi1)))
39.2b	(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))))

rewrite982.0ms

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:

218.0ms	(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
18.0ms	(cos (* 0.5 (+ phi2 phi1)))
23.0ms	(cos (* 0.5 (+ phi2 phi1)))
717.0ms	(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))))

series1.5s

Counts

4 → 12

Calls

4 calls:

455.0ms	(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
40.0ms	(cos (* 0.5 (+ phi2 phi1)))
48.0ms	(cos (* 0.5 (+ phi2 phi1)))
979.0ms	(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))))

simplify1.5s

Counts

75 → 75

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	227	5490
1	570	4982
2	2517	4684
done	5000	4533

prune648.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.8b

localize106.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
2.4b	(- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))
4.6b	(cos (* 0.5 (+ phi2 phi1)))
39.2b	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))

rewrite1.3s

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:

85.0ms	(pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
498.0ms	(- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))
21.0ms	(cos (* 0.5 (+ phi2 phi1)))
740.0ms	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))

series3.8s

Counts

4 → 12

Calls

4 calls:

181.0ms	(pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
1.5s	(- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))
34.0ms	(cos (* 0.5 (+ phi2 phi1)))
2.1s	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))

simplify2.1s

Counts

84 → 84

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	313	7871
1	813	6698
2	3315	6531
done	5002	6527

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.8b

localize81.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (* 0.5 (+ phi2 phi1)))
4.6b	(cos (* 0.5 (+ phi2 phi1)))
39.2b	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))
39.2b	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

40×	`flip3--` `flip--`
36×	`sqrt-div`
32×	`frac-add`
16×	`frac-times`
8×	`add-sqr-sqrt` `associate-r/` `associate-l/`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `cos-sum` `add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 80

Calls

4 calls:

11.0ms	(cos (* 0.5 (+ phi2 phi1)))
11.0ms	(cos (* 0.5 (+ phi2 phi1)))
612.0ms	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))
703.0ms	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))

series4.3s

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (* 0.5 (+ phi2 phi1)))
49.0ms	(cos (* 0.5 (+ phi2 phi1)))
2.1s	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))
2.1s	(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))))

simplify1.3s

Counts

92 → 92

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	209	12096
1	540	11238
2	2461	10042
done	5000	10038

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.8b

Details

sample161.0ms

simplify5.2s

prune7.0ms

localize44.0ms

rewrite411.0ms

series869.0ms

simplify826.0ms

prune730.0ms

localize49.0ms

rewrite982.0ms

series1.5s

simplify1.5s

prune648.0ms

localize106.0ms

rewrite1.3s

series3.8s

simplify2.1s

prune1.2s

localize81.0ms

rewrite1.3s

series4.3s

simplify1.3s

prune1.6s

regimes771.0ms

bsearch3.0ms