Details

sample129.0ms

Algorithm

intervals

Results

31.0ms	254×	body	80	valid
25.0ms	46×	body	640	valid
22.0ms	26×	body	1280	valid
11.0ms	28×	body	320	valid
2.0ms	8×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
5	2141
4	757
3	225
2	66
1	32
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
1.6b	(cos (/ (+ phi1 phi2) 2.0))
1.6b	(cos (/ (+ phi1 phi2) 2.0))
33.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite265.0ms

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-cbrt-cube` `add-exp-log`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
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:

78.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
141.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series876.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))
674.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
1	1355
0	458

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.3b

localize88.0ms

Local error

Found 4 expressions with local error:

1.6b	(cos (/ (+ phi1 phi2) 2.0))
1.6b	(cos (/ (+ phi1 phi2) 2.0))
1.6b	(cos (/ (+ phi1 phi2) 2.0))
33.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

290×	`associate-*l/`
198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
74×	`associate-*r/`
72×	`cbrt-div` `cos-mult`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 172

Calls

4 calls:

18.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
173.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series773.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(cos (/ (+ phi1 phi2) 2.0))
51.0ms	(cos (/ (+ phi1 phi2) 2.0))
48.0ms	(cos (/ (+ phi1 phi2) 2.0))
625.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.7s

Counts

184 → 184

Iterations

Iter	Nodes
done	5002
1	2515
0	830

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.1b

localize118.0ms

Local error

Found 4 expressions with local error:

28.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
28.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
28.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
33.5b	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

29930×	`associate-*l/`
20428×	`frac-times`
16050×	`flip3--` `flip--`
15576×	`cbrt-div`
5990×	`associate-*r/`
5826×	`sqrt-div`
5824×	`frac-add`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5890

Calls

4 calls:

81.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
46.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
78.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
836.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.8s

Counts

4 → 12

Calls

4 calls:

417.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
393.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
375.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
636.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify45.8s

Counts

5902 → 5902

Iterations

Iter	Nodes
done	22400
0	22400

prune1.9m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.1b

localize97.0ms

Local error

Found 4 expressions with local error:

28.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
28.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
28.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
33.5b	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite28.1s

Algorithm

rewrite-expression-head

Rules

350762×	`associate-*l/`
253708×	`frac-times`
186648×	`cbrt-div`
179346×	`flip3--` `flip--`
145794×	`sqrt-div`
70790×	`associate-*r/`
52480×	`frac-add`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52546

Calls

4 calls:

39.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
38.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
44.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
3.6s	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
258.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
260.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
452.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify6.6m

Iterations

Iter	Nodes
done	190016
0	190016