Details

Time bar (total: 1.5m)

sample183.0ms

Algorithm
intervals
Results
72.0ms279×body80valid
33.0ms27×body1280valid
33.0ms37×body640valid
17.0ms24×body320valid
5.0ms10×body160valid

simplify371.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
371.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize45.0ms

Local error

Found 4 expressions with local error:

34.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
4.6b
(cos (/ (+ phi1 phi2) 2))
4.6b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite550.0ms

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 insert-posit16 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 → 139
Calls
4 calls:
Slowest
396.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
117.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
14.0ms
(cos (/ (+ phi1 phi2) 2))
14.0ms
(cos (/ (+ phi1 phi2) 2))

series751.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
587.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
109.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
31.0ms
(cos (/ (+ phi1 phi2) 2))
23.0ms
(cos (/ (+ phi1 phi2) 2))

simplify43.1s

Counts
129 → 151
Calls
129 calls:
Slowest
1.1s
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
1.1s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
1.0s
(* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))))
917.0ms
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2)))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))
905.0ms
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.7b

localize95.0ms

Local error

Found 4 expressions with local error:

34.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
4.6b
(cos (/ (+ phi1 phi2) 2))
4.6b
(cos (/ (+ phi1 phi2) 2))
4.6b
(cos (/ (+ phi1 phi2) 2))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 104
Calls
4 calls:
Slowest
398.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
15.0ms
(cos (/ (+ phi1 phi2) 2))
14.0ms
(cos (/ (+ phi1 phi2) 2))
14.0ms
(cos (/ (+ phi1 phi2) 2))

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
572.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
41.0ms
(cos (/ (+ phi1 phi2) 2))
38.0ms
(cos (/ (+ phi1 phi2) 2))
37.0ms
(cos (/ (+ phi1 phi2) 2))

simplify36.3s

Counts
83 → 116
Calls
83 calls:
Slowest
1.2s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ lambda1 lambda2) (* (- phi1 phi2) (- (pow phi1 3) (pow phi2 3))))))
991.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
964.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
948.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
916.0ms
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.4b

localize71.0ms

Local error

Found 4 expressions with local error:

34.9b
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
25.6b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
25.6b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
25.6b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))

rewrite2.3s

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 insert-posit16 add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 5894
Calls
4 calls:
Slowest
439.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
89.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
57.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
54.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
556.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
376.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
351.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
315.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))