Details

Time bar (total: 6.7m)

sample187.0ms

Algorithm
intervals
Results
53.0ms27×body1280valid
51.0ms262×body80valid
40.0ms48×body640valid
21.0ms34×body320valid
3.0ms6×body160valid

simplify264.0ms

Calls
1 calls:
Slowest
264.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize42.0ms

Local error

Found 4 expressions with local error:

39.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.4b
(cos (/ (+ phi1 phi2) 2))
3.4b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
276×*-un-lft-identity
142×associate-*l/
113×associate-*l*
102×flip3-- flip--
92×swap-sqr
75×distribute-lft-out--
68×frac-times
66×sqrt-div
64×frac-add
51×sqrt-prod
48×distribute-lft-out
46×add-sqr-sqrt
44×pow1
34×associate-*r/
26×associate-*r*
17×pow-prod-down add-cube-cbrt
16×add-cbrt-cube add-exp-log
12×unswap-sqr
8×prod-exp cbrt-unprod
5×*-commutative
4×pow-sqr pow-prod-up insert-posit16 add-log-exp difference-of-squares
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
1.2s
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
310.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
25.0ms
(cos (/ (+ phi1 phi2) 2))
17.0ms
(cos (/ (+ phi1 phi2) 2))

series783.0ms

Calls
4 calls:
Slowest
565.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
145.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
37.0ms
(cos (/ (+ phi1 phi2) 2))
36.0ms
(cos (/ (+ phi1 phi2) 2))

simplify49.8s

Calls
246 calls:
Slowest
1.0s
(* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))))
1.0s
(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
(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))))))
950.0ms
(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))))))
920.0ms
(* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

prune4.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 25.8b

localize45.0ms

Local error

Found 4 expressions with local error:

39.1b
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.4b
(cos (/ (+ phi1 phi2) 2))
3.4b
(cos (/ (+ phi1 phi2) 2))
0.6b
(cbrt (- lambda1 lambda2))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
1424×associate-*l/
1408×frac-times
1345×flip3-- flip--
1298×cbrt-div
642×sqrt-div
640×frac-add
512×associate-*r/
46×*-un-lft-identity
37×associate-*l*
18×sqrt-prod
15×distribute-lft-out
9×add-sqr-sqrt distribute-lft-out--
6×add-cube-cbrt
5×cbrt-prod pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-+ difference-of-squares
Calls
4 calls:
Slowest
3.3s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
33.0ms
(cos (/ (+ phi1 phi2) 2))
22.0ms
(cos (/ (+ phi1 phi2) 2))
3.0ms
(cbrt (- lambda1 lambda2))

series801.0ms

Calls
4 calls:
Slowest
529.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
207.0ms
(cbrt (- lambda1 lambda2))
35.0ms
(cos (/ (+ phi1 phi2) 2))
29.0ms
(cos (/ (+ phi1 phi2) 2))

simplify5.1m

Calls
681 calls:
Slowest
1.5s
(sqrt (+ (* (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- (* lambda1 lambda1) (* lambda2 lambda2))))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (* (+ lambda1 lambda2) (cbrt (+ lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
1.4s
(sqrt (+ (* (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- (* lambda1 lambda1) (* lambda2 lambda2))) (cbrt (- (pow lambda1 3) (pow lambda2 3))))) (* (cbrt (- (pow lambda1 3) (pow lambda2 3))) (cos (/ (+ phi1 phi2) 2)))) (+ phi1 phi2)) (* (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))))) (cbrt (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))))) (* (- phi1 phi2) (- (* phi1 phi1) (* phi2 phi2))))))
1.3s
(sqrt (+ (* (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- (* lambda1 lambda1) (* lambda2 lambda2))) (cbrt (- (* lambda1 lambda1) (* lambda2 lambda2))))) (* (cbrt (- (pow lambda1 3) (pow lambda2 3))) (cos (/ (+ phi1 phi2) 2)))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (* (* (+ lambda1 lambda2) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))
1.2s
(sqrt (+ (* (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
1.2s
(sqrt (+ (* (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- (* lambda1 lambda1) (* lambda2 lambda2))) (cbrt (- (* lambda1 lambda1) (* lambda2 lambda2))))) (* (cbrt (- (pow lambda1 3) (pow lambda2 3))) (cos (/ (+ phi1 phi2) 2)))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (* (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2))) (cbrt (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))

prune26.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.3b

localize79.0ms

Local error

Found 4 expressions with local error:

39.1b
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
39.1b
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
39.1b
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.4b
(cos (/ (+ phi1 phi2) 2))

rewrite11.5s

Algorithm
rewrite-expression-head
Rules
4272×associate-*l/
4224×frac-times
4032×flip3-- flip--
3888×cbrt-div
1926×sqrt-div
1920×frac-add
1536×associate-*r/
121×*-un-lft-identity
111×associate-*l*
54×sqrt-prod
45×distribute-lft-out
24×distribute-lft-out--
10×add-sqr-sqrt
7×pow1 add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
3.9s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.7s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.5s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms
(cos (/ (+ phi1 phi2) 2))

series1.8s

Calls
4 calls:
Slowest
589.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
577.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
566.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
22.0ms
(cos (/ (+ phi1 phi2) 2))