Details

Time bar (total: 3.6m)

sample208.0ms

Algorithm
intervals
Results
89.0ms60×body640valid
56.0ms262×body80valid
23.0ms18×body1280valid
11.0ms18×body320valid
6.0ms12×body160valid

simplify258.0ms

Calls
1 calls:
Slowest
258.0ms
(* 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: 37.0b

localize61.0ms

Local error

Found 4 expressions with local error:

36.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
2.8b
(cos (/ (+ phi1 phi2) 2))
2.8b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite197.0ms

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-+
Calls
4 calls:
Slowest
87.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
76.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
14.0ms
(cos (/ (+ phi1 phi2) 2))
12.0ms
(cos (/ (+ phi1 phi2) 2))

series802.0ms

Calls
4 calls:
Slowest
582.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
147.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
42.0ms
(cos (/ (+ phi1 phi2) 2))
30.0ms
(cos (/ (+ phi1 phi2) 2))

simplify44.0s

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))))))
1.0s
(* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))))
916.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 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))))))
903.0ms
(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))))))
901.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.1b

localize36.0ms

Local error

Found 4 expressions with local error:

36.1b
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
1.8b
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
0.0b
(* R (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))))
0.0b
(+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
48×frac-add
36×flip3-- sqrt-div flip--
30×associate-*r/
28×flip3-+ flip-+
24×frac-times
13×add-sqr-sqrt
12×associate-*l/
11×add-log-exp
8×*-un-lft-identity add-cube-cbrt
7×pow1 sqrt-prod
6×add-cbrt-cube associate-*r* add-exp-log
4×associate-+r+ sum-log insert-posit16
3×associate-*l*
2×distribute-rgt-in +-commutative sub-neg distribute-lft-in unswap-sqr
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
119.0ms
(* R (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))))
58.0ms
(+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))
42.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
8.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))

series780.0ms

Calls
4 calls:
Slowest
295.0ms
(* R (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))))
242.0ms
(+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))
216.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
28.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))

simplify37.1s

Calls
108 calls:
Slowest
740.0ms
(- (+ (* lambda1 R) (+ (/ (* phi1 (* lambda1 (* R phi2))) (pow lambda2 2)) (/ (* phi1 (* R phi2)) lambda2))))
739.0ms
(* (sqrt R) (sqrt (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))))
734.0ms
(+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2)))))
729.0ms
(+ (* (+ (pow (* lambda2 lambda2) 3) (pow (* (- lambda1 (* lambda2 2)) lambda1) 3)) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* (* lambda2 lambda2) (* lambda2 lambda2)) (- (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1)) (* (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)))) (* (- phi1 phi2) (- (pow phi1 3) (pow phi2 3)))))
728.0ms
(sqrt (+ (pow (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) 3) (pow (* (- phi1 phi2) (- phi1 phi2)) 3)))

prune2.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 20.3b

localize87.0ms

Local error

Found 4 expressions with local error:

45.3b
(cbrt (* (* (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))))
36.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
36.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
36.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.1m

Algorithm
rewrite-expression-head
Rules
1733070×associate-*l/
1450140×frac-times
1293120×flip3-- flip--
889020×sqrt-div
862080×frac-add
435528×associate-*r/
300762×cbrt-div
13470×flip3-+ flip-+
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
6.1s
(cbrt (* (* (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))))
185.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
116.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
87.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.3s

Calls
4 calls:
Slowest
630.0ms
(cbrt (* (* (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))))
584.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
531.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
522.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))