Details

simplify15.1m (62.9%)

sample3.1m (13.1%)

Algorithm
61×intervals
Results
46.6s253418×body80valid
35.1s29403×body1280valid
28.1s160338×body80nan
18.6s20091×body640valid
14.4s8792×body2560valid
7.4s3435×body5120valid
6.3s10024×body320valid
2.7s8958×body160valid
642.0ms669×body10240exit
494.0ms591×body1280nan
344.0ms610×body640nan
196.0ms8256×pre80true
104.0ms352×body320nan
36.0ms188×body160nan

series2.7m (11.3%)

Calls

454 calls:

8.0s
(sqrt (* (sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))) (sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.4s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))

prune1.8m (7.5%)

rewrite49.8s (3.5%)

Algorithm
119×rewrite-expression-head
Calls

454 calls:

1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.4s
(* (* 2.0 (* (/ (* (cbrt l) (cbrt l)) (pow k (/ 2 2))) (* (/ (cbrt l) (pow k 1)) (pow (/ 1 (pow t 1.0)) 1.0)))) (/ (/ l (sin k)) (tan k)))
1.4s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.4s
(* (* 2.0 (* (/ (* (cbrt l) (cbrt l)) (pow k (/ 2 2))) (* (/ (cbrt l) (pow k 1)) (pow (/ 1 (pow t 1.0)) 1.0)))) (/ l (* (sin k) (tan k))))
Rules
30712×add-exp-log
19649×prod-exp
10780×times-frac
9614×div-exp
8769×add-sqr-sqrt
7487×pow-exp
6967×*-un-lft-identity
5534×add-cube-cbrt
3500×pow-to-exp
2974×add-cbrt-cube
2601×sqrt-prod
2198×unpow-prod-down
1780×pow1
1747×associate-*l*
1320×cbrt-unprod
1127×associate-*r*
968×difference-of-squares
896×rec-exp 1-exp
832×sqr-pow
719×pow-prod-down
699×cbrt-prod
678×associate-*r/
590×add-log-exp
589×cbrt-undiv
567×pow-unpow
556×unswap-sqr
499×distribute-lft-out--
487×sqrt-div
466×associate-/r*
421×div-inv
371×sqrt-pow1
354×associate-/l*
318×flip3-- flip--
306×associate-/r/
305×associate-*l/
285×frac-times
266×distribute-lft-out
226×flip-+ flip3-+ exp-prod
154×*-commutative
109×unpow2
100×frac-sub
90×pow1/2 frac-2neg clear-num
88×pow-prod-up
84×rem-sqrt-square pow-pow
78×cbrt-div
77×associate-/l/ tan-quot
63×pow1/3
61×distribute-rgt-in distribute-lft-in
57×pow-sqr
52×sub-neg
51×sum-log
40×cube-prod
36×div-sub
32×distribute-rgt-neg-in
29×+-commutative
26×distribute-lft-neg-in
22×pow-plus
20×swap-sqr log-prod
19×diff-log log-pow
17×pow2
15×pow-sub
14×associate--l+
12×neg-sub0
11×unpow3 cube-mult
10×associate--r+
exp-diff rem-cube-cbrt
cube-div rem-exp-log frac-add pow-flip neg-log pow-neg
associate-+r+
cos-sum difference-cubes inv-pow acos-asin
exp-sum rem-log-exp
associate-+l+ distribute-neg-frac associate-+l-
un-div-inv cos-diff
pow-div associate--l- asin-acos neg-mul-1 associate--r- exp-to-pow
sqrt-unprod rem-square-sqrt mul0 sum-cubes rem-cbrt-cube

regimes16.6s (1.2%)

Accuracy

Total 39.7b remaining (20.1%)

Threshold costs 5.9b (3%)

8.5b15.7%Toniolo and Linder, Equation (13)
6.2b0%Henrywood and Agarwal, Equation (12)
5.9b75.5%Toniolo and Linder, Equation (7)
4.7b33.5%Toniolo and Linder, Equation (10+)
3.4b21.1%Toniolo and Linder, Equation (10-)

localize5.0s (0.3%)

bsearch2.9s (0.2%)

end0.0ms (0.0%)