Details

simplify7.2m (43.7%)

sample3.3m (20.4%)

Algorithm
61×intervals
Results
41.0s252181×body80valid
39.7s29453×body1280valid
31.5s160173×body80nan
19.4s20296×body640valid
17.2s8772×body2560valid
10.9s3360×body5120valid
5.7s9995×body320valid
4.4s9078×body160valid
963.0ms644×body10240exit
351.0ms623×body1280nan
343.0ms670×body640nan
174.0ms8256×pre80true
132.0ms340×body320nan
33.0ms176×body160nan

series2.6m (16.0%)

Calls

445 calls:

7.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
2.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))

prune2.0m (11.9%)

rewrite40.4s (4.1%)

Algorithm
114×rewrite-expression-head
Calls

445 calls:

3.1s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.7s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
1.3s
(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))))
1.1s
(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
Rules
20424×add-exp-log
13613×prod-exp
5197×div-exp
4652×pow-exp
3874×add-sqr-sqrt
3662×times-frac
3506×*-un-lft-identity
2941×add-cube-cbrt
2832×add-cbrt-cube
2232×sqrt-prod
2224×pow-to-exp
1325×pow1
1300×associate-*l*
1248×cbrt-unprod
869×associate-*l/
773×frac-times
766×associate-*r*
763×associate-*r/
725×sqrt-div
675×unpow-prod-down
614×1-exp rec-exp
568×cbrt-undiv
555×add-log-exp
442×pow-prod-down
359×flip-+ flip3-+ frac-add
358×pow-unpow
332×associate-/l*
310×cbrt-prod
292×flip3-- flip--
278×associate-/r*
259×unswap-sqr
229×div-inv
216×frac-sub
196×sqr-pow
185×distribute-lft-out
166×cbrt-div
150×*-commutative
146×difference-of-squares
143×sqrt-pow1
127×distribute-lft-out--
125×associate-/r/
111×pow1/2
109×tan-quot
96×rem-sqrt-square
86×frac-2neg clear-num
75×sub-neg
71×distribute-rgt-in distribute-lft-in
61×swap-sqr
54×pow1/3
49×associate-/l/
45×distribute-rgt-neg-in distribute-lft-neg-in
43×pow-pow
34×associate--l+
31×diff-log
29×div-sub
27×sum-log
25×+-commutative pow-sub
23×pow-prod-up
21×sub-div
20×exp-prod
13×exp-sum pow-sqr
12×neg-sub0 associate--r+ pow-neg
pow-plus neg-mul-1
unpow-prod-up
pow-flip pow2 inv-pow rem-exp-log
log-pow un-div-inv
associate--l- log-prod associate-+r- associate-+r+ distribute-frac-neg asin-acos acos-asin
sqrt-unprod
associate-+l+ exp-diff cos-sum rem-square-sqrt e-exp-1
sqrt-undiv distribute-rgt-neg-out distribute-rgt-out-- cos-diff rem-log-exp

regimes26.0s (2.6%)

Accuracy

Total 56.4b remaining (24.4%)

Threshold costs 4.0b (1.7%)

10.8b11.2%Toniolo and Linder, Equation (13)
8.1b13.9%Maksimov and Kolovsky, Equation (3)
7.9b45.1%Henrywood and Agarwal, Equation (3)
6.8b0%Henrywood and Agarwal, Equation (12)
5.6b76.4%Toniolo and Linder, Equation (7)

localize8.2s (0.8%)

bsearch3.9s (0.4%)

end1.0ms (0.0%)