Details

simplify42.9m

Calls

14534 calls:

Slowest
3.3s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
3.3s
(/ (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* h h) h) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))))
3.2s
(/ (* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
3.1s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
2.9s
(* (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))

prune4.2m

sample3.5m

Algorithm
54×intervals
Results
58.5s238960×body80valid
43.9s160852×body80nan
32.2s18043×body1280valid
19.5s8572×body10240exit
16.7s13953×body640valid
6.3s4942×body2560valid
6.3s7035×body320valid
5.7s2323×body5120valid
4.7s7859×body160valid
960.0ms635×body640nan
653.0ms610×body1280nan
187.0ms357×body320nan
102.0ms217×body160nan

series1.3m

Calls

400 calls:

Slowest
3.2s
(sqrt (+ (pow (* (* U t) (* n 2)) 1) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))
1.7s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite26.8s

Algorithm
103×rewrite-expression-head
Calls

400 calls:

Slowest
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
Rules
25381×times-frac
12433×add-exp-log
11864×add-sqr-sqrt
11604×*-un-lft-identity
11081×add-cube-cbrt
6179×add-cbrt-cube
6076×prod-exp
4359×div-exp
2756×sqrt-prod
2544×cbrt-unprod
2411×cbrt-undiv
1343×pow1
1177×div-inv
1155×associate-/r/
921×associate-/l*
886×associate-/r*
765×associate-*r*
751×pow-exp
697×associate-*l*
665×sqrt-div
586×associate-*r/
514×1-exp
465×add-log-exp
438×associate-*l/
424×pow-prod-down
403×flip-+ flip3-+
400×insert-posit16
388×rec-exp
361×frac-times
282×cbrt-prod
263×unpow-prod-down
242×difference-of-squares
241×pow-unpow
223×pow-to-exp
203×unswap-sqr
165×flip3-- flip--
163×frac-add
157×swap-sqr
147×*-commutative
119×distribute-lft-out
114×tan-quot
110×sqrt-pow1
105×distribute-rgt-out--
100×distribute-lft-out--
89×frac-2neg clear-num
83×sqr-pow
80×pow1/2
71×exp-prod
70×sin-mult
65×cbrt-div
60×rem-sqrt-square
53×distribute-rgt-neg-in
52×pow-prod-up
49×distribute-lft-neg-in
47×sub-neg
43×distribute-rgt-in associate-/l/ distribute-lft-in
41×pow1/3
29×pow-sqr
28×pow-pow
25×pow2 pow-plus div-sub
24×diff-log
21×log-pow
18×frac-sub
14×unpow2
12×pow-flip sum-log
11×associate-+r+ difference-of-sqr-1
10×associate--l+ +-commutative inv-pow sqr-sin
log-prod
sub-div neg-mul-1 pow-sub
exp-sum cos-sum
neg-sub0 pow3 neg-log associate--r+ asin-acos rem-exp-log acos-asin
associate-+l+ remove-posit16 un-div-inv cos-diff
associate--l- associate-+r- cube-unmult distribute-frac-neg rem-log-exp distribute-neg-frac associate--r-
exp-diff sqrt-undiv sqrt-unprod exp-neg rem-square-sqrt rem-cbrt-cube

regimes16.0s

Accuracy

Total 52.7b remaining (39.9%)

17.2b-4.4%Henrywood and Agarwal, Equation (13)
9.1b7%Toniolo and Linder, Equation (13)
8.7b-1.8%Maksimov and Kolovsky, Equation (3)
6.4b73.5%Toniolo and Linder, Equation (7)
4.1b0%Henrywood and Agarwal, Equation (12)

localize5.8s

bsearch3.8s

end1.0ms