Details

simplify5.8m (40.2%)

sample3.4m (23.8%)

Algorithm
61×intervals
Results
45.3s252717×body80valid
44.1s29655×body1280valid
27.1s160168×body80nan
18.6s8843×body2560valid
17.4s19798×body640valid
10.3s3394×body5120valid
7.2s10182×body320valid
4.5s9191×body160valid
1.1s635×body10240exit
881.0ms599×body1280nan
637.0ms8256×pre80true
310.0ms619×body640nan
150.0ms361×body320nan
73.0ms209×body160nan

series2.5m (17.0%)

Calls

434 calls:

7.7s
(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*)))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
3.3s
(sqrt (* (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))) (* (* 2.0 n) U)))
3.1s
(sqrt (* (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))) (* (* 2.0 n) U)))

prune1.5m (10.3%)

rewrite50.7s (5.8%)

Algorithm
113×rewrite-expression-head
Calls

434 calls:

2.8s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.7s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.0s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.8s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
49946×add-exp-log
36299×prod-exp
25641×pow-exp
18224×div-exp
12109×pow-to-exp
6682×times-frac
6264×add-sqr-sqrt
5315×*-un-lft-identity
3981×add-cube-cbrt
3604×1-exp rec-exp
2903×sqrt-prod
2373×add-cbrt-cube
1868×associate-*l*
1718×unpow-prod-down
1560×cbrt-prod
1232×pow1
901×cbrt-unprod
891×associate-*r*
675×difference-of-squares
560×add-log-exp
482×sqr-pow
446×cbrt-undiv
444×associate-*r/
426×associate-/l*
411×distribute-lft-out
403×sqrt-div
394×unswap-sqr
377×pow-unpow
361×pow-prod-down
358×associate-/r*
318×div-inv
311×associate-*l/
270×distribute-lft-out--
242×associate-/r/
227×frac-times
226×cube-prod
220×flip3-- flip--
167×flip-+ flip3-+
143×*-commutative
125×sqrt-pow1
109×exp-prod distribute-rgt-neg-in
99×tan-quot
90×frac-2neg clear-num
84×pow1/2
75×distribute-lft-neg-in
72×rem-sqrt-square
57×distribute-rgt-in unpow2 pow1/3 distribute-lft-in
55×sub-neg
49×pow-prod-up
47×pow-pow
46×cbrt-div
41×associate-/l/
40×frac-sub
38×div-sub
36×diff-log
31×pow-sqr sum-log
29×pow-sub
24×frac-add
23×cube-div +-commutative
22×swap-sqr
20×pow-plus
17×neg-sub0
16×unpow3 cube-mult
15×pow2
14×neg-log associate--l+
13×rem-exp-log
9×rem-cube-cbrt inv-pow pow-flip exp-sum neg-mul-1
8×cos-sum pow-neg associate-+r+ associate--r+
6×exp-diff associate--r- distribute-neg-frac
5×difference-cubes un-div-inv acos-asin
4×pow-div cos-diff rem-cbrt-cube associate-+l-
3×associate--l- unpow-prod-up asin-acos log-prod
2×associate-+l+ sqrt-unprod associate-+r- unsub-neg distribute-frac-neg
1×sqrt-undiv e-exp-1 quot-tan exp-neg log-pow rem-square-sqrt mul0

regimes16.1s (1.9%)

Accuracy

Total 43.4b remaining (20.2%)

Threshold costs 4.3b (2%)

9.2b18.6%Toniolo and Linder, Equation (13)
6.8b-20%Maksimov and Kolovsky, Equation (3)
5.7b76.5%Toniolo and Linder, Equation (7)
4.6b15.2%Toniolo and Linder, Equation (10+)
3.5b28.6%Henrywood and Agarwal, Equation (12)

bsearch4.2s (0.5%)

localize4.0s (0.5%)

end1.0ms (0.0%)