Details

simplify6.3m (42.6%)

sample3.3m (22.5%)

Algorithm
61×intervals
Results
45.5s252717×body80valid
41.6s29655×body1280valid
28.8s160168×body80nan
21.0s19798×body640valid
18.6s8784×body2560valid
11.2s3453×body5120valid
7.2s10182×body320valid
3.3s9191×body160valid
947.0ms635×body10240exit
336.0ms596×body1280nan
289.0ms621×body640nan
239.0ms8256×pre80true
107.0ms362×body320nan
43.0ms209×body160nan

series2.7m (17.9%)

Calls

435 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*)))))
7.1s
(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*)))))
2.9s
(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))
2.6s
(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))

prune1.5m (9.9%)

rewrite38.8s (4.4%)

Algorithm
115×rewrite-expression-head
Calls

435 calls:

1.9s
(* (* (* (/ (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))
1.7s
(+ (/ (* 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
(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
1.3s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
1.3s
(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
Rules
39332×add-exp-log
27618×prod-exp
17054×pow-exp
13069×div-exp
8416×pow-to-exp
4406×add-sqr-sqrt
4344×times-frac
3713×*-un-lft-identity
3223×add-cube-cbrt
2443×add-cbrt-cube
1558×unpow-prod-down
1524×1-exp
1515×rec-exp
1381×pow1
1142×associate-*l*
1029×sqrt-prod
962×cbrt-unprod
906×cbrt-prod
719×associate-*r*
522×add-log-exp
482×cbrt-undiv
437×sqr-pow
435×log1p-expm1-u expm1-log1p-u
395×pow-prod-down
376×pow-unpow
373×difference-of-squares
371×associate-/l*
370×associate-*r/
343×div-inv
340×associate-/r*
314×prod-diff
273×associate-*l/
242×unswap-sqr
224×sqrt-div
214×frac-times
184×fma-def
176×flip-- flip3--
162×associate-/r/ distribute-rgt-neg-in
157×distribute-lft-out--
147×sqrt-pow1
142×distribute-rgt-in cube-prod distribute-lft-in
139×distribute-lft-neg-in
137×*-commutative
135×distribute-lft-out
129×exp-prod
106×pow-prod-up
97×tan-quot
93×frac-2neg clear-num
80×pow1/2
70×flip-+ flip3-+
68×pow1/3
60×pow-sqr
54×associate-/l/
51×pow-plus
50×rem-sqrt-square
44×unpow2 sub-neg
40×pow-pow
38×div-sub
35×swap-sqr
34×fma-udef sum-log
33×associate-+r+ pow2
32×associate--l+
29×log-pow
25×pow-sub
24×cos-sum frac-sub
20×unpow3 cube-mult +-commutative
16×fma-neg
15×hypot-def
14×neg-mul-1
11×neg-sub0 diff-log
10×frac-add
9×rem-exp-log log-prod
8×rem-cube-cbrt associate-+r-
7×cbrt-div
6×exp-diff
5×inv-pow pow-flip acos-asin exp-sum
4×cube-div pow-neg un-div-inv distribute-neg-frac
3×associate-+l- hypot-udef neg-log rem-cbrt-cube
2×associate-+l+ asin-acos sqrt-unprod pow3 unsub-neg rem-square-sqrt distribute-frac-neg rem-log-exp
1×e-exp-1 exp-neg sin-sum cos-diff unpow-prod-up distribute-rgt-out mul0

regimes15.5s (1.7%)

Accuracy

Total 36.7b remaining (18.8%)

Threshold costs 4.5b (2.3%)

8.8b19.4%Toniolo and Linder, Equation (13)
5.7b76.4%Toniolo and Linder, Equation (7)
4.6b50.9%Toniolo and Linder, Equation (10-)
3.5b28.7%Henrywood and Agarwal, Equation (12)
3.2b57.8%Toniolo and Linder, Equation (10+)

bsearch4.8s (0.5%)

localize4.1s (0.5%)

end0.0ms (0.0%)