Details

simplify6.4m (41.5%)

sample3.3m (21.8%)

Algorithm
61×intervals
Results
41.8s29536×body1280valid
40.0s252518×body80valid
27.6s160829×body80nan
19.9s8657×body2560valid
19.0s20035×body640valid
11.4s3467×body5120valid
7.9s9925×body320valid
2.6s8868×body160valid
1.2s814×body10240exit
346.0ms620×body1280nan
268.0ms598×body640nan
245.0ms401×body320nan
210.0ms8256×pre80true
40.0ms190×body160nan

series2.9m (18.7%)

Calls

440 calls:

7.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
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*)))))
7.6s
(/ (sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ 1.0 (hypot 1.0 x)) 3)))) (sqrt (fma 1.0 1.0 (* (/ 1.0 (hypot 1.0 x)) (- (/ 1.0 (hypot 1.0 x)) 1.0)))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune1.7m (11.1%)

rewrite42.1s (4.6%)

Algorithm
117×rewrite-expression-head
Calls

440 calls:

9.2s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
1.3s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
888.0ms
(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
828.0ms
(* (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0))))
826.0ms
(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
Rules
45549×add-exp-log
33255×prod-exp
23988×pow-exp
17044×div-exp
11758×pow-to-exp
10527×times-frac
7318×add-sqr-sqrt
7156×*-un-lft-identity
6338×add-cube-cbrt
5380×sqrt-prod
3604×1-exp rec-exp
2641×add-cbrt-cube
1755×cbrt-prod
1628×unpow-prod-down
1302×associate-*r*
1158×prod-diff
1057×associate-*l*
1039×pow1
989×cbrt-unprod
590×div-inv
565×associate-/l*
562×cbrt-undiv
499×add-log-exp
487×associate-/r*
442×log1p-expm1-u
441×expm1-log1p-u
366×associate-*r/
359×sqr-pow
328×pow-unpow
299×pow-prod-down
276×associate-/r/
271×distribute-lft-out--
253×associate-*l/
236×unswap-sqr
230×difference-of-squares
211×distribute-lft-out
171×flip3-- flip--
164×frac-times
160×sin-sum
158×cube-prod
146×distribute-rgt-in distribute-lft-in
139×sqrt-div
128×*-commutative
126×cos-sum
124×exp-sum
121×tan-quot
106×clear-num frac-2neg
102×distribute-lft-neg-in distribute-rgt-neg-in
91×div-sub
90×swap-sqr
83×pow1/3
80×fma-neg
75×fma-def
68×pow-sub
67×sub-neg sqrt-pow1
49×pow1/2
47×associate-/l/
45×rem-sqrt-square associate--l+
39×frac-sub
35×pow-pow
34×cbrt-div
31×flip-+ flip3-+
29×exp-prod
27×unpow2
22×fma-udef associate--r+ pow-neg
21×neg-sub0
18×diff-log
14×unpow3 cube-mult
13×pow-flip
12×hypot-def sum-log
10×+-commutative
9×neg-mul-1
8×un-div-inv pow-prod-up pow-sqr
7×inv-pow
6×frac-add
5×exp-diff rem-cube-cbrt log-pow associate-+r- acos-asin
4×pow2 expm1-log1p hypot-udef pow-plus expm1-udef log-prod
3×cube-div cos-diff asin-acos
2×log1p-udef pow-div log1p-expm1 sin-diff
1×rem-exp-log sqrt-undiv associate-+l+ associate--l- sum-cubes difference-of-sqr-1 expm1-def associate--r- mul0 rem-cbrt-cube rem-log-exp

regimes14.8s (1.6%)

Accuracy

Total 34.6b remaining (18.8%)

Threshold costs 4.3b (2.3%)

9.4b6.5%Toniolo and Linder, Equation (13)
5.6b76.5%Toniolo and Linder, Equation (7)
4.9b-7.9%Henrywood and Agarwal, Equation (12)
3.9b52.6%Toniolo and Linder, Equation (10-)
2.7b0%Henrywood and Agarwal, Equation (13)

localize4.3s (0.5%)

bsearch2.4s (0.3%)

end1.0ms (0.0%)