Details

simplify5.4m (33.6%)

prune3.9m (24.3%)

sample3.1m (19.5%)

Algorithm
61×intervals
Results
39.9s253680×body80valid
38.9s29202×body1280valid
27.9s160143×body80nan
20.0s20532×body640valid
19.2s9016×body2560valid
11.9s3411×body5120valid
5.0s9904×body320valid
2.9s8844×body160valid
868.0ms652×body10240exit
693.0ms598×body640nan
334.0ms661×body1280nan
158.0ms8256×pre80true
89.0ms348×body320nan
70.0ms202×body160nan

series2.5m (15.6%)

Calls

403 calls:

7.7s
(- (/ (* 1.0 1.0) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))) (/ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))))
4.8s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
4.8s
(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))
4.3s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite34.8s (3.6%)

Algorithm
112×rewrite-expression-head
Calls

403 calls:

4.5s
(* (/ (/ (sqrt (- 1.0 (* (* v v) 5.0))) (+ (sqrt 1.0) v)) (* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* 3.0 (* v v)) (* (* 3.0 (* v v)) (* 3.0 (* v v))))))) PI)) (/ (/ (sqrt (- 1.0 (* (* v v) 5.0))) (- (sqrt 1.0) v)) t))
4.4s
(/ (/ (- 1.0 (* (* v v) 5.0)) (- 1.0 (* v v))) (* (* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* 3.0 (* v v)) (* (* 3.0 (* v v)) (* 3.0 (* v v))))))) PI) t))
2.3s
(+ (sqrt (- (* (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (* M M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
2.0s
(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
881.0ms
(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))
Rules
53888×add-exp-log
31974×prod-exp
20662×div-exp
19635×times-frac
14864×pow-exp
11054×add-sqr-sqrt
9720×*-un-lft-identity
9405×add-cube-cbrt
7772×cbrt-prod
5920×associate-*l*
5499×pow-to-exp
4211×add-cbrt-cube
3120×unpow-prod-down
2261×cbrt-undiv
2201×1-exp rec-exp
1935×cbrt-unprod
1268×associate-*r*
1244×pow1
1181×sqrt-prod
824×sqr-pow
657×prod-diff
585×div-inv
455×add-log-exp
444×unswap-sqr
439×cos-sum
403×expm1-log1p-u log1p-expm1-u
376×pow-prod-down
354×associate-/l*
287×associate-*r/
248×pow-unpow
231×associate-/r*
179×pow1/3
148×difference-of-squares
146×sqrt-div
135×associate-/r/
133×*-commutative
113×sqrt-pow1
106×distribute-lft-out--
104×swap-sqr
99×pow-prod-up
94×associate-*l/
90×frac-times
75×frac-2neg clear-num
67×pow-sqr
63×distribute-lft-neg-in distribute-rgt-neg-in
62×pow1/2
61×distribute-lft-out
59×flip3-- flip--
58×flip-+ flip3-+
43×pow-plus fma-neg
40×rem-sqrt-square
37×cbrt-div fma-def tan-quot
35×pow-pow associate-/l/
31×fma-udef
30×pow2 distribute-rgt-in distribute-lft-in
28×div-sub
25×exp-prod
23×sub-neg
21×neg-mul-1
19×frac-sub
16×sum-log
15×pow-sub
13×+-commutative
12×hypot-def
11×neg-sub0 distribute-frac-neg
10×diff-log
pow-neg
sub-div frac-add
un-div-inv cos-diff
pow-flip inv-pow
associate-+r- associate-+r+ pow3 sqrt-unprod associate--r+ acos-asin
distribute-rgt-out-- associate--l+ asin-acos rem-exp-log associate-+l- rem-square-sqrt
associate-+l+ exp-diff sqrt-undiv mul0 exp-sum hypot-udef rem-cbrt-cube

regimes25.0s (2.6%)

Accuracy

Total 44.0b remaining (24.6%)

Threshold costs 4.7b (2.6%)

10.2b23.3%Toniolo and Linder, Equation (13)
7.5b0%Henrywood and Agarwal, Equation (13)
6.1b50.8%Henrywood and Agarwal, Equation (3)
5.3b77.5%Toniolo and Linder, Equation (7)
4.8b0%Henrywood and Agarwal, Equation (12)

localize7.0s (0.7%)

bsearch983.0ms (0.1%)

end1.0ms (0.0%)