Details

simplify5.4m (32.2%)

prune4.2m (25.2%)

sample3.2m (19.0%)

Algorithm
61×intervals
Results
41.3s252181×body80valid
41.1s29453×body1280valid
26.5s160173×body80nan
20.4s20296×body640valid
18.0s8772×body2560valid
13.0s3360×body5120valid
6.0s9995×body320valid
3.1s9078×body160valid
1.1s644×body10240exit
408.0ms8256×pre80true
406.0ms670×body640nan
390.0ms623×body1280nan
97.0ms340×body320nan
32.0ms176×body160nan

series2.6m (15.4%)

Calls

430 calls:

5.2s
(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)))))
5.2s
(sqrt (* (* (cbrt (* (* (* 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))))) (cbrt (* (* (* 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)))))) (cbrt (* (* (* 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)))))))
5.0s
(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)))))
4.7s
(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)))))
4.5s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

rewrite47.3s (4.7%)

Algorithm
114×rewrite-expression-head
Calls

430 calls:

2.4s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.3s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.3s
(* (/ (/ (sqrt (* (cbrt 2.0) (cbrt 2.0))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
2.2s
(+ (sqrt (- (* (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (* M M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
2.2s
(+ (sqrt (- (* (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (* M M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
Rules
42006×add-exp-log
23780×prod-exp
23720×times-frac
17272×div-exp
14075×add-sqr-sqrt
12472×*-un-lft-identity
11621×add-cube-cbrt
10999×pow-exp
6557×associate-*l*
5451×cbrt-prod
4844×sqrt-prod
4397×pow-to-exp
4324×add-cbrt-cube
3672×unpow-prod-down
2028×cbrt-undiv
1904×prod-diff
1898×1-exp
1896×rec-exp
1700×cbrt-unprod
1150×pow1
1059×associate-*r*
1058×sqr-pow
700×div-inv
596×difference-of-squares
522×add-log-exp
431×associate-/l*
430×expm1-log1p-u log1p-expm1-u
414×unswap-sqr
393×distribute-rgt-neg-in
381×distribute-lft-neg-in associate-/r*
360×distribute-lft-out--
343×associate-*r/
338×pow-prod-down
331×pow-unpow
247×exp-sum
246×unpow-prod-up
229×associate-/r/
205×frac-times
204×sqrt-div
191×flip3-- flip--
154×associate-*l/
132×*-commutative fma-neg
121×sqrt-pow1
94×pow1/3
89×pow1/2
85×frac-2neg clear-num
82×distribute-lft-out
81×distribute-rgt-in swap-sqr distribute-lft-in
67×rem-sqrt-square
62×flip-+ flip3-+
61×fma-def
53×neg-mul-1
49×pow-pow
43×frac-add
35×tan-quot diff-log
34×pow-prod-up associate-/l/ sub-neg
30×div-sub
28×fma-udef
24×associate--r+
23×cos-sum
22×pow-sqr
20×exp-prod
19×cbrt-div pow-sub
14×sum-log pow-plus +-commutative
13×neg-sub0 hypot-def
11×distribute-frac-neg
10×pow2 rem-exp-log
pow-neg
pow-flip neg-log
hypot-udef
inv-pow log-pow associate--r-
cube-prod frac-sub
log-prod cube-unmult sqrt-unprod difference-cubes un-div-inv acos-asin
rem-cube-cbrt rem-square-sqrt
exp-diff associate-+r- sqrt-undiv associate--l+ pow3 associate--l- asin-acos associate-+l- e-exp-1 distribute-rgt-out
expm1-log1p expm1-udef mul0 distribute-rgt-neg-out unpow3 sub-div rem-log-exp cube-mult cos-diff rem-cbrt-cube

regimes24.6s (2.4%)

Accuracy

Total 45.4b remaining (23.9%)

Threshold costs 4.4b (2.3%)

8.3b-0.4%Henrywood and Agarwal, Equation (12)
8.1b16%Toniolo and Linder, Equation (13)
7.7b0.8%Henrywood and Agarwal, Equation (13)
5.7b54.8%Henrywood and Agarwal, Equation (3)
5.7b76.2%Toniolo and Linder, Equation (7)

localize7.7s (0.8%)

bsearch2.3s (0.2%)

end1.0ms (0.0%)