Details

prune7.9m (43.6%)

sample4.3m (23.6%)

Algorithm
61×intervals
Results
59.8s253094×body80valid
56.4s29579×body1280valid
38.9s161693×body80nan
26.8s20380×body640valid
24.0s8839×body2560valid
13.7s3318×body5120valid
10.7s9914×body320valid
5.0s8759×body160valid
1.9s659×body10240exit
1.0s632×body1280nan
553.0ms605×body640nan
318.0ms370×body320nan
308.0ms8256×pre80true
96.0ms176×body160nan

simplify3.8m (21.0%)

series1.2m (6.7%)

Calls

433 calls:

1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.4s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite28.9s (2.7%)

Algorithm
114×rewrite-expression-head
Calls

433 calls:

2.0s
(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))
1.5s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.5s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))))
1.4s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* c0 (/ (/ (* (/ d D) (/ d D)) w) h)))
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
Rules
24089×times-frac
20950×add-exp-log
14426×add-sqr-sqrt
13377×*-un-lft-identity
12523×add-cube-cbrt
9783×div-exp
8984×prod-exp
7555×add-cbrt-cube
3124×cbrt-undiv
2930×cbrt-unprod
2784×prod-diff
2504×sqrt-prod
2195×sqrt-div
2151×frac-times
1948×associate-*l*
1812×pow1
1722×unpow-prod-up
1647×associate-*r*
1477×1-exp
1389×div-inv
1190×associate-*l/
1142×rec-exp
1081×associate-*r/
813×associate-/r*
749×flip3-- flip--
669×associate-/l*
601×pow-prod-down
562×difference-of-squares
515×add-log-exp
436×expm1-log1p-u
434×log1p-expm1-u
433×insert-posit16
369×unpow-prod-down
346×unswap-sqr
232×pow-exp
228×distribute-lft-out--
219×cbrt-prod
193×distribute-rgt-neg-in
187×distribute-lft-neg-in
169×sqrt-pow1
162×pow-prod-up
159×distribute-rgt-in distribute-lft-in
143×*-commutative
140×associate-/r/
137×pow-unpow
133×exp-sum
119×fma-neg
115×cos-sum
112×frac-2neg clear-num
108×sqr-pow
107×frac-sub sub-neg
102×pow-sqr
99×distribute-lft-out
98×pow-to-exp
96×exp-prod
95×tan-quot
93×pow1/2
85×associate--l+
78×pow-plus swap-sqr
58×rem-sqrt-square
57×pow2
54×flip-+ flip3-+
51×fma-def
49×associate-/l/
46×log-pow
44×unpow2
39×pow1/3
31×pow-pow
30×diff-log
27×fma-udef
24×cbrt-div
22×associate--r+
17×neg-mul-1
15×pow-flip
13×sum-log +-commutative div-sub
12×frac-add pow-sub
11×inv-pow
7×rem-exp-log
6×pow-div log-prod neg-log un-div-inv
5×acos-asin cos-diff
4×associate-+r- log1p-expm1 sqrt-unprod associate-+l- rem-square-sqrt log1p-udef
3×expm1-log1p expm1-udef exp-diff associate--l- distribute-rgt-out-- associate--r-
2×neg-sub0 associate-+r+ sub-div hypot-udef asin-acos hypot-def rem-log-exp
1×associate-+l+ remove-posit16 cos-mult sqr-sin sin-mult

regimes18.4s (1.7%)

Accuracy

Total 48.2b remaining (24.9%)

Threshold costs 4.5b (2.3%)

9.5b4.2%Toniolo and Linder, Equation (13)
7.8b39.7%Henrywood and Agarwal, Equation (3)
6.8b12.5%Henrywood and Agarwal, Equation (13)
5.4b77.2%Toniolo and Linder, Equation (7)
4.1b30.4%Henrywood and Agarwal, Equation (12)

localize5.6s (0.5%)

bsearch2.3s (0.2%)

end1.0ms (0.0%)