Details

sample4.3m (31.7%)

Algorithm
61×intervals
Results
1.0m253094×body80valid
56.5s29579×body1280valid
39.3s161693×body80nan
27.7s20380×body640valid
23.6s8839×body2560valid
13.2s3318×body5120valid
10.0s9914×body320valid
5.0s8759×body160valid
2.0s659×body10240exit
1.4s632×body1280nan
484.0ms605×body640nan
308.0ms8256×pre80true
191.0ms370×body320nan
61.0ms176×body160nan

simplify3.9m (28.3%)

prune3.3m (24.4%)

series1.2m (8.9%)

Calls

432 calls:

1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(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*)))))

rewrite27.4s (3.3%)

Algorithm
114×rewrite-expression-head
Calls

432 calls:

1.7s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.6s
(* (* (/ 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)))))
1.3s
(* (* (* (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)))))
Rules
24151×times-frac
20935×add-exp-log
14471×add-sqr-sqrt
13415×*-un-lft-identity
12561×add-cube-cbrt
9779×div-exp
8979×prod-exp
7538×add-cbrt-cube
3120×cbrt-undiv
2925×cbrt-unprod
2784×prod-diff
2483×sqrt-prod
2195×sqrt-div
2152×frac-times
1965×associate-*l*
1800×pow1
1722×unpow-prod-up
1640×associate-*r*
1477×1-exp
1394×div-inv
1192×associate-*l/
1142×rec-exp
1080×associate-*r/
812×associate-/r*
749×flip3-- flip--
666×associate-/l*
599×pow-prod-down
562×difference-of-squares
514×add-log-exp
434×expm1-log1p-u
433×log1p-expm1-u
432×insert-posit16
369×unpow-prod-down
349×unswap-sqr
322×cbrt-prod
232×pow-exp
228×distribute-lft-out--
193×distribute-rgt-neg-in
187×distribute-lft-neg-in
160×sqrt-pow1
159×distribute-rgt-in pow-prod-up distribute-lft-in
142×*-commutative
140×associate-/r/
137×pow-unpow
133×exp-sum
119×fma-neg
115×cos-sum
111×frac-2neg clear-num
108×sqr-pow
107×frac-sub sub-neg
101×pow-sqr
99×distribute-lft-out
98×pow-to-exp
96×exp-prod
95×tan-quot
86×swap-sqr
85×associate--l+
84×pow1/2
78×pow-plus
57×pow2 rem-sqrt-square
54×flip-+ flip3-+
51×fma-def
49×associate-/l/
48×pow1/3
46×log-pow
44×unpow2
31×cbrt-div pow-pow
30×diff-log
27×fma-udef
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- associate-+l-
3×exp-diff associate--l- log1p-expm1 sqrt-unprod hypot-udef distribute-rgt-out-- rem-square-sqrt associate--r- log1p-udef
2×expm1-log1p neg-sub0 expm1-udef associate-+r+ sub-div asin-acos hypot-def rem-log-exp
1×associate-+l+ remove-posit16 cos-mult sqr-sin sin-mult

regimes19.3s (2.3%)

Accuracy

Total 48.2b remaining (25%)

Threshold costs 4.5b (2.4%)

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)

localize5.8s (0.7%)

bsearch2.2s (0.3%)

end1.0ms (0.0%)