Details

simplify4.0m (29.6%)

sample3.4m (25.2%)

Algorithm
61×intervals
Results
45.6s253431×body80valid
38.7s29598×body1280valid
28.7s159961×body80nan
19.7s20274×body640valid
18.7s8763×body2560valid
12.4s3367×body5120valid
6.4s9945×body320valid
4.0s9170×body160valid
1.1s764×body10240exit
827.0ms606×body1280nan
351.0ms712×body640nan
218.0ms8256×pre80true
93.0ms330×body320nan
91.0ms205×body160nan

series3.2m (23.5%)

Calls

421 calls:

15.3s
(- (/ (* 1.0 1.0) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
9.5s
(+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
7.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* 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 (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune1.8m (12.9%)

rewrite47.6s (5.8%)

Algorithm
112×rewrite-expression-head
Calls

421 calls:

10.2s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.0s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
2.0s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.9s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
32056×add-exp-log
22131×prod-exp
14517×pow-exp
12854×times-frac
11496×div-exp
9130×add-sqr-sqrt
8711×*-un-lft-identity
7626×pow-to-exp
7522×add-cube-cbrt
4469×sqrt-prod
2845×prod-diff
2460×add-cbrt-cube
1611×unpow-prod-down
1574×1-exp rec-exp
1558×associate-*r*
1278×cbrt-prod
1056×associate-*l*
1029×pow1
950×div-inv
940×cbrt-unprod
593×pow-unpow
498×add-log-exp
495×cbrt-undiv
438×associate-/l*
421×log1p-expm1-u expm1-log1p-u
405×associate-/r*
402×associate-*r/
381×fma-def
366×associate-/r/
335×difference-of-squares
329×sqr-pow
316×distribute-lft-out
312×unswap-sqr
305×pow-prod-down
286×distribute-lft-out--
252×associate-*l/
210×tan-quot
200×distribute-rgt-neg-in
196×distribute-lft-neg-in
190×sqrt-div
178×distribute-rgt-in distribute-lft-in
177×cube-prod
168×frac-times
145×flip-+ flip3-+
139×flip3-- flip--
137×fma-neg
129×exp-sum
126×*-commutative
109×clear-num frac-2neg
79×sqrt-pow1
61×sub-neg
54×frac-sub
53×pow1/2
52×pow1/3
50×pow-pow
47×cos-sum
43×associate-/l/ associate--l+
40×rem-sqrt-square
37×sum-cubes
36×div-sub
32×unpow2
30×exp-prod
29×fma-udef
24×diff-log
22×pow-flip associate--r+
19×neg-mul-1
17×sum-log swap-sqr
16×pow-sub
13×+-commutative cbrt-div
12×cube-div hypot-def
10×inv-pow log-prod
8×unpow3 cube-mult
7×distribute-rgt-out--
6×sub-div frac-add
5×pow-sqr acos-asin pow-prod-up
4×pow-div associate-+r- hypot-udef neg-sub0 neg-log
3×rem-exp-log pow2 log-pow asin-acos associate--r-
2×exp-diff rem-cube-cbrt sqrt-pow2 associate-+l+ log1p-udef associate--l- cos-diff log1p-expm1 pow-plus associate-+r+ pow-neg log-div
1×e-exp-1 sin-sum mul0 rem-log-exp

regimes15.5s (1.9%)

Accuracy

Total 43.5b remaining (22%)

Threshold costs 4.1b (2.1%)

8.6b8%Toniolo and Linder, Equation (13)
6.2b0%Henrywood and Agarwal, Equation (12)
6.2b74.2%Toniolo and Linder, Equation (7)
4.8b28.6%Toniolo and Linder, Equation (10-)
3.9b0%Given's Rotation SVD example

localize4.9s (0.6%)

bsearch3.8s (0.5%)

end0.0ms (0.0%)