Details

simplify12.7m (57.1%)

sample3.4m (15.2%)

Algorithm
61×intervals
Results
47.8s253418×body80valid
37.3s29403×body1280valid
26.9s160338×body80nan
21.8s20091×body640valid
18.2s8792×body2560valid
10.3s3435×body5120valid
6.5s10024×body320valid
3.9s8958×body160valid
894.0ms669×body10240exit
562.0ms352×body320nan
387.0ms591×body1280nan
299.0ms610×body640nan
162.0ms8256×pre80true
36.0ms188×body160nan

series3.2m (14.2%)

Calls

444 calls:

17.2s
(/ (- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
8.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune1.7m (7.8%)

rewrite49.8s (3.7%)

Algorithm
118×rewrite-expression-head
Calls

444 calls:

12.0s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
1.5s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
1.1s
(* (* (* (/ (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))
1.1s
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
40708×add-exp-log
27159×prod-exp
15482×pow-exp
15178×div-exp
8486×pow-to-exp
4787×times-frac
4760×add-sqr-sqrt
4307×*-un-lft-identity
3618×add-cube-cbrt
2708×add-cbrt-cube
1907×1-exp rec-exp
1516×cbrt-prod
1342×associate-*r*
1251×pow1
1184×cbrt-unprod
1138×sqrt-prod
1035×unpow-prod-down
720×associate-*l*
597×cbrt-undiv
567×associate-*r/
524×sqrt-div
498×pow-unpow
495×add-log-exp
457×frac-times
445×log1p-expm1-u
444×expm1-log1p-u
442×prod-diff
415×pow-prod-down
384×div-inv
381×flip3-- flip--
342×cbrt-div
333×associate-/l*
330×unswap-sqr
315×associate-/r*
312×associate-*l/
311×sqr-pow
276×exp-prod
253×distribute-lft-out--
235×associate-/r/
208×difference-of-squares
192×distribute-rgt-in distribute-lft-in
171×cube-prod
157×distribute-lft-out
150×*-commutative
111×pow-pow
106×sqrt-pow1
90×frac-2neg clear-num
89×tan-quot
79×pow1/3 unpow2
71×pow1/2
67×rem-sqrt-square
65×flip-+ flip3-+ swap-sqr
58×fma-def
47×cos-sum
46×sub-neg
44×associate-/l/
36×frac-sub
35×div-sub
32×associate--l+
27×unpow3 distribute-lft-neg-in cube-mult distribute-rgt-neg-in
20×fma-neg log-prod
19×pow-prod-up log-pow exp-sum
18×pow-sub
17×fma-udef
15×pow-sqr
13×sum-log pow-neg
12×exp-diff rem-cube-cbrt hypot-def
11×pow-flip +-commutative
10×neg-sub0
9×cube-div rem-exp-log
8×diff-log difference-cubes
6×pow-div pow2 pow-plus acos-asin
5×inv-pow frac-add hypot-udef rem-log-exp
4×un-div-inv
3×neg-mul-1 rem-cbrt-cube
2×asin-acos cos-diff exp-to-pow
1×sqrt-pow2 sqrt-unprod sin-sum sum-cubes distribute-neg-frac expm1-log1p rem-square-sqrt neg-log mul0 expm1-udef associate-+l- associate--r+

regimes15.0s (1.1%)

Accuracy

Total 38.9b remaining (24.1%)

Threshold costs 3.8b (2.4%)

9.2b15.3%Toniolo and Linder, Equation (13)
6.3b0%Henrywood and Agarwal, Equation (12)
5.9b75.5%Toniolo and Linder, Equation (7)
5.3b-38%Henrywood and Agarwal, Equation (13)
4.8b32.6%Toniolo and Linder, Equation (10+)

bsearch6.3s (0.5%)

localize5.0s (0.4%)

end1.0ms (0.0%)