Details

prune1.8m (29.5%)

series1.7m (28.0%)

Calls

435 calls:

5.1s
(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*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(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*))))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s
(* (* (* 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*))))

sample1.4m (22.6%)

Algorithm
61×intervals
Results
15.2s29668×body1280valid
15.0s253308×body80valid
9.1s158961×body80nan
8.7s8874×body2560valid
7.0s20222×body640valid
5.1s3241×body5120valid
2.2s9790×body320valid
1.2s8922×body160valid
403.0ms641×body10240exit
127.0ms565×body1280nan
112.0ms648×body640nan
104.0ms8256×pre80true
47.0ms362×body320nan
18.0ms204×body160nan

rewrite44.6s (12.3%)

Algorithm
115×rewrite-expression-head
Calls

435 calls:

3.3s
(* (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))) (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.4s
(* (/ 2.0 (* (* (* (* (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))) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
1.9s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
1.8s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
1.8s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
Rules
34212×times-frac
32744×add-exp-log
20164×prod-exp
16584×add-sqr-sqrt
16203×*-un-lft-identity
15195×add-cube-cbrt
13049×div-exp
11710×pow-exp
9131×unpow-prod-down
6286×pow-to-exp
4714×cbrt-prod
4535×associate-*r*
3391×sqrt-prod
2599×add-cbrt-cube
1692×sqr-pow
1302×pow1
1203×1-exp rec-exp
1083×cbrt-unprod
807×associate-*r/
793×associate-*l*
765×associate-/l*
763×unpow2
582×div-inv
539×add-log-exp
488×sqrt-div
472×cbrt-undiv
431×associate-/r*
408×associate-*l/
407×pow-prod-down
387×unswap-sqr
381×pow-unpow
367×frac-times
324×cbrt-div
313×flip3-- flip--
299×associate-/r/
297×distribute-lft-out
292×distribute-lft-out--
201×exp-prod
193×flip-+ flip3-+
174×difference-of-squares
167×distribute-rgt-neg-in
152×*-commutative
120×cube-prod
115×sqrt-pow1
95×frac-2neg clear-num
89×distribute-lft-neg-in
85×tan-quot
76×distribute-rgt-in distribute-lft-in
72×pow1/2
71×sub-neg
60×log-prod
59×pow1/3
57×associate-/l/
55×frac-sub
54×exp-sum
53×rem-sqrt-square
50×pow-prod-up
48×pow-pow
47×swap-sqr
32×pow-sqr div-sub
31×diff-log
29×pow-flip
27×pow-sub neg-sub0
24×associate--l+
22×pow-plus
21×pow-neg sum-log
18×frac-add
17×unpow3 rem-exp-log cube-mult +-commutative pow2
13×exp-diff log-pow
11×neg-mul-1
10×associate-+r+
6×neg-log associate--r+
5×acos-asin
4×cube-div inv-pow associate-+r- unsub-neg cos-sum rem-log-exp
3×associate--r- exp-to-pow
2×rem-cube-cbrt cos-diff distribute-frac-neg asin-acos distribute-neg-frac log-div
1×difference-cubes associate-+l+ un-div-inv associate--l- sqrt-unprod exp-neg rem-square-sqrt sub-div mul0 distribute-rgt-neg-out

simplify13.7s (3.8%)

regimes10.3s (2.8%)

Accuracy

Total 49.6b remaining (22.1%)

Threshold costs 5.0b (2.2%)

8.9b38.9%Henrywood and Agarwal, Equation (3)
7.8b16.7%Toniolo and Linder, Equation (13)
6.4b73.5%Toniolo and Linder, Equation (7)
5.8b20.6%Toniolo and Linder, Equation (10+)
5.6b-13.3%Toniolo and Linder, Equation (10-)

localize2.3s (0.6%)

bsearch1.7s (0.5%)

end0.0ms (0.0%)