Details

prune1.9m (31.0%)

series1.8m (29.5%)

Calls

428 calls:

5.4s
(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*)))))
5.1s
(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*))))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

sample1.4m (23.4%)

Algorithm
61×intervals
Results
16.0s29668×body1280valid
15.6s253308×body80valid
9.6s158961×body80nan
8.9s8874×body2560valid
7.4s20222×body640valid
5.2s3241×body5120valid
2.3s9790×body320valid
1.3s8922×body160valid
406.0ms641×body10240exit
135.0ms565×body1280nan
122.0ms648×body640nan
105.0ms8256×pre80true
58.0ms362×body320nan
20.0ms204×body160nan

rewrite30.7s (8.4%)

Algorithm
115×rewrite-expression-head
Calls

428 calls:

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)))))
1.7s
(* (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)))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
713.0ms
(* (/ (/ 1 PI) (* (sqrt (* 2.0 (- (* (* 1.0 1.0) (* 1.0 1.0)) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* (* 3.0 (* v v)) (* 3.0 (* v v))))))) (fma (* 1.0 1.0) 1.0 (pow v 6)))) (/ (/ (- 1.0 (* 5.0 (* v v))) t) (- (pow 1.0 3) (pow (* v v) 3))))
Rules
32235×times-frac
30609×add-exp-log
18797×prod-exp
16262×add-sqr-sqrt
15290×*-un-lft-identity
14330×add-cube-cbrt
12339×div-exp
11263×pow-exp
8773×unpow-prod-down
6001×pow-to-exp
5004×associate-*r*
4323×cbrt-prod
2782×add-cbrt-cube
1839×sqrt-prod
1704×sqr-pow
1232×pow1
1219×1-exp rec-exp
1106×cbrt-unprod
823×associate-*l*
703×prod-diff
693×unpow2
599×associate-/l*
592×cbrt-undiv
591×div-inv
521×add-log-exp
484×difference-of-squares
428×log1p-expm1-u expm1-log1p-u
408×pow-prod-down
398×unswap-sqr
372×pow-unpow
334×associate-*r/
323×distribute-lft-out--
322×associate-/r*
303×distribute-rgt-neg-in
254×distribute-lft-neg-in exp-sum
248×sqrt-div
221×distribute-lft-out
218×exp-prod
182×distribute-rgt-in distribute-lft-in
168×flip3-- flip--
150×*-commutative
146×associate-/r/
141×cube-prod
114×frac-times
109×fma-def
108×associate-*l/
102×sqrt-pow1
94×flip-+ flip3-+
86×frac-2neg clear-num
63×sub-neg
59×pow1/2 pow1/3
58×cbrt-div
47×swap-sqr
46×cos-sum associate--l+
43×fma-neg pow-pow
40×fma-udef div-sub
36×rem-sqrt-square log-pow pow-flip
32×frac-sub
31×neg-mul-1
28×associate-/l/
27×tan-quot
26×diff-log
24×pow-prod-up
22×log-prod
20×pow-sqr
19×sum-log
18×pow-sub
17×rem-exp-log
16×+-commutative neg-sub0
13×difference-cubes
12×hypot-def
11×exp-diff associate--r+
8×frac-add neg-log
7×unpow3 inv-pow cube-mult pow-plus
6×rem-cube-cbrt pow-neg associate-+r+
5×cube-div acos-asin pow2 rem-log-exp
4×associate-+r- hypot-udef unsub-neg associate-+l- distribute-neg-frac
3×associate--r- exp-to-pow
2×asin-acos cos-diff distribute-frac-neg
1×associate-+l+ un-div-inv associate--l- sqrt-unprod exp-neg rem-square-sqrt mul0 rem-cbrt-cube distribute-rgt-neg-out

simplify13.3s (3.7%)

regimes10.5s (2.9%)

Accuracy

Total 44.9b remaining (22.2%)

Threshold costs 3.5b (1.7%)

8.9b38.9%Henrywood and Agarwal, Equation (3)
7.8b16.7%Toniolo and Linder, Equation (13)
6.4b73.5%Toniolo and Linder, Equation (7)
5.6b-13.3%Toniolo and Linder, Equation (10-)
4.6b0%Henrywood and Agarwal, Equation (12)

localize2.3s (0.6%)

bsearch2.1s (0.6%)

end0.0ms (0.0%)