Details

prune2.2m (34.2%)

series1.7m (26.8%)

Calls

442 calls:

4.9s
(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*))))))
4.6s
(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*)))))
4.6s
(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*))))))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* (* 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*))))

sample1.4m (22.4%)

Algorithm
61×intervals
Results
15.7s29589×body1280valid
15.3s252893×body80valid
9.4s158314×body80nan
8.6s8774×body2560valid
7.1s19902×body640valid
5.6s3378×body5120valid
2.5s9973×body320valid
1.2s8891×body160valid
424.0ms773×body10240exit
143.0ms604×body1280nan
113.0ms617×body640nan
104.0ms8256×pre80true
48.0ms354×body320nan
18.0ms186×body160nan

rewrite31.8s (8.4%)

Algorithm
117×rewrite-expression-head
Calls

442 calls:

2.4s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
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)))
1.7s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
820.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
804.0ms
(/ 1 (/ (+ 1.0 (cbrt (pow (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) 3))) NaChar))
Rules
39320×add-exp-log
32226×times-frac
25841×prod-exp
15986×add-sqr-sqrt
15327×*-un-lft-identity
14769×div-exp
14667×pow-exp
14352×add-cube-cbrt
8857×unpow-prod-down
7257×pow-to-exp
4469×cbrt-prod
4393×associate-*r*
2658×add-cbrt-cube
2311×1-exp
1719×rec-exp
1708×sqr-pow
1233×pow1
1182×cbrt-unprod
903×sqrt-prod
730×associate-*l*
693×unpow2
670×associate-/l*
616×div-inv
600×prod-diff
525×pow-unpow
523×cbrt-undiv
518×add-log-exp
443×expm1-log1p-u
442×log1p-expm1-u
441×associate-*r/
414×distribute-lft-out unswap-sqr
401×associate-/r*
398×pow-prod-down
323×frac-times
321×associate-*l/
228×sqrt-div
189×distribute-rgt-neg-in
182×distribute-lft-out--
178×difference-of-squares
174×flip-- flip3--
166×distribute-rgt-in distribute-lft-in
153×cube-prod
145×exp-prod
136×flip-+ flip3-+
131×*-commutative
117×associate-/r/
104×distribute-lft-neg-in
102×sqrt-pow1
97×tan-quot
95×frac-2neg clear-num
92×fma-def
73×cbrt-div
72×pow1/2
71×pow1/3
61×div-sub
60×fma-neg swap-sqr pow-pow
59×sub-neg
47×rem-sqrt-square
42×associate--l+
38×unpow3 cube-mult
35×fma-udef
34×frac-sub
31×associate-/l/
26×pow-prod-up
25×cos-sum
24×associate-+r+
23×sum-log
20×pow-sub
19×log-pow
18×pow-sqr log-prod
16×exp-diff +-commutative neg-sub0
15×hypot-def
14×frac-add pow-flip diff-log
13×neg-mul-1
12×pow-plus associate-+r-
10×pow2
9×inv-pow unsub-neg
8×exp-neg exp-sum distribute-rgt-neg-out
6×cube-div rem-cube-cbrt rem-exp-log distribute-neg-frac
5×un-div-inv
4×acos-asin log-rec mul-1-neg
3×pow-neg hypot-udef asin-acos distribute-rgt-out-- rem-log-exp
2×sqrt-unprod sin-sum rem-square-sqrt distribute-frac-neg neg-log associate-+l-
1×difference-cubes sqrt-pow2 log1p-udef quot-tan pow3 log1p-expm1 cos-diff associate-+l+ expm1-log1p expm1-udef sub-div mul0 rem-cbrt-cube

simplify14.5s (3.8%)

Algorithm
177×egg-herbie

regimes11.3s (3.0%)

Accuracy

Total 45.3b remaining (23.7%)

Threshold costs 6.0b (3.1%)

7.7b30.9%Henrywood and Agarwal, Equation (3)
7.3b23.7%Toniolo and Linder, Equation (13)
7.0b15.7%Toniolo and Linder, Equation (10+)
6.5b0%Henrywood and Agarwal, Equation (12)
5.6b76.5%Toniolo and Linder, Equation (7)

bsearch3.0s (0.8%)

localize2.4s (0.6%)

end0.0ms (0.0%)