Details

series1.9m (32.1%)

Calls

455 calls:

5.0s
(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*))))))
5.0s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.5m (26.0%)

sample1.4m (24.1%)

Algorithm
61×intervals
Results
15.5s253029×body80valid
15.0s28894×body1280valid
9.6s161881×body80nan
8.8s8880×body2560valid
7.2s20339×body640valid
5.4s3349×body5120valid
2.3s9946×body320valid
1.2s9146×body160valid
542.0ms976×body10240exit
138.0ms619×body1280nan
114.0ms652×body640nan
106.0ms8256×pre80true
52.0ms348×body320nan
17.0ms194×body160nan

rewrite31.9s (9.1%)

Algorithm
119×rewrite-expression-head
Calls

455 calls:

1.6s
(* (sqrt (* (* (* (/ (sqrt 2.0) 4.0) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))) (sqrt (* (* (* (/ (sqrt 2.0) 4.0) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))
1.6s
(* (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))) (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.1s
(* (* (* (/ (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))
Rules
52781×add-exp-log
38701×prod-exp
26891×pow-exp
21717×sqrt-div
18843×div-exp
12381×pow-to-exp
11919×frac-times
6047×flip3-- flip--
5101×add-sqr-sqrt
4979×*-un-lft-identity
4964×times-frac
4716×associate-*l/
4081×1-exp
4074×rec-exp
3867×add-cube-cbrt
3252×associate-*r/
2660×add-cbrt-cube
2126×sqrt-prod
1488×pow1
1284×unpow-prod-down
1184×associate-*l*
1086×cbrt-unprod
867×associate-*r*
652×prod-diff
571×cbrt-prod
554×pow-prod-down
544×add-log-exp
513×cbrt-undiv
455×log1p-expm1-u expm1-log1p-u
422×associate-/l*
392×pow-unpow
373×distribute-lft-out--
362×associate-/r*
324×div-inv
311×distribute-rgt-neg-in
305×sqr-pow
300×difference-of-squares
285×distribute-lft-out
273×unswap-sqr
259×distribute-lft-neg-in
207×distribute-rgt-in sqrt-pow1 distribute-lft-in
152×*-commutative
126×flip-+ flip3-+
118×exp-prod
111×associate-/r/
97×clear-num frac-2neg
84×fma-neg
80×pow1/2
70×sub-neg
67×fma-def
64×associate--l+
59×pow1/3
56×tan-quot
51×rem-sqrt-square
44×pow-pow
42×swap-sqr
41×pow-prod-up div-sub
39×associate-/l/ fma-udef
37×frac-sub
36×cbrt-div
31×neg-mul-1
30×unpow2 pow-sqr
25×sum-log cos-sum
23×diff-log
22×associate--r+
21×+-commutative
17×pow-sub
16×pow-flip
14×neg-sub0 hypot-def
12×log-prod
11×log-pow
9×log-div
8×inv-pow
7×associate-+r+ pow2
6×pow-plus frac-add associate-+r- distribute-neg-frac
5×hypot-udef distribute-frac-neg associate-+l-
4×associate-+l+ pow-neg unsub-neg acos-asin neg-log
3×sqrt-undiv un-div-inv asin-acos distribute-rgt-out--
2×rem-exp-log exp-diff associate--l- sqrt-unprod exp-neg sin-sum rem-square-sqrt associate--r- rem-log-exp
1×cos-diff sub-div mul0

simplify14.7s (4.2%)

Algorithm
179×egg-herbie

regimes11.5s (3.3%)

Accuracy

Total 47.1b remaining (24%)

Threshold costs 4.6b (2.4%)

10.2b23.2%Toniolo and Linder, Equation (13)
9.3b31.6%Henrywood and Agarwal, Equation (3)
5.5b76.9%Toniolo and Linder, Equation (7)
4.7b-3.9%Henrywood and Agarwal, Equation (12)
4.3b37.3%Toniolo and Linder, Equation (10-)

localize2.3s (0.6%)

bsearch1.6s (0.5%)

end0.0ms (0.0%)