Details

series1.7m (36.6%)

Calls

438 calls:

5.2s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- 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*))))

sample1.3m (28.5%)

Algorithm
61×intervals
Results
15.7s29267×body1280valid
15.6s252878×body80valid
9.9s162042×body80nan
8.7s8861×body2560valid
7.4s20556×body640valid
5.5s3434×body5120valid
2.3s9875×body320valid
1.3s9091×body160valid
546.0ms748×body10240exit
142.0ms607×body1280nan
113.0ms637×body640nan
109.0ms8256×pre80true
49.0ms365×body320nan
19.0ms186×body160nan

prune49.8s (17.5%)

rewrite20.7s (7.3%)

Algorithm
114×rewrite-expression-head
Calls

438 calls:

3.4s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
1.2s
(- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))
1.1s
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
625.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
570.0ms
(* NaChar (/ 1 (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
Rules
46867×add-exp-log
34282×prod-exp
24302×pow-exp
17383×div-exp
11710×pow-to-exp
4375×add-sqr-sqrt
4269×*-un-lft-identity
4171×times-frac
3829×1-exp
3597×rec-exp
3077×add-cube-cbrt
2743×sqrt-prod
2445×add-cbrt-cube
1116×pow1
1036×cbrt-unprod
979×associate-*r*
954×unpow-prod-down
820×associate-*l*
701×associate-*r/
632×cbrt-prod
522×add-log-exp
504×distribute-lft-out
453×cbrt-undiv
373×sqrt-div
351×associate-/l*
334×associate-/r*
325×unswap-sqr
322×pow-prod-down
274×associate-*l/
273×pow-unpow
268×difference-of-squares
255×sqr-pow
251×frac-times
230×div-inv
188×flip3-- flip--
186×div-sub
181×flip-+ flip3-+
176×distribute-lft-out--
168×exp-diff
148×associate-/r/
139×*-commutative
135×distribute-rgt-neg-in
116×cbrt-div
109×distribute-rgt-in distribute-lft-in
107×frac-sub sqrt-pow1
88×clear-num frac-2neg
86×pow1/2
84×sub-neg
82×tan-quot
80×rem-sqrt-square
75×exp-prod
74×pow-pow
73×pow1/3
69×distribute-lft-neg-in
64×neg-sub0
59×associate-+r- unsub-neg
55×unpow2
54×swap-sqr
46×associate--l+
32×sum-log
31×associate-/l/
27×+-commutative
20×frac-add
19×sub-div
18×log-prod
16×pow-prod-up
14×associate-+r+
12×pow-sqr exp-sum
11×log-pow
10×diff-log cube-prod
9×pow-sub neg-mul-1
8×pow-flip log-div
6×inv-pow cos-sum
5×pow-plus pow2
4×pow-neg distribute-neg-in associate-+l+ acos-asin distribute-neg-frac
3×cube-div un-div-inv rem-exp-log cos-diff unpow3 cube-mult rem-log-exp
2×rem-cube-cbrt sqrt-unprod rem-square-sqrt distribute-frac-neg asin-acos
1×distribute-rgt-out-- neg-log associate--r- mul0 sum-cubes exp-to-pow

simplify13.2s (4.7%)

Algorithm
174×egg-herbie

regimes10.9s (3.8%)

Accuracy

Total 49.7b remaining (22.3%)

Threshold costs 4.4b (2%)

10.0b27.1%Toniolo and Linder, Equation (13)
8.0b9.2%Toniolo and Linder, Equation (10+)
7.9b28%Henrywood and Agarwal, Equation (3)
6.5b72.6%Toniolo and Linder, Equation (7)
3.9b18%Henrywood and Agarwal, Equation (12)

localize2.3s (0.8%)

bsearch2.3s (0.8%)

end1.0ms (0.0%)