Details

simplify47.9m

Calls

18300 calls:

Slowest
3.4s
(/ (* (* (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (* (* (/ (* t (/ (sin k) (/ l t))) (* (cbrt (cos k)) (cbrt (cos k)))) (/ (* t (/ (sin k) (/ l t))) (* (cbrt (cos k)) (cbrt (cos k))))) (/ (* t (/ (sin k) (/ l t))) (* (cbrt (cos k)) (cbrt (cos k))))))
3.1s
(/ (* (* (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (/ (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (cos k) (cos k))))
2.9s
(/ (* (* (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (/ (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (cos k) (cos k))))
2.8s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.8s
(/ (* (* (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2)))) (cbrt (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))))))) (/ (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (cos k) (cos k))))

prune5.2m

sample4.0m

Algorithm
59×intervals
Results
1.1m256263×body80valid
42.5s159729×body80nan
41.5s23736×body1280valid
22.2s16884×body640valid
19.5s8774×body10240exit
7.7s5707×body2560valid
7.0s8529×body320valid
6.8s2404×body5120valid
4.4s8590×body160valid
691.0ms593×body1280nan
561.0ms595×body640nan
297.0ms8256×pre80true
247.0ms342×body320nan
70.0ms190×body160nan

series1.4m

Calls

424 calls:

Slowest
2.4s
(sqrt (* 2 (* (* U n) (- (- t (* (* l (/ l Om)) 2)) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))
2.3s
(sqrt (* 2 (+ (* (* U n) t) (* (* U (- (/ (* -2 l) (/ Om l)) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))) n))))
2.3s
(sqrt (* 2 (* (* U n) (- (- t (* (/ (* l l) Om) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
2.1s
(sqrt (* 2 (* (* U n) (- (- t (* (* l (/ l Om)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite34.5s

Algorithm
110×rewrite-expression-head
Calls

424 calls:

Slowest
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.3s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
931.0ms
(+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)
Rules
16122×times-frac
9261×add-sqr-sqrt
8846×*-un-lft-identity
7936×add-cube-cbrt
7069×add-exp-log
5485×add-cbrt-cube
4631×sqrt-prod
3107×prod-exp
2523×associate-*l*
2318×cbrt-unprod
2255×pow1
2190×div-exp
1780×cbrt-undiv
1006×associate-/l*
826×div-inv
823×associate-*r/
802×cbrt-prod
795×associate-*r*
679×associate-/r/
676×pow-prod-down
562×add-log-exp
531×unpow-prod-down
474×associate-/r*
459×frac-times
439×sqrt-div
431×associate-*l/
424×insert-posit16
401×difference-of-squares
306×pow-prod-up
300×pow-unpow
289×unswap-sqr
283×distribute-lft-out--
279×pow-exp
266×flip-+ flip3-+
249×flip3-- flip--
222×sqr-pow
187×cube-prod
185×distribute-lft-out
183×pow-sqr
167×*-commutative
158×pow-plus
142×swap-sqr
139×frac-add
124×distribute-rgt-neg-in
122×sqrt-pow1
120×pow-to-exp
117×frac-sub
115×tan-quot
113×pow2
112×distribute-lft-neg-in
100×cbrt-div
92×pow1/2
90×frac-2neg clear-num
81×1-exp rec-exp
74×sub-neg
68×distribute-rgt-in distribute-lft-in
62×associate-/l/
58×rem-sqrt-square
50×diff-log
49×pow1/3
42×sin-mult
41×exp-prod
37×div-sub
33×pow-pow
25×log-pow
23×sum-log +-commutative
20×pow-flip
19×pow-sub
16×neg-mul-1
15×rem-exp-log
14×associate--l+
12×neg-log inv-pow
11×log-prod exp-sum
8×sqr-sin distribute-neg-frac cos-sum
7×neg-sub0
6×associate-+l+ associate--r+ cube-mult associate--r-
5×difference-cubes unpow2 distribute-rgt-out--
4×exp-diff distribute-frac-neg difference-of-sqr-1 acos-asin cos-diff distribute-rgt1-in
3×associate--l- rem-log-exp asin-acos
2×remove-posit16 associate-+r+ cube-unmult pow-div sqrt-unprod sub-div sqrt-pow2 un-div-inv rem-square-sqrt cube-div
1×associate-+r- sqrt-undiv rem-cube-cbrt pow3 unpow3 exp-to-pow distribute-rgt-out log-div

regimes19.4s

Accuracy

Total 38.3b remaining (20.2%)

7.9b11.4%Maksimov and Kolovsky, Equation (3)
7.3b-3.4%Toniolo and Linder, Equation (13)
6.1b75.2%Toniolo and Linder, Equation (7)
3.5b35%Henrywood and Agarwal, Equation (12)
3.3b26.6%Henrywood and Agarwal, Equation (13)

localize6.6s

bsearch5.5s

end1.0ms