Details

simplify55.4m

Calls

20358 calls:

Slowest
2.5s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
2.5s
(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
2.4s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.4s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
2.4s
(* (* (* h h) h) (/ (* (/ (* (* 1 1) 1) (* (* l l) l)) (* (* (* M M) M) (* (* D D) D))) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune4.9m

sample3.7m

Algorithm
57×intervals
Results
1.1m246407×body80valid
42.1s159729×body80nan
32.9s18739×body1280valid
20.5s8774×body10240exit
18.6s14500×body640valid
7.8s5707×body2560valid
7.7s7370×body320valid
5.2s2404×body5120valid
4.4s8004×body160valid
809.0ms593×body1280nan
669.0ms595×body640nan
420.0ms8256×pre80true
263.0ms342×body320nan
75.0ms190×body160nan

series1.3m

Calls

403 calls:

Slowest
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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
1.6s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- 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))))
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite22.9s

Algorithm
109×rewrite-expression-head
Calls

403 calls:

Slowest
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.2s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
1.1s
(+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)
Rules
23383×times-frac
13851×add-sqr-sqrt
13434×*-un-lft-identity
12002×add-cube-cbrt
6936×sqrt-prod
5743×add-exp-log
3840×add-cbrt-cube
2727×prod-diff
2391×prod-exp
1850×div-exp
1545×pow1
1445×unpow-prod-down
1395×cbrt-unprod
1380×associate-*l*
1353×cbrt-undiv
1185×associate-/l*
1145×div-inv
807×associate-*r*
775×cube-prod
772×difference-of-squares
678×cbrt-prod
649×associate-/r/
550×associate-/r*
486×add-log-exp
440×associate-*r/
421×sqr-pow
418×distribute-lft-out--
416×pow-prod-down
404×log1p-expm1-u
403×expm1-log1p-u insert-posit16
362×distribute-rgt-neg-in
354×distribute-lft-neg-in
320×pow-unpow
317×pow-exp
289×exp-sum
282×unswap-sqr
271×associate-*l/
260×distribute-lft-out
249×frac-times
229×distribute-rgt-in distribute-lft-in
173×pow-prod-up
163×flip-- flip3--
155×fma-neg
154×pow-to-exp
138×cube-mult
136×*-commutative
133×unpow3
114×1-exp rec-exp
107×pow-sqr
106×sqrt-div
101×sqrt-pow1
97×swap-sqr
95×frac-2neg clear-num
86×pow-plus
76×pow1/2
75×sub-neg
72×cbrt-div
63×pow2
62×rem-sqrt-square
59×pow1/3
52×associate--l+ unpow2
49×flip-+ flip3-+
43×fma-udef
42×frac-sub
40×associate-/l/
39×exp-prod
38×neg-mul-1
37×diff-log
35×log-prod
32×log-pow
31×pow-pow
30×tan-quot
27×div-sub
26×frac-add
25×cos-sum
22×associate--r+ fma-def
20×pow-flip
19×pow-sub
10×inv-pow rem-exp-log
neg-log distribute-neg-frac
sum-log +-commutative
neg-sub0
difference-cubes
distribute-frac-neg difference-of-sqr-1 un-div-inv rem-log-exp acos-asin associate--r-
exp-diff sub-div distribute-rgt-out-- asin-acos
sin-sum mul0 pow-div associate--l- sqrt-unprod hypot-udef rem-square-sqrt cube-div
expm1-log1p expm1-udef remove-posit16 associate-+r- sqrt-undiv rem-cube-cbrt pow3 sqrt-pow2 exp-to-pow cos-diff distribute-rgt-out log-div

regimes18.3s

Accuracy

Total 39.8b remaining (28%)

10.1b30.1%Toniolo and Linder, Equation (13)
6.5b17.1%Henrywood and Agarwal, Equation (13)
5.3b77.8%Toniolo and Linder, Equation (7)
4.6b-13.8%Maksimov and Kolovsky, Equation (3)
4.6b24.3%Henrywood and Agarwal, Equation (12)

localize5.9s

bsearch4.8s

end1.0ms