Details

simplify1.1hr

Calls

28028 calls:

Slowest
13.1s
(/ (* (cbrt (pow k m)) (cbrt (pow k m))) 1)
10.7s
(sqrt (+ 1 (* (* (sqrt (/ h l)) (/ (* (sqrt M) (sqrt D)) (sqrt (* 2 d)))) (/ (sqrt (* M D)) (* (sqrt 2) (sqrt d))))))
10.4s
(* (/ h (sqrt l)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d)))))
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune6.8m

rewrite5.6m

Algorithm
86×rewrite-expression-head
Calls

328 calls:

Slowest
1.8m
(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d)))) (/ (* M D) (* 2 d)))))
39.7s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
29.2s
(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
3.8s
(cos (- (* (* (/ K 2) (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) M))
3.8s
(/ (/ (/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t)))) (tan k)) (* (/ k t) (/ k t)))
Rules
3033849×times-frac
1933043×add-sqr-sqrt
1175972×*-un-lft-identity
1153056×add-cube-cbrt
391617×unswap-sqr
319603×associate-*r*
292104×associate-*l*
253770×swap-sqr
233281×cbrt-prod
211837×associate-/r/
201384×frac-times
167967×associate-/l*
155870×associate-/r*
106679×div-inv
57281×sqrt-prod
53536×associate-*r/
49681×sqrt-div
46358×clear-num
44268×frac-2neg
39572×*-commutative
35707×difference-of-squares
20280×associate-*l/
7746×unpow-prod-down
6527×associate-/l/
5126×sqr-pow
4884×add-cbrt-cube
4715×prod-diff
4359×add-exp-log
4184×un-div-inv
2772×cbrt-unprod
2242×fma-def
2222×frac-add
2107×prod-exp
1830×cbrt-undiv
1310×flip-- flip3--
1265×div-exp
1231×pow1
1060×cos-sum
1018×distribute-lft-out--
842×distribute-rgt-in distribute-lft-in
608×cbrt-div
530×distribute-lft-out
396×pow-prod-down
395×associate--l+
358×add-log-exp
349×frac-sub
330×log1p-expm1-u
328×expm1-log1p-u
327×insert-posit16
266×pow-exp
240×pow-to-exp
210×distribute-lft-neg-in distribute-rgt-neg-in
196×tan-quot
166×exp-prod
120×fma-neg
116×pow-prod-up
104×difference-of-sqr-1
100×rem-sqrt-square
87×div-sub
82×flip-+ pow1/3 flip3-+
81×unpow2
66×pow-sqr
63×pow-sub
56×pow-unpow
55×sqrt-pow1
50×pow-plus
44×pow-flip
40×1-exp
39×pow1/2
38×pow2 fma-udef
30×neg-mul-1
22×+-commutative
21×sub-neg
20×rec-exp
12×exp-diff associate--r+ distribute-neg-frac
pow-pow
diff-log
associate-+l+ sub-div inv-pow
expm1-log1p neg-sub0 sum-log distribute-frac-neg
distribute-rgt-out--
pow-div
expm1-udef associate-+r- asin-acos rem-exp-log cos-diff
remove-double-div cube-unmult exp-neg hypot-udef acos-asin
remove-posit16 sqrt-undiv log1p-expm1 sqr-sin sin-mult log1p-udef

sample1.9m

Algorithm
44×intervals
Results
36.4s155010×body80valid
19.6s12789×body1280valid
18.4s8118×body10240exit
12.1s52009×body80nan
10.9s9634×body640valid
5.3s4894×body320valid
3.4s3189×body2560valid
3.1s6807×body160valid
434.0ms94×body5120valid
23.0ms18×body1280nan
18.0ms19×body640nan
9.0ms13×body320nan
5.0ms10×body160nan

series1.3m

Calls

328 calls:

Slowest
6.5s
(sqrt (* (* (cbrt (* (* n (sqrt 2)) U)) (cbrt (sqrt 2))) (- (fma (/ (* l l) Om) -2 t) (* (* (- U U*) (* n (/ l Om))) (/ l Om)))))
5.7s
(sqrt (* (* (cbrt (sqrt 2)) (cbrt (* (* (sqrt 2) n) U))) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
4.7s
(sqrt (* (cbrt (* (* 2 n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes8.5s

Accuracy

Total 6.8b remaining (24%)

3.9b0%Maksimov and Kolovsky, Equation (3)
0.9b0%Toniolo and Linder, Equation (3a)
0.4b0%Bouland and Aaronson, Equation (25)
0.4b0%Migdal et al, Equation (64)
0.3b0%Maksimov and Kolovsky, Equation (4)

localize2.8s

bsearch973.0ms

end1.0ms