Details

simplify5.6m (32.0%)

prune4.9m (28.3%)

sample4.6m (26.4%)

Algorithm
61×intervals
Results
1.0m257647×body80valid
52.5s28008×body1280valid
43.0s160351×body80nan
28.4s19304×body640valid
20.2s8707×body10240exit
17.1s7880×body2560valid
16.3s3435×body5120valid
11.5s9538×body320valid
5.2s8917×body160valid
608.0ms563×body1280nan
497.0ms622×body640nan
307.0ms8256×pre80true
216.0ms362×body320nan
61.0ms191×body160nan

series1.5m (8.5%)

Calls

441 calls:

4.0s
(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n))))
3.9s
(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n))))
3.8s
(sqrt (* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n))))
2.4s
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* -1/2 (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) (/ h l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
2.4s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))

rewrite22.3s (2.1%)

Algorithm
117×rewrite-expression-head
Calls

441 calls:

1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
882.0ms
(* (+ (* (* (* l (* l l)) (* l l)) (* 1/60 J)) (* (fma (* l l) 1/3 2) (* J l))) (cos (/ K 2)))
706.0ms
(/ (/ NaChar (sqrt (+ 1 (exp (/ (+ EAccept (+ (- Vef mu) Ev)) KbT))))) (sqrt (+ 1 (exp (/ (+ EAccept (+ (- Vef mu) Ev)) KbT)))))
Rules
9737×times-frac
6562×add-sqr-sqrt
6160×*-un-lft-identity
5616×add-cube-cbrt
5596×add-exp-log
4152×add-cbrt-cube
2338×prod-exp
2056×sqrt-prod
1785×cbrt-unprod
1784×pow1
1748×div-exp
1551×associate-*l*
1341×cbrt-undiv
970×cbrt-prod
921×associate-*r*
671×associate-/r*
631×div-inv
595×pow-prod-down
505×add-log-exp
483×associate-/l*
443×expm1-log1p-u
442×log1p-expm1-u
441×insert-posit16
430×prod-diff
427×associate-*r/
318×associate-*l/
296×unpow-prod-down
288×associate-/r/
278×sqrt-div
277×unswap-sqr
265×frac-times
205×pow-prod-up
193×flip-+ flip3-+
172×distribute-lft-out sqr-pow
152×*-commutative
150×tan-quot
146×1-exp
139×difference-of-squares
134×pow-unpow
127×flip3-- flip--
126×pow-exp
125×distribute-rgt-in distribute-lft-in
114×sqrt-pow1
111×frac-2neg clear-num
101×distribute-lft-out--
97×pow-to-exp pow1/2
92×pow-plus
87×rec-exp
76×pow-sqr
73×rem-sqrt-square
62×fma-def
60×fma-neg
48×fma-udef
45×pow1/3
44×exp-sum pow2 swap-sqr
42×sub-neg
38×frac-add
33×associate-/l/
22×div-sub
20×cube-unmult pow-pow exp-prod
18×diff-log
15×cos-sum pow-sub
13×sum-log
12×pow-flip inv-pow
10×cbrt-div +-commutative
associate--r+ un-div-inv
rem-exp-log
associate-+r- associate-+r+ unpow2 acos-asin
expm1-log1p expm1-udef remove-posit16 exp-diff frac-sub hypot-udef associate-+l-
associate--l+ cos-diff
log1p-expm1 pow3 difference-cubes hypot-def log1p-udef
associate-+l+ associate--l- difference-of-sqr-1 sub-div asin-acos expm1-def

regimes18.6s (1.8%)

Accuracy

Total 36.9b remaining (24.2%)

Threshold costs 3.1b (2%)

8.3b0.9%Henrywood and Agarwal, Equation (13)
5.5b32.7%Toniolo and Linder, Equation (13)
5.2b78.1%Toniolo and Linder, Equation (7)
4.2b34.9%Toniolo and Linder, Equation (10+)
3.8b0%Maksimov and Kolovsky, Equation (3)

localize6.1s (0.6%)

bsearch3.5s (0.3%)

end1.0ms (0.0%)