Details

prune4.8m (32.7%)

sample4.3m (29.1%)

Algorithm
61×intervals
Results
1.0m252992×body80valid
54.6s29380×body1280valid
40.9s160644×body80nan
28.6s20130×body640valid
22.7s8782×body2560valid
13.0s3372×body5120valid
10.8s9706×body320valid
4.4s9263×body160valid
1.6s670×body10240exit
1.2s638×body1280nan
545.0ms610×body640nan
263.0ms8256×pre80true
221.0ms321×body320nan
69.0ms197×body160nan

simplify3.5m (24.0%)

series1.2m (8.5%)

Calls

424 calls:

2.4s
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
1.8s
(fma (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))
1.7s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite21.6s (2.4%)

Algorithm
115×rewrite-expression-head
Calls

424 calls:

2.0s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
785.0ms
(/ (/ NaChar (sqrt (+ 1 (exp (/ (+ EAccept (+ (- Vef mu) Ev)) KbT))))) (sqrt (+ 1 (exp (/ (+ EAccept (+ (- Vef mu) Ev)) KbT)))))
685.0ms
(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2))
680.0ms
(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))
659.0ms
(/ (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (sin k)) (fma (/ k t) (/ k t) 2)) (* (/ l t) (cos k)))
Rules
65362×times-frac
33223×add-sqr-sqrt
32483×*-un-lft-identity
29701×add-cube-cbrt
11796×sqrt-prod
6386×add-exp-log
5420×associate-*l*
5268×cbrt-prod
5099×add-cbrt-cube
4374×prod-diff
2697×div-exp
2214×div-inv
2176×cos-sum
2144×prod-exp
2065×cbrt-undiv
1808×cbrt-unprod
1674×associate-/r*
1646×unpow-prod-up
1480×difference-of-squares
1315×pow1
1053×associate-*r*
923×associate-/l*
764×distribute-lft-out
671×associate-*r/
614×unswap-sqr
469×add-log-exp
448×associate-/r/
425×expm1-log1p-u
424×insert-posit16 log1p-expm1-u
400×pow-prod-down
210×flip-+ flip3-+
209×unpow-prod-down
201×distribute-lft-out--
196×frac-times
195×flip3-- flip--
194×1-exp
177×associate-*l/
176×sqrt-div
143×tan-quot
130×exp-prod
125×sqrt-pow1 cbrt-div
124×sqr-pow
121×frac-sub
120×*-commutative
109×pow-unpow
106×fma-neg
105×frac-2neg clear-num
97×pow-exp distribute-rgt-in distribute-lft-in
89×swap-sqr
88×pow1/2
78×frac-add
77×rem-sqrt-square
74×sub-neg
73×pow1/3
68×pow-prod-up
66×rec-exp
62×pow-to-exp
53×associate-/l/
42×pow-sqr
40×fma-udef
34×pow-plus fma-def
32×associate--l+
26×pow2 unpow2
22×pow-pow log-pow
18×log-prod div-sub
16×pow-flip
13×pow-sub
12×inv-pow
10×sum-log
9×+-commutative diff-log
7×exp-sum rem-exp-log
5×exp-diff associate-+l-
4×pow3
3×sqrt-unprod distribute-rgt-out-- asin-acos rem-cbrt-cube
2×remove-posit16 associate-+r- sub-div un-div-inv exp-to-pow hypot-udef rem-log-exp acos-asin cos-diff
1×expm1-udef sqrt-undiv cube-unmult log1p-expm1 associate--r+ sqr-sin rem-square-sqrt sin-mult e-exp-1 log1p-udef

regimes18.5s (2.1%)

Accuracy

Total 54.8b remaining (31.3%)

Threshold costs 4.3b (2.5%)

10.1b12.8%Toniolo and Linder, Equation (13)
9.9b-36.2%Henrywood and Agarwal, Equation (13)
8.7b40.1%Henrywood and Agarwal, Equation (3)
5.2b58.8%Toniolo and Linder, Equation (10+)
5.2b77.6%Toniolo and Linder, Equation (7)

localize5.7s (0.6%)

bsearch4.9s (0.6%)

end2.0ms (0.0%)