Details

simplify10.4m (46.9%)

prune5.1m (23.1%)

sample4.3m (19.5%)

Algorithm
61×intervals
Results
1.0m257142×body80valid
45.1s27503×body1280valid
43.1s159862×body80nan
26.5s19248×body640valid
18.8s8679×body10240exit
14.7s7991×body2560valid
12.5s3465×body5120valid
8.7s9505×body320valid
5.2s8988×body160valid
711.0ms620×body1280nan
603.0ms8256×pre80true
566.0ms614×body640nan
183.0ms335×body320nan
71.0ms202×body160nan

series1.6m (7.2%)

Calls

437 calls:

4.2s
(* (- (* (cos (fma K (/ (+ m n) 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1)))) (* (sin (fma K (/ (+ m n) 2) (- (* M 1)))) (sin (fma (- M) 1 (* M 1))))) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))
2.6s
(sqrt (* (* U 2) (* n (* (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))))
2.5s
(sqrt (* (* U 2) (* n (* (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))))
2.4s
(sqrt (* (* U 2) (* n (* (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))))
2.3s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))

rewrite18.7s (1.4%)

Algorithm
117×rewrite-expression-head
Calls

437 calls:

1.8s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.4s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.3s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
566.0ms
(+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)
498.0ms
(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
Rules
13118×add-exp-log
12523×times-frac
8333×add-sqr-sqrt
7739×*-un-lft-identity
6902×add-cube-cbrt
6468×div-exp
6009×add-cbrt-cube
4669×prod-exp
2625×cbrt-undiv
2432×sqrt-prod
2237×cbrt-unprod
1727×associate-*l*
1694×pow1
1176×pow-unpow
881×associate-*r*
710×div-inv
687×prod-diff
652×pow-prod-down
590×difference-of-squares
559×associate-/r*
539×1-exp
526×associate-/l*
480×rec-exp
477×add-log-exp
438×log1p-expm1-u
437×expm1-log1p-u insert-posit16
416×cbrt-prod
292×associate-*r/
260×unswap-sqr
259×associate-/r/
255×distribute-lft-out--
187×associate-*l/
144×*-commutative
138×tan-quot
136×unpow-prod-down
135×sqrt-pow1
120×pow-exp
111×frac-2neg clear-num
101×flip3-- pow-prod-up flip--
91×swap-sqr
83×pow1/3
81×sqrt-div
79×frac-times
74×distribute-rgt-in sqr-pow distribute-lft-in
69×pow1/2
67×fma-neg
65×rem-sqrt-square
60×pow-to-exp
56×div-sub
54×distribute-lft-out
51×pow-sqr
43×fma-def
42×associate-/l/
36×pow-plus
35×sub-neg
33×pow-pow fma-udef
26×pow2 frac-add
22×exp-sum flip-+ flip3-+
21×cos-sum
18×pow-flip pow-sub
14×log-pow
13×inv-pow diff-log
12×exp-prod
10×exp-diff
9×un-div-inv
7×sum-log cbrt-div +-commutative
6×log-prod hypot-udef
5×frac-sub sin-mult
4×cos-mult associate-+r+ cube-unmult unpow2 acos-asin cos-diff
3×expm1-log1p expm1-udef remove-posit16 sqrt-unprod sub-div associate--r+ asin-acos
2×associate-+r- associate--l+ pow3 associate-+l- hypot-def rem-log-exp
1×sin-sum sqrt-undiv sqr-sin rem-square-sqrt

regimes16.4s (1.2%)

Accuracy

Total 37.6b remaining (24%)

Threshold costs 3.6b (2.3%)

6.4b19%Henrywood and Agarwal, Equation (13)
5.9b34%Toniolo and Linder, Equation (13)
5.5b76.5%Toniolo and Linder, Equation (7)
4.3b-0.3%Toniolo and Linder, Equation (10+)
3.8b0%Maksimov and Kolovsky, Equation (3)

localize6.0s (0.5%)

bsearch2.8s (0.2%)

end1.0ms (0.0%)