Details

simplify10.3m (42.1%)

prune7.6m (31.0%)

sample4.3m (17.6%)

Algorithm
61×intervals
Results
59.5s253926×body80valid
54.6s29250×body1280valid
43.1s159936×body80nan
26.9s20581×body640valid
22.6s8764×body2560valid
13.9s3377×body5120valid
10.6s10053×body320valid
4.8s8806×body160valid
1.3s648×body10240exit
1.1s632×body1280nan
604.0ms628×body640nan
298.0ms8256×pre80true
255.0ms360×body320nan
71.0ms193×body160nan

series1.5m (5.9%)

Calls

426 calls:

2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.4s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.3s
(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
2.3s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite20.7s (1.4%)

Algorithm
115×rewrite-expression-head
Calls

426 calls:

1.8s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))))
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)))
1.3s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
842.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
562.0ms
(+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)
Rules
32042×times-frac
16829×add-sqr-sqrt
15993×*-un-lft-identity
15170×add-cube-cbrt
8812×sqrt-prod
7674×add-exp-log
5800×add-cbrt-cube
3892×associate-*l*
3195×prod-exp
3131×cbrt-prod
2655×div-exp
2273×cbrt-unprod
2140×cbrt-undiv
1734×associate-*r*
1539×frac-times
1523×associate-/l*
1480×pow1
1367×associate-*l/
1328×prod-diff
1129×sqrt-div
1116×div-inv
773×associate-*r/
735×difference-of-squares
574×associate-/r/
476×add-log-exp
469×pow-prod-down
428×expm1-log1p-u
427×log1p-expm1-u
426×insert-posit16
420×associate-/r*
403×unswap-sqr
328×unpow-prod-up
285×flip3-- flip--
272×pow-exp
176×distribute-lft-out
157×swap-sqr *-commutative
146×unpow-prod-down
129×pow-unpow
118×pow-to-exp
107×fma-neg
102×sqrt-pow1 1-exp rec-exp
99×frac-2neg clear-num
98×pow1/3
91×pow-prod-up
81×distribute-rgt-in distribute-lft-in
72×sqr-pow
69×distribute-lft-out--
60×pow-plus
59×associate-/l/ pow-sqr
57×rem-sqrt-square
55×pow1/2
46×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
44×sub-neg
41×fma-udef
39×fma-def
38×pow2
36×tan-quot
35×distribute-rgt-out--
33×flip-+ flip3-+
30×cbrt-div
23×unpow2
21×pow-pow
15×cos-sum
14×pow-flip frac-add
13×div-sub diff-log
12×exp-prod
11×sum-log +-commutative
9×pow-sub
8×log-prod inv-pow log-pow
5×pow3 acos-asin
4×hypot-udef
3×exp-sum un-div-inv rem-exp-log cos-diff log1p-udef
2×expm1-log1p expm1-udef remove-posit16 associate-+r- frac-sub associate-+r+ associate--l+ log1p-expm1 sqr-sin rem-log-exp distribute-neg-frac asin-acos associate-+l- sin-mult
1×sub-div rem-cbrt-cube

regimes19.6s (1.3%)

Accuracy

Total 43.1b remaining (24.3%)

Threshold costs 5.7b (3.2%)

6.6b35.1%Toniolo and Linder, Equation (10-)
6.3b22.6%Henrywood and Agarwal, Equation (13)
5.8b37.7%Toniolo and Linder, Equation (13)
5.5b-25.2%Henrywood and Agarwal, Equation (12)
5.1b78.1%Toniolo and Linder, Equation (7)

localize6.1s (0.4%)

bsearch2.6s (0.2%)

end1.0ms (0.0%)