Details

prune10.8m (48.1%)

simplify5.2m (23.1%)

sample4.2m (18.8%)

Algorithm
60×intervals
Results
1.0m257610×body80valid
46.0s27972×body1280valid
43.9s160268×body80nan
23.3s18950×body640valid
20.1s8621×body10240exit
14.1s7950×body2560valid
10.9s3405×body5120valid
8.7s9698×body320valid
4.7s8913×body160valid
976.0ms669×body640nan
597.0ms581×body1280nan
553.0ms355×body320nan
345.0ms8256×pre80true
68.0ms211×body160nan

series1.4m (6.2%)

Calls

447 calls:

Slowest
4.0s
(sqrt (* (* U 2) (+ (* t n) (* (* (- n) (- (* l 2) (* (* (- n) (/ l Om)) (- U U*)))) (/ l Om)))))
3.4s
(sqrt (* (* U 2) (+ (* t n) (* (- n) (* (- (* l 2) (* (* (- n) (/ l Om)) (- U U*))) (/ l Om))))))
1.8s
(sqrt (* (* U 2) (* n (- t (* (/ l Om) (- (* 2 l) (* (* (- n) (- U U*)) (/ l Om))))))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.2s
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M)))

rewrite24.4s (1.8%)

Algorithm
114×rewrite-expression-head
Calls

447 calls:

Slowest
662.0ms
(/ NdChar (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1))
560.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
504.0ms
(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1))
474.0ms
(* (- (+ (* (+ a 3) (* b b)) (* a a)) (* a (* a a))) 4)
454.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
Rules
86104×times-frac
36540×add-sqr-sqrt
36136×*-un-lft-identity
35152×add-cube-cbrt
10038×sqrt-prod
8505×add-exp-log
7433×add-cbrt-cube
3752×div-inv
3429×div-exp
3195×prod-exp
3132×associate-/l*
2874×cbrt-unprod
2865×cbrt-undiv
1558×pow1
1376×associate-/r/
1308×associate-*r*
1259×associate-/r*
962×associate-*l*
772×sqrt-div
767×flip-+ flip3-+
722×difference-of-squares
593×cbrt-prod
568×frac-times
567×add-log-exp
447×insert-posit16
442×pow-prod-down
433×associate-*r/
406×associate-*l/
323×unswap-sqr
290×flip3-- flip--
223×distribute-lft-out
179×unpow-prod-down
169×sqrt-pow1
153×*-commutative
130×distribute-lft-out--
121×rem-sqrt-square
120×pow1/2
119×pow-exp
103×pow-prod-up
101×pow-to-exp
100×frac-2neg clear-num
98×sqr-pow
92×swap-sqr
91×1-exp frac-add
88×associate-/l/
87×cbrt-div
81×rec-exp sin-mult
64×log-pow
59×distribute-rgt-in distribute-lft-in
58×pow-plus
53×distribute-rgt-out--
50×pow-sqr
48×pow-unpow sub-neg
44×sum-log
36×pow1/3
35×pow2
28×exp-prod
25×+-commutative pow-pow
23×diff-log
20×cube-prod
19×div-sub
15×tan-quot
14×associate--r+
12×log-prod cube-div
11×distribute-lft-neg-out
distribute-rgt-neg-in distribute-lft-neg-in
associate-+l+ difference-of-sqr-1
remove-posit16 asin-acos
associate-+r+ cube-unmult
pow-flip associate--l+ pow3 inv-pow associate--r-
exp-sum neg-mul-1 un-div-inv sqr-sin rem-log-exp
exp-diff frac-sub unpow3 cube-mult cos-sum rem-cbrt-cube acos-asin log-div distribute-rgt1-in
unpow1/2 sub-div sqrt-pow2 exp-to-pow cos-diff

regimes16.3s (1.2%)

Accuracy

Total 39.8b remaining (20.4%)

Threshold costs 3.4b (1.8%)

7.6b7.1%Maksimov and Kolovsky, Equation (3)
6.2b29.9%Toniolo and Linder, Equation (13)
5.5b76.4%Toniolo and Linder, Equation (7)
4.9b22.6%Henrywood and Agarwal, Equation (13)
3.5b29.7%Henrywood and Agarwal, Equation (12)

localize6.3s (0.5%)

bsearch2.5s (0.2%)

end1.0ms (0.0%)