Details

simplify6.9m (42.2%)

sample3.3m (20.4%)

Algorithm
61×intervals
Results
40.7s253418×body80valid
40.1s29403×body1280valid
30.4s160338×body80nan
18.0s20091×body640valid
17.3s8792×body2560valid
14.2s3435×body5120valid
7.8s10024×body320valid
2.8s8958×body160valid
882.0ms669×body10240exit
532.0ms8256×pre80true
461.0ms610×body640nan
293.0ms591×body1280nan
97.0ms352×body320nan
33.0ms188×body160nan

series3.1m (18.9%)

Calls

447 calls:

15.7s
(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
7.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
3.1s
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))

prune2.0m (12.0%)

rewrite38.9s (3.9%)

Algorithm
119×rewrite-expression-head
Calls

447 calls:

1.8s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.8s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.5s
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
1.5s
(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
950.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
Rules
55600×add-exp-log
40862×prod-exp
28679×pow-exp
19955×div-exp
18701×times-frac
12681×pow-to-exp
11411×add-sqr-sqrt
10721×*-un-lft-identity
9886×add-cube-cbrt
9195×sqrt-prod
4775×rec-exp 1-exp
3400×unpow-prod-down
2454×add-cbrt-cube
1677×prod-diff
1513×associate-*r*
1233×pow1
1152×associate-*l*
1139×sqr-pow
951×cbrt-unprod
712×div-inv
611×cbrt-prod
553×pow-unpow
547×associate-/l*
546×cbrt-undiv
540×difference-of-squares
516×add-log-exp
482×distribute-rgt-in distribute-lft-in
469×associate-*r/
448×log1p-expm1-u
447×expm1-log1p-u
401×associate-/r*
378×distribute-lft-out--
351×pow-prod-down
314×exp-prod
287×associate-*l/
276×distribute-rgt-neg-in
274×sqrt-div
272×flip3-- frac-times flip--
262×distribute-lft-neg-in
227×associate-/r/
225×unswap-sqr
198×cbrt-div
185×cube-prod
165×unpow2
160×sin-sum
129×cos-sum
121×pow-pow
120×*-commutative
114×fma-def
110×tan-quot
107×sqrt-pow1
102×distribute-lft-out
92×frac-2neg clear-num
90×fma-neg
87×pow1/3
85×cube-div
72×pow1/2
68×frac-sub
58×rem-sqrt-square
57×unpow-prod-up
53×sub-neg pow-prod-up
50×swap-sqr
37×associate-/l/
35×pow-sqr div-sub
32×associate--l+
31×unpow3 cube-mult neg-mul-1
29×flip-+ flip3-+
25×fma-udef
23×pow-plus
22×associate--r+
20×diff-log
19×rem-cube-cbrt
18×pow2
13×pow-sub neg-sub0 hypot-def sum-log log-prod
11×exp-diff +-commutative
10×log-pow
7×rem-exp-log
6×frac-add acos-asin neg-log distribute-rgt-out--
4×pow-neg asin-acos inv-pow sqrt-undiv hypot-udef pow-flip distribute-frac-neg exp-sum distribute-neg-frac
3×exp-neg cos-diff rem-cbrt-cube rem-log-exp
2×associate--l- sub-div associate--r- associate-+l- sin-diff
1×sqrt-pow2 un-div-inv sqrt-unprod associate-+r- expm1-log1p unsub-neg rem-square-sqrt mul0 expm1-udef exp-to-pow

regimes15.1s (1.5%)

Accuracy

Total 38.4b remaining (19.2%)

Threshold costs 4.0b (2%)

8.6b14%Toniolo and Linder, Equation (13)
5.8b75.7%Toniolo and Linder, Equation (7)
5.6b4%Henrywood and Agarwal, Equation (12)
5.0b-41.3%Henrywood and Agarwal, Equation (13)
4.9b48%Toniolo and Linder, Equation (10-)

bsearch5.1s (0.5%)

localize4.0s (0.4%)

end1.0ms (0.0%)