Details

simplify10.3m (39.3%)

series6.5m (24.8%)

Calls

422 calls:

5.3m
(/ (/ 1 (/ 1 (pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1)))))) (/ (sqrt k) (pow (* PI (* n 2)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))))
2.3s
(sqrt (* (* 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) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.2s
(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

sample4.3m (16.5%)

Algorithm
60×intervals
Results
1.0m241718×body80valid
56.0s29708×body1280valid
37.6s139150×body80nan
28.8s19948×body640valid
23.7s8866×body2560valid
15.0s3429×body5120valid
10.0s9757×body320valid
5.7s8986×body160valid
2.1s633×body10240exit
1.9s620×body1280nan
570.0ms607×body640nan
316.0ms8256×pre80true
205.0ms398×body320nan
147.0ms180×body160nan

prune4.2m (16.0%)

regimes19.3s (1.2%)

Accuracy

Total 43.9b remaining (28.2%)

Threshold costs 3.2b (2%)

7.7b38.9%Toniolo and Linder, Equation (10-)
7.4b-6.1%Toniolo and Linder, Equation (13)
7.0b13.7%Henrywood and Agarwal, Equation (13)
5.1b78.5%Toniolo and Linder, Equation (7)
4.0b0%Maksimov and Kolovsky, Equation (3)

rewrite18.4s (1.2%)

Algorithm
115×rewrite-expression-head
Calls

422 calls:

2.0s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.8s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (* (/ c0 w) (* (/ d D) (/ d D))) (/ 1 h)))
525.0ms
(+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)
447.0ms
(/ (/ -2 (* (/ k t) (* (* (* (/ t l) (/ k t)) (/ t l)) t))) (- (* (sin k) (tan k))))
435.0ms
(/ (/ -2 (* (* (/ k t) (* (* (/ t l) (/ k t)) (/ t l))) t)) (- (* (sin k) (tan k))))
Rules
33945×times-frac
17207×*-un-lft-identity
17019×add-sqr-sqrt
15617×add-cube-cbrt
9004×sqrt-prod
7351×add-exp-log
5925×add-cbrt-cube
2927×div-exp
2839×prod-exp
2466×cbrt-unprod
2442×unpow-prod-up
1935×cbrt-undiv
1799×prod-diff
1493×difference-of-squares
1277×associate-/r*
1214×pow1
1097×associate-/l*
1085×div-inv
992×unpow-prod-down
902×sqr-pow
861×fma-udef
692×associate-/r/
661×associate-*l*
654×associate-*l/
621×associate-*r*
518×cbrt-prod
469×frac-times
467×add-log-exp
424×expm1-log1p-u log1p-expm1-u
422×insert-posit16
406×associate-*r/
380×distribute-lft-out--
368×pow-prod-down
356×pow-exp
221×flip-- flip3--
216×unswap-sqr
210×1-exp
202×rec-exp
142×distribute-lft-out
135×exp-prod
134×pow-to-exp
126×swap-sqr
117×*-commutative
112×frac-2neg clear-num
111×sqrt-pow1
98×sqrt-div
85×pow1/3
73×pow1/2
66×fma-neg
64×rem-sqrt-square
61×pow-prod-up sub-neg
51×associate-/l/
50×frac-add
46×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
42×fma-def
40×flip-+ flip3-+
39×distribute-rgt-in distribute-lft-in
31×pow-plus
30×pow-unpow
29×pow-sqr
27×distribute-rgt-out--
25×unpow2
19×pow2
16×tan-quot
15×cbrt-div cos-sum
14×pow-pow
12×div-sub diff-log
10×log-prod exp-sum
sum-log exp-diff rem-exp-log pow-sub
pow-flip inv-pow
+-commutative
un-div-inv asin-acos
pow3 hypot-def log1p-udef
expm1-udef cube-unmult log1p-expm1 acos-asin cos-diff distribute-rgt-out
expm1-log1p associate-+r- associate--l+ sqrt-unprod distribute-neg-frac hypot-udef rem-square-sqrt log-div
associate-+l+ remove-posit16 distribute-lft1-in sqrt-undiv associate-+r+ sqr-sin log-pow associate--r- sin-mult

bsearch9.1s (0.6%)

localize6.6s (0.4%)

end0.0ms (0.0%)