Details

series1.6m (34.4%)

Calls

429 calls:

4.9s
(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*))))))
4.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.3m (28.8%)

Algorithm
61×intervals
Results
15.4s29286×body1280valid
15.2s252823×body80valid
9.8s161730×body80nan
8.4s8627×body2560valid
7.7s20781×body640valid
5.1s3283×body5120valid
2.4s10084×body320valid
1.2s8933×body160valid
457.0ms623×body10240exit
147.0ms596×body1280nan
122.0ms647×body640nan
108.0ms8256×pre80true
52.0ms378×body320nan
16.0ms174×body160nan

prune59.3s (21.4%)

rewrite13.9s (5.0%)

Algorithm
114×rewrite-expression-head
Calls

429 calls:

778.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
466.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
430.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
415.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
378.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
Rules
29480×add-exp-log
19846×prod-exp
10025×pow-exp
8840×div-exp
8431×times-frac
6086×add-sqr-sqrt
5314×*-un-lft-identity
4861×add-cube-cbrt
4734×pow-to-exp
2591×add-cbrt-cube
2187×cbrt-prod
1640×associate-*r*
1284×sqrt-prod
1218×unpow-prod-down
1159×pow1
1155×associate-*l*
1064×cbrt-unprod
801×1-exp rec-exp
521×cbrt-undiv
515×add-log-exp
472×pow-unpow
466×associate-/l*
435×associate-*r/
378×unswap-sqr
366×div-inv
321×pow-prod-down
317×sqr-pow
310×associate-/r*
258×sqrt-div
222×associate-*l/
180×flip-+ flip3-+
167×frac-times
140×flip3-- flip--
137×distribute-lft-out
133×*-commutative
121×distribute-lft-out--
115×associate-/r/
103×difference-of-squares
93×sqrt-pow1
92×distribute-rgt-neg-in
88×frac-2neg clear-num
87×distribute-rgt-in distribute-lft-in
80×distribute-lft-neg-in
71×cube-prod
67×pow1/2
64×sub-neg
63×rem-sqrt-square
58×pow1/3 tan-quot
55×unpow2
50×log-pow
43×cbrt-div
42×exp-prod pow-prod-up frac-sub
39×associate-/l/ div-sub pow-pow
38×pow-sub
31×sum-log
30×associate--l+
29×+-commutative
28×pow-sqr
24×swap-sqr
22×frac-add pow-plus
17×pow2
16×pow-neg
15×log-prod
14×neg-sub0
13×diff-log
12×unpow3 associate-+r+ cube-mult
neg-mul-1
rem-cube-cbrt un-div-inv sub-div
associate-+l+ distribute-rgt-out-- acos-asin rem-log-exp
cube-div associate-+r- exp-sum
cos-sum inv-pow pow-flip asin-acos sin-mult distribute-neg-frac
rem-exp-log cos-diff unsub-neg distribute-frac-neg cos-mult mul0 rem-cbrt-cube

simplify12.8s (4.6%)

Algorithm
174×egg-herbie

regimes11.5s (4.2%)

Accuracy

Total 35.9b remaining (17.9%)

Threshold costs 6.4b (3.2%)

8.1b34.9%Toniolo and Linder, Equation (13)
5.3b77.8%Toniolo and Linder, Equation (7)
4.2b0%Henrywood and Agarwal, Equation (12)
3.4b57.8%Toniolo and Linder, Equation (10+)
3.1b0%Henrywood and Agarwal, Equation (13)

localize2.3s (0.8%)

bsearch1.8s (0.7%)

end1.0ms (0.0%)