Details

prune1.8m (31.4%)

series1.8m (30.4%)

Calls

436 calls:

5.2s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
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*))))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.3s
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (/ (cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M))) (cbrt (+ (/ (* K (+ m n)) 2.0) M)))))

sample1.4m (23.5%)

Algorithm
61×intervals
Results
16.0s253099×body80valid
16.0s29318×body1280valid
10.1s159299×body80nan
9.0s8984×body2560valid
7.2s20018×body640valid
5.6s3415×body5120valid
2.5s10071×body320valid
1.3s8932×body160valid
460.0ms638×body10240exit
154.0ms620×body1280nan
119.0ms8256×pre80true
119.0ms640×body640nan
48.0ms341×body320nan
17.0ms188×body160nan

rewrite21.9s (6.2%)

Algorithm
115×rewrite-expression-head
Calls

436 calls:

2.3s
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0))))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.5s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
830.0ms
(* (* (* (/ (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))
502.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI (* t (* (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
489.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
Rules
32779×times-frac
23838×add-exp-log
15830×add-sqr-sqrt
15086×*-un-lft-identity
14375×add-cube-cbrt
12751×prod-exp
11228×div-exp
9110×unpow-prod-down
7538×pow-exp
4759×associate-*r*
4714×cbrt-prod
3851×pow-to-exp
2323×add-cbrt-cube
1748×1-exp
1701×sqr-pow
1304×associate-*r/
1215×pow1
979×cbrt-unprod
925×sqrt-prod
923×rec-exp
850×associate-*l*
717×unpow2
707×sqrt-div
616×associate-/l*
572×div-inv
541×cbrt-div
507×add-log-exp
504×frac-times
457×flip3-- flip--
448×unswap-sqr
425×pow-prod-down
413×associate-*l/
391×cbrt-undiv
375×associate-/r*
365×pow-unpow
303×associate-/r/
302×distribute-lft-out--
191×exp-prod
160×distribute-lft-neg-in distribute-rgt-neg-in
148×flip-+ flip3-+
146×*-commutative
133×difference-of-squares
106×distribute-lft-out
95×distribute-rgt-in distribute-lft-in
88×pow1/3
79×clear-num frac-2neg
77×sqrt-pow1
71×sub-neg tan-quot
57×pow1/2
51×pow-pow
50×cube-prod
49×rem-sqrt-square
46×frac-sub
44×associate-/l/
38×associate--l+
28×frac-add
24×div-sub sum-log swap-sqr
22×neg-mul-1
20×+-commutative
18×log-prod
17×log-pow
16×cube-div
14×pow-sub
11×diff-log
9×rem-cube-cbrt associate-+r+ neg-sub0 exp-sum
7×pow-prod-up pow-sqr unpow3 cube-mult
6×inv-pow pow-flip distribute-frac-neg distribute-neg-frac
5×un-div-inv acos-asin
4×exp-diff pow-neg rem-exp-log
3×pow-plus exp-neg pow2 distribute-rgt-out-- rem-cbrt-cube rem-log-exp
2×cos-sum associate--r+
1×associate-+l+ sqrt-unprod sum-cubes cos-diff rem-square-sqrt sub-div asin-acos mul0 log-div

simplify13.8s (3.9%)

Algorithm
175×egg-herbie

regimes11.6s (3.3%)

Accuracy

Total 41.4b remaining (20.3%)

Threshold costs 4.3b (2.1%)

8.7b31.6%Toniolo and Linder, Equation (13)
7.7b21.2%Henrywood and Agarwal, Equation (12)
5.6b77%Toniolo and Linder, Equation (7)
4.0b45.4%Toniolo and Linder, Equation (10+)
3.8b21.9%Toniolo and Linder, Equation (10-)

localize2.4s (0.7%)

bsearch2.3s (0.7%)

end1.0ms (0.0%)