Details

prune1.9m (32.0%)

series1.6m (26.1%)

Calls

440 calls:

4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.6s
(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 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
4.5s
(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 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (23.3%)

Algorithm
61×intervals
Results
16.2s257126×body80valid
14.6s26180×body1280valid
9.9s158433×body80nan
8.9s8874×body2560valid
6.6s17814×body640valid
5.4s3322×body5120valid
2.1s8574×body320valid
1.2s8473×body160valid
609.0ms11239×body80overflowed
573.0ms627×body10240exit
139.0ms609×body1280nan
117.0ms661×body640nan
105.0ms8256×pre80true
46.0ms344×body320nan
18.0ms195×body160nan

rewrite38.3s (10.6%)

Algorithm
116×rewrite-expression-head
Calls

440 calls:

5.0s
(* (* (cbrt (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (cbrt (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))) (cbrt (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
1.7s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
1.5s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
1.1s
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
833.0ms
(/ NdChar (* (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
Rules
41044×add-exp-log
32226×times-frac
26230×prod-exp
15644×add-sqr-sqrt
14934×div-exp
14715×*-un-lft-identity
14244×pow-exp
14177×add-cube-cbrt
8947×unpow-prod-down
6882×pow-to-exp
4624×cbrt-prod
4422×associate-*r*
2682×add-cbrt-cube
1860×sqrt-prod
1669×sqr-pow
1527×rec-exp 1-exp
1233×pow1
1140×cbrt-unprod
912×associate-*r/
897×associate-*l*
738×unpow2
695×associate-/l*
689×sqrt-div
571×add-log-exp
554×div-inv
458×cbrt-undiv
451×unswap-sqr
447×frac-times
440×associate-/r*
398×pow-prod-down cbrt-div
340×associate-*l/
328×flip-- flip3--
316×pow-unpow
237×associate-/r/
231×flip-+ flip3-+
185×cube-prod distribute-lft-out
174×difference-of-squares
148×*-commutative
125×sqrt-pow1
109×distribute-lft-out--
93×exp-prod
92×clear-num frac-2neg
89×log-pow
79×pow1/2
74×distribute-rgt-in distribute-lft-in
71×tan-quot
66×sub-neg pow-pow
58×pow1/3
55×sum-log frac-sub
54×distribute-rgt-neg-in rem-sqrt-square
41×distribute-lft-neg-in
32×cube-div
29×+-commutative
27×associate-/l/
25×pow-prod-up associate--l+
24×unpow3 cube-mult log-prod
19×frac-add diff-log
18×div-sub
16×exp-sum
15×associate-+r+
12×pow-sqr pow-sub swap-sqr
10×distribute-rgt-out-- pow-flip
9×pow-plus
8×neg-sub0
7×rem-cube-cbrt sub-div
6×cos-sum
5×un-div-inv inv-pow neg-mul-1 rem-cbrt-cube distribute-neg-frac
4×pow-neg associate-+r- pow2 acos-asin rem-log-exp
3×associate-+l+ sqrt-unprod cos-diff neg-log asin-acos associate-+l-
2×sqrt-undiv difference-cubes sqrt-pow2 rem-square-sqrt
1×exp-diff rem-exp-log pow3 unsub-neg distribute-frac-neg mul0

simplify14.4s (4.0%)

Algorithm
176×egg-herbie

regimes10.8s (3.0%)

Accuracy

Total 39.4b remaining (18.7%)

Threshold costs 4.7b (2.3%)

7.6b21.4%Toniolo and Linder, Equation (13)
6.2b73.1%Toniolo and Linder, Equation (7)
5.8b22.5%Toniolo and Linder, Equation (10+)
4.0b29.6%Henrywood and Agarwal, Equation (12)
3.8b32.9%Toniolo and Linder, Equation (10-)

localize2.2s (0.6%)

bsearch1.5s (0.4%)

end1.0ms (0.0%)