Details

series1.9m (35.6%)

Calls

442 calls:

5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.6s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (26.5%)

Algorithm
61×intervals
Results
15.6s29927×body1280valid
14.8s253499×body80valid
9.3s162099×body80nan
8.9s8827×body2560valid
6.8s19931×body640valid
5.4s3356×body5120valid
2.2s9848×body320valid
1.2s8907×body160valid
490.0ms880×body10240exit
154.0ms641×body1280nan
109.0ms8256×pre80true
108.0ms599×body640nan
50.0ms375×body320nan
20.0ms203×body160nan

prune1.0m (20.0%)

rewrite28.2s (9.0%)

Algorithm
117×rewrite-expression-head
Calls

442 calls:

1.2s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
875.0ms
(/ NdChar (* (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
870.0ms
(cbrt (/ NdChar (* (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))))
863.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
863.0ms
(cbrt (/ NdChar (* (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))))
Rules
25440×add-exp-log
17045×prod-exp
8696×pow-exp
7954×div-exp
7783×times-frac
6202×add-sqr-sqrt
5400×*-un-lft-identity
4952×add-cube-cbrt
4384×pow-to-exp
3650×cbrt-prod
2601×add-cbrt-cube
2038×sqrt-prod
1105×pow1
1082×associate-*r*
1079×cbrt-unprod
1071×1-exp
1066×unpow-prod-down
869×associate-*l*
839×rec-exp
585×associate-/r*
568×cbrt-undiv
511×prod-diff
504×add-log-exp
487×associate-/l*
443×expm1-log1p-u
442×log1p-expm1-u
437×pow-unpow
390×associate-*r/
350×div-inv
349×sqr-pow
339×pow-prod-down
325×unswap-sqr
250×distribute-rgt-in distribute-lft-in
241×frac-times
230×sqrt-div
224×associate-*l/
178×flip3-- flip--
175×difference-of-squares
169×flip-+ flip3-+
164×associate-/r/
156×cbrt-div
154×distribute-rgt-neg-in
149×distribute-lft-out--
140×distribute-lft-neg-in
134×*-commutative
101×frac-2neg clear-num
97×distribute-lft-out
74×fma-def pow1/3
71×sub-neg sqrt-pow1
68×tan-quot
50×fma-neg
49×pow1/2
44×pow-pow
42×swap-sqr
41×rem-sqrt-square
37×associate-/l/ fma-udef log-prod
32×cube-prod associate--l+
30×unpow2 exp-sum
29×div-sub
28×frac-sub
25×cos-sum
24×associate-+l+
20×sum-log
18×pow-sub +-commutative
16×exp-prod
15×hypot-def
14×neg-mul-1
13×log-pow
12×frac-add diff-log
11×associate--r+
9×pow-prod-up pow-sqr
8×pow-flip
7×neg-sub0
6×inv-pow associate-+r+ asin-acos pow2
4×pow-plus pow-neg log-div
3×rem-cube-cbrt unpow3 rem-exp-log cube-mult hypot-udef
2×cube-div exp-diff sin-sum neg-log associate--r- distribute-neg-frac rem-log-exp
1×sqrt-undiv sqrt-pow2 log1p-udef associate--l- associate-+r- log1p-expm1 cos-diff expm1-log1p unsub-neg expm1-udef distribute-frac-neg acos-asin mul0 rem-cbrt-cube exp-to-pow

simplify11.8s (3.8%)

regimes10.2s (3.2%)

Accuracy

Total 36.1b remaining (20.4%)

Threshold costs 4.1b (2.3%)

8.3b15%Toniolo and Linder, Equation (13)
5.5b76.9%Toniolo and Linder, Equation (7)
4.9b0%Henrywood and Agarwal, Equation (12)
4.4b36.5%Toniolo and Linder, Equation (10+)
3.2b55.3%Toniolo and Linder, Equation (10-)

bsearch3.5s (1.1%)

localize2.4s (0.7%)

end1.0ms (0.0%)