Details

sample2.2m (35.8%)

Algorithm
61×intervals
Results
36.3s252956×body80valid
23.9s160708×body80nan
21.5s29672×body1280valid
11.2s8913×body2560valid
10.4s20020×body640valid
7.0s3403×body5120valid
3.7s9784×body320valid
2.3s8912×body160valid
645.0ms620×body10240exit
337.0ms620×body1280nan
266.0ms612×body640nan
185.0ms8256×pre80true
115.0ms328×body320nan
41.0ms167×body160nan
8.0ms75×body80overflowed

series2.0m (33.0%)

Calls

446 calls:

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

prune1.1m (18.0%)

rewrite20.2s (5.5%)

Algorithm
117×rewrite-expression-head
Calls

446 calls:

1.0s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
929.0ms
(pow (pow (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) 3) 3)
865.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
865.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
856.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
Rules
25635×add-exp-log
17489×prod-exp
8985×pow-exp
8254×times-frac
7688×div-exp
6502×add-sqr-sqrt
6071×*-un-lft-identity
5072×add-cube-cbrt
4416×pow-to-exp
2729×add-cbrt-cube
2089×sqrt-prod
1642×sqrt-div
1385×unpow-prod-down
1340×pow1
1261×cbrt-prod
1119×cbrt-unprod
1103×associate-*l*
1097×1-exp rec-exp
1042×frac-times
970×prod-diff
939×associate-*r*
858×pow-unpow
774×associate-*r/
708×flip3-- flip--
567×div-inv
555×difference-of-squares
534×add-log-exp cbrt-undiv
500×associate-*l/
477×pow-prod-down
447×log1p-expm1-u associate-/r*
446×expm1-log1p-u
431×associate-/l*
402×sqr-pow
333×distribute-lft-out--
291×associate-/r/
245×distribute-lft-out
231×unswap-sqr
212×distribute-rgt-in distribute-lft-in
175×distribute-rgt-neg-in
150×exp-prod
149×*-commutative
141×sqrt-pow1
136×distribute-lft-neg-in
115×flip-+ flip3-+
94×clear-num frac-2neg
93×fma-neg
89×cube-prod unpow2
81×fma-def
80×pow1/2
75×tan-quot
72×sub-neg
60×pow-pow
55×log-pow
49×associate-/l/ associate--l+
46×cos-sum frac-sub
44×pow1/3
40×rem-sqrt-square
39×div-sub
34×cbrt-div
29×fma-udef
27×pow-neg pow-flip sum-log
25×pow-sub
24×associate-+l+
23×neg-sub0
22×associate--r+
21×+-commutative
20×pow-prod-up
17×diff-log associate-+r+ exp-sum
16×neg-mul-1
15×hypot-def log-prod
14×cube-div pow-sqr
13×exp-diff unpow3 un-div-inv cube-mult swap-sqr
12×inv-pow
rem-cube-cbrt associate-+r- rem-log-exp
sqrt-unprod frac-add
pow-div rem-exp-log distribute-neg-frac
difference-cubes pow-plus hypot-udef unsub-neg asin-acos
pow2 distribute-frac-neg acos-asin
cos-diff expm1-log1p rem-square-sqrt rem-cbrt-cube expm1-udef log-div
sqrt-undiv log1p-udef associate--l- log1p-expm1 mul0 sum-cubes

simplify12.3s (3.3%)

Algorithm
177×egg-herbie

regimes11.2s (3.0%)

Accuracy

Total 37.6b remaining (20.4%)

Threshold costs 4.6b (2.5%)

7.9b19%Toniolo and Linder, Equation (13)
5.5b77.5%Toniolo and Linder, Equation (7)
4.7b0%Henrywood and Agarwal, Equation (12)
3.6b53.7%Toniolo and Linder, Equation (10+)
3.2b56.5%Toniolo and Linder, Equation (10-)

bsearch3.1s (0.8%)

localize2.2s (0.6%)

end1.0ms (0.0%)