Details

sample1.9m (36.1%)

Algorithm
61×intervals
Results
28.2s253101×body80valid
20.3s29512×body1280valid
17.8s159180×body80nan
10.8s8739×body2560valid
9.9s20266×body640valid
6.5s3393×body5120valid
3.3s9929×body320valid
2.0s9102×body160valid
513.0ms583×body10240exit
262.0ms578×body1280nan
232.0ms643×body640nan
163.0ms8256×pre80true
93.0ms335×body320nan
35.0ms188×body160nan
6.0ms72×body80overflowed

series1.8m (34.6%)

Calls

423 calls:

5.9s
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
4.8s
(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 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

prune52.0s (16.4%)

rewrite15.5s (4.9%)

Algorithm
116×rewrite-expression-head
Calls

423 calls:

1.9s
(* (/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
670.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
669.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
475.0ms
(/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
472.0ms
(/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
Rules
39649×add-exp-log
27648×prod-exp
17022×pow-exp
13285×div-exp
8295×pow-to-exp
4996×add-sqr-sqrt
4574×*-un-lft-identity
4523×times-frac
3645×add-cube-cbrt
2705×add-cbrt-cube
1616×1-exp
1613×rec-exp
1464×sqrt-prod
1233×unpow-prod-down
1197×pow1
1043×cbrt-unprod
1037×associate-*r*
881×prod-diff
770×associate-*l*
566×cbrt-undiv
508×add-log-exp
439×pow-unpow
423×log1p-expm1-u expm1-log1p-u
419×associate-/r*
396×pow-prod-down
378×distribute-lft-out--
377×associate-*r/
345×sqr-pow
338×associate-/l*
326×div-inv
325×distribute-rgt-neg-in
322×difference-of-squares
311×cbrt-prod unswap-sqr
294×distribute-lft-neg-in
224×distribute-rgt-in distribute-lft-in
214×cube-prod
207×sqrt-div
191×flip-- flip3--
161×distribute-lft-out
156×exp-prod
142×*-commutative
137×associate-/r/
115×cos-sum
95×frac-times
94×frac-2neg clear-num
82×associate-*l/
81×fma-neg
71×sub-neg
69×flip-+ flip3-+
66×sqrt-pow1
60×pow-pow
53×fma-def swap-sqr
47×pow1/2 pow1/3
43×rem-sqrt-square
42×associate--l+
37×cbrt-div
35×associate-/l/
34×neg-mul-1
33×unpow3 cube-mult frac-sub
30×fma-udef
28×unpow2
25×sum-log
24×div-sub
23×pow-prod-up log-prod
22×pow-sqr associate--r+
21×+-commutative tan-quot
20×exp-sum
18×hypot-udef diff-log
16×frac-add
14×neg-sub0
13×pow-sub pow-flip hypot-def
10×cube-div exp-diff
9×pow-plus inv-pow exp-neg pow2
8×un-div-inv distribute-rgt-neg-out
7×sqrt-pow2 pow-neg
6×rem-cube-cbrt
5×rem-exp-log difference-cubes cos-diff asin-acos
4×neg-log log-pow distribute-neg-frac log-rec mul-1-neg
3×sqrt-undiv associate-+l+ sqrt-unprod associate-+r- unsub-neg distribute-frac-neg associate--r-
2×associate--l- rem-square-sqrt
1×acos-asin mul0 exp-to-pow rem-log-exp rem-cbrt-cube

simplify12.2s (3.8%)

Algorithm
176×egg-herbie

regimes9.0s (2.8%)

Accuracy

Total 33.1b remaining (17.7%)

Threshold costs 3.6b (1.9%)

7.5b18.2%Toniolo and Linder, Equation (13)
5.5b77.1%Toniolo and Linder, Equation (7)
4.5b-0.7%Henrywood and Agarwal, Equation (12)
2.6b0%Toniolo and Linder, Equation (10+)
2.5b31.4%VandenBroeck and Keller, Equation (6)

localize2.2s (0.7%)

bsearch2.0s (0.6%)

end1.0ms (0.0%)