Details

series1.9m (36.2%)

Calls

427 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0s
(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*)))))
4.9s
(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 (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (27.1%)

Algorithm
61×intervals
Results
15.5s29350×body1280valid
15.3s253224×body80valid
9.4s158091×body80nan
8.7s8786×body2560valid
7.3s20641×body640valid
5.1s3346×body5120valid
2.4s9945×body320valid
1.3s9119×body160valid
400.0ms677×body10240exit
152.0ms617×body1280nan
118.0ms615×body640nan
107.0ms8256×pre80true
50.0ms340×body320nan
18.0ms195×body160nan

prune53.8s (17.4%)

rewrite33.7s (10.9%)

Algorithm
116×rewrite-expression-head
Calls

427 calls:

2.7s
(* (* (* (* (* (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))
2.6s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar))
878.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
859.0ms
(/ (sqrt NdChar) (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar)))
Rules
42481×add-exp-log
30564×prod-exp
18625×pow-exp
13531×div-exp
8803×pow-to-exp
4086×add-sqr-sqrt
3660×*-un-lft-identity
3478×times-frac
3003×add-cube-cbrt
2449×add-cbrt-cube
2033×1-exp
1987×rec-exp
1651×sqrt-prod
1221×pow1
1069×cbrt-unprod
968×cbrt-prod
908×associate-*r*
877×associate-*r/
855×unpow-prod-down
712×associate-*l*
515×sqrt-div
501×add-log-exp
492×frac-times
427×log1p-expm1-u expm1-log1p-u
422×pow-prod-down
399×cbrt-undiv
387×associate-*l/
381×flip-- flip3--
356×pow-unpow
353×cbrt-div
348×associate-/l*
315×associate-/r*
308×prod-diff
278×associate-/r/
277×unswap-sqr
250×sqr-pow
245×difference-of-squares
242×div-inv
204×distribute-lft-out
176×distribute-lft-out--
163×distribute-rgt-in distribute-lft-in
151×*-commutative
146×flip-+ flip3-+
135×distribute-rgt-neg-in
108×distribute-lft-neg-in
104×pow1/3
98×swap-sqr
90×clear-num frac-2neg
73×tan-quot
65×fma-def
63×sqrt-pow1
54×sub-neg
53×pow-pow
48×pow1/2
45×rem-sqrt-square
42×associate--l+
39×associate-/l/
36×sum-log
34×cube-div
33×frac-sub
31×unpow2
27×fma-udef
24×div-sub
23×cos-sum
21×+-commutative
20×pow-prod-up pow-sub
19×pow-neg
18×pow-sqr
17×neg-sub0
16×exp-diff log-div
13×un-div-inv hypot-def
12×frac-add neg-mul-1
11×fma-neg
10×exp-prod
9×log-prod
8×exp-neg pow2 log-pow pow-plus cube-prod distribute-rgt-neg-out
6×exp-sum
5×diff-log
4×rem-cube-cbrt mul-1-neg associate-+l+ unpow3 cube-mult distribute-neg-frac log-rec
3×inv-pow unsub-neg pow-flip associate-+r- neg-log
2×unpow1/3 associate-+r+ hypot-udef distribute-frac-neg acos-asin
1×rem-exp-log sqrt-undiv sqrt-unprod cos-diff expm1-log1p expm1-udef rem-square-sqrt mul0 rem-log-exp rem-cbrt-cube

simplify12.2s (3.9%)

Algorithm
176×egg-herbie

regimes9.4s (3.0%)

Accuracy

Total 40.4b remaining (21.4%)

Threshold costs 3.9b (2%)

7.9b22.9%Toniolo and Linder, Equation (13)
6.0b8.5%Toniolo and Linder, Equation (10+)
5.7b0%Henrywood and Agarwal, Equation (12)
5.0b78.6%Toniolo and Linder, Equation (7)
3.3b38.1%Toniolo and Linder, Equation (10-)

bsearch2.4s (0.8%)

localize2.2s (0.7%)

end1.0ms (0.0%)