Details

series1.6m (36.1%)

Calls

436 calls:

4.9s
(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 l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
1.4s
(* (* (* 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*))))

sample1.4m (30.7%)

Algorithm
61×intervals
Results
16.3s29802×body1280valid
16.3s252281×body80valid
10.5s160918×body80nan
9.2s8820×body2560valid
7.3s19767×body640valid
5.1s3260×body5120valid
2.6s10066×body320valid
1.4s9200×body160valid
529.0ms850×body10240exit
164.0ms615×body1280nan
128.0ms8256×pre80true
126.0ms610×body640nan
57.0ms367×body320nan
23.0ms219×body160nan

prune52.4s (19.3%)

rewrite12.2s (4.5%)

Algorithm
116×rewrite-expression-head
Calls

436 calls:

661.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
659.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
607.0ms
(* (* (/ 1 (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3)))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v))))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
476.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
340.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
Rules
24542×add-exp-log
16644×prod-exp
7256×pow-exp
6045×div-exp
4052×add-sqr-sqrt
3819×*-un-lft-identity
3321×times-frac
3023×add-cube-cbrt
2737×add-cbrt-cube
2482×pow-to-exp
1956×sqrt-prod
1552×pow1
1074×cbrt-unprod
894×unpow-prod-down
767×associate-*r*
695×1-exp rec-exp
664×associate-*l*
570×prod-diff
539×cbrt-undiv
513×add-log-exp
437×expm1-log1p-u
436×log1p-expm1-u
415×pow-prod-down
398×cbrt-prod
353×associate-/l*
319×associate-/r*
302×pow-unpow associate-*r/
286×distribute-lft-out--
265×div-inv
247×unswap-sqr
237×sqr-pow
235×distribute-rgt-neg-in
216×difference-of-squares
199×sqrt-div
195×distribute-lft-neg-in
192×distribute-lft-out
179×distribute-rgt-in distribute-lft-in
162×pow-prod-up
158×flip3-- flip--
146×*-commutative
110×exp-prod
107×associate-/r/
101×frac-times
99×associate-*l/
98×pow-sqr
97×clear-num frac-2neg
90×sqrt-pow1
82×pow-plus
78×fma-def
76×flip-+ flip3-+
63×fma-neg sub-neg pow-pow
59×pow2
55×pow1/2
50×hypot-def
49×swap-sqr
47×cos-sum
46×log-pow
45×pow1/3
44×fma-udef
41×cbrt-div rem-sqrt-square unpow2
37×associate--l+
36×associate-/l/
31×log-prod
28×div-sub frac-sub tan-quot
22×associate--r+
21×sum-log neg-mul-1
19×diff-log +-commutative
16×pow-sub
15×neg-sub0
14×pow-neg
13×pow-flip exp-sum
6×rem-cube-cbrt e-exp-1 un-div-inv rem-log-exp
5×inv-pow distribute-rgt-neg-out
4×exp-diff frac-add acos-asin neg-log
3×unpow3 associate-+r- hypot-udef unsub-neg cube-mult cube-prod log-div
2×pow-div rem-exp-log associate-+l+ quot-tan associate--l- cos-diff expm1-log1p associate-+r+ distribute-frac-neg asin-acos associate--r- expm1-udef distribute-neg-frac
1×sqrt-pow2 log1p-udef sqrt-unprod pow3 exp-neg sin-sum log1p-expm1 rem-square-sqrt mul0

simplify10.9s (4.0%)

Algorithm
176×egg-herbie

regimes10.2s (3.7%)

Accuracy

Total 39.9b remaining (19.8%)

Threshold costs 3.6b (1.8%)

9.0b5.2%Toniolo and Linder, Equation (13)
6.1b-3.6%Henrywood and Agarwal, Equation (12)
5.7b54.8%Henrywood and Agarwal, Equation (3)
5.3b77.8%Toniolo and Linder, Equation (7)
3.4b0%Henrywood and Agarwal, Equation (13)

localize2.2s (0.8%)

bsearch2.0s (0.7%)

end1.0ms (0.0%)