Details

simplify7.0m (38.2%)

series3.8m (20.7%)

Calls

442 calls:

39.3s
(/ (cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
38.2s
(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
3.6s
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F)
3.2s
(pow (exp (sqrt (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))) (sqrt (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
2.9s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U)))

sample3.2m (17.7%)

Algorithm
61×intervals
Results
45.0s253560×body80valid
40.3s29210×body1280valid
30.1s160234×body80nan
18.8s20401×body640valid
17.3s8958×body2560valid
10.9s3343×body5120valid
6.9s10108×body320valid
3.1s8732×body160valid
930.0ms658×body10240exit
362.0ms586×body1280nan
248.0ms662×body640nan
209.0ms8256×pre80true
109.0ms381×body320nan
29.0ms155×body160nan

prune2.6m (14.4%)

rewrite1.2m (6.7%)

Algorithm
118×rewrite-expression-head
Calls

442 calls:

29.6s
(* (/ NaChar (+ (pow 1.0 3) (pow (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 3))) (+ (* 1.0 1.0) (- (* (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))) (* 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))))))
2.9s
(- (* (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))) (* 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))))
2.3s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (* (pow (/ 1 (cbrt (* (cbrt l) (cbrt l)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt l))) (/ 1.0 2.0))))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.6s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(* (* (* (/ (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))
Rules
93408×add-exp-log
71106×prod-exp
44337×pow-exp
28972×div-exp
17428×pow-to-exp
10297×times-frac
6689×add-sqr-sqrt
6531×*-un-lft-identity
6336×1-exp rec-exp
5836×add-cube-cbrt
2616×unpow-prod-down
2429×add-cbrt-cube
1986×cbrt-prod
1292×pow1
1117×associate-*l*
964×cbrt-unprod
769×associate-*r*
720×sqrt-prod
637×div-inv
566×sqr-pow
565×associate-/r*
554×prod-diff
493×add-log-exp
458×pow-unpow
445×cbrt-undiv
443×expm1-log1p-u
442×log1p-expm1-u
436×pow-prod-down
389×associate-/l*
323×associate-*r/
313×distribute-lft-neg-in distribute-rgt-neg-in
279×associate-*l/
241×exp-prod
224×unswap-sqr
219×difference-of-squares
211×distribute-lft-out
200×distribute-lft-out--
197×frac-times
160×fma-def
146×*-commutative
145×associate-/r/
129×distribute-rgt-in distribute-lft-in
124×log-pow
115×flip3-- cos-sum flip--
112×sqrt-div
111×cube-prod
104×tan-quot
101×neg-mul-1
100×cbrt-div
98×flip-+ flip3-+ pow-pow
90×clear-num frac-2neg
82×sqrt-pow1
74×pow1/3
53×div-sub
51×pow1/2 fma-neg
50×sub-neg
48×rem-sqrt-square
41×unpow3 cube-mult
39×swap-sqr
37×associate-/l/
28×pow-sub
26×fma-udef unpow2
23×pow-prod-up
22×associate-+r+
17×pow-sqr pow-plus
15×exp-diff log-prod
14×sum-log
12×pow2 +-commutative hypot-def
11×diff-log
10×difference-cubes
9×cube-div
8×rem-cube-cbrt inv-pow pow-flip
7×associate-+l+
6×acos-asin
5×cos-diff pow-neg frac-sub associate-+r-
4×un-div-inv neg-sub0
3×rem-exp-log sum-cubes rem-log-exp
2×sub-div frac-add hypot-udef asin-acos associate--l+ exp-to-pow
1×log1p-udef log1p-expm1 expm1-log1p mul0 distribute-rgt-out-- rem-cbrt-cube expm1-udef

regimes16.2s (1.5%)

Accuracy

Total 40.8b remaining (21%)

Threshold costs 4.8b (2.5%)

9.7b12.8%Toniolo and Linder, Equation (13)
6.4b73.3%Toniolo and Linder, Equation (7)
5.4b0%Henrywood and Agarwal, Equation (12)
5.4b40.2%Toniolo and Linder, Equation (10-)
3.7b53.2%Toniolo and Linder, Equation (10+)

bsearch4.9s (0.4%)

localize4.4s (0.4%)

end0.0ms (0.0%)