Details

simplify6.7m (35.9%)

series4.2m (22.8%)

Calls

440 calls:

39.2s
(/ (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))))
38.9s
(/ (- (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))))
8.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.7s
(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*)))))

sample3.3m (18.0%)

Algorithm
61×intervals
Results
41.9s253560×body80valid
38.2s29210×body1280valid
27.7s160234×body80nan
21.6s20401×body640valid
18.6s8958×body2560valid
11.8s3343×body5120valid
6.9s10108×body320valid
4.1s8732×body160valid
762.0ms658×body10240exit
397.0ms586×body1280nan
344.0ms662×body640nan
153.0ms8256×pre80true
107.0ms381×body320nan
30.0ms155×body160nan

prune2.6m (14.0%)

rewrite1.3m (7.1%)

Algorithm
118×rewrite-expression-head
Calls

440 calls:

29.4s
(* (/ NaChar (+ (pow (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 3) (pow 1.0 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))))))
3.3s
(- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))
2.7s
(* (* (* (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))))
2.5s
(/ (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0) NaChar)
1.7s
(* (* (* (/ (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))
Rules
94110×add-exp-log
71661×prod-exp
44547×pow-exp
29082×div-exp
17514×pow-to-exp
9482×times-frac
6386×*-un-lft-identity
6330×1-exp rec-exp
6259×add-sqr-sqrt
5408×add-cube-cbrt
2431×add-cbrt-cube
2058×unpow-prod-down
1593×cbrt-prod
1327×pow1
1149×associate-*l*
964×cbrt-unprod
766×associate-*r*
754×sqrt-prod
580×div-inv
579×sqr-pow associate-/r*
536×prod-diff
517×add-log-exp
461×pow-unpow
454×associate-/l*
448×cbrt-undiv
441×expm1-log1p-u
440×log1p-expm1-u
439×associate-*r/
427×pow-prod-down
341×distribute-lft-out
273×associate-*l/
254×distribute-lft-out--
244×unswap-sqr
210×difference-of-squares
201×div-sub
196×distribute-rgt-in distribute-lft-in
190×frac-times
188×associate-/r/
168×exp-prod
163×exp-diff
152×flip3-- flip--
150×distribute-rgt-neg-in
145×*-commutative
139×sqrt-div
123×cube-prod
115×cos-sum
104×flip-+ flip3-+
101×fma-def
100×distribute-lft-neg-in
97×pow-pow
96×tan-quot
92×clear-num frac-2neg
81×frac-sub
69×sub-neg
65×sqrt-pow1
64×neg-sub0
61×pow1/3
56×associate-+r-
54×unsub-neg
51×pow-prod-up log-prod
46×associate-/l/
45×associate--l+
42×pow1/2
41×unpow3 cube-mult
40×unpow2
38×rem-sqrt-square
36×swap-sqr
35×log-pow
33×pow-sqr
31×fma-neg associate-+r+
29×pow-plus
28×pow-sub
26×fma-udef
25×sum-log
22×associate--r+
21×pow2
20×+-commutative
18×sub-div
16×neg-mul-1
15×cbrt-div
13×diff-log
12×hypot-def
10×difference-cubes
9×cube-div frac-add distribute-neg-frac
8×rem-cube-cbrt
7×inv-pow pow-flip
6×acos-asin sum-cubes rem-log-exp
5×pow-neg cos-diff log-div
4×rem-exp-log exp-sum
3×un-div-inv neg-log distribute-frac-neg associate-+l-
2×hypot-udef exp-to-pow
1×associate-+l+ log1p-udef associate--l- log1p-expm1 expm1-log1p distribute-rgt-out asin-acos mul0 distribute-rgt-out-- expm1-udef rem-cbrt-cube

regimes16.5s (1.5%)

Accuracy

Total 43.6b remaining (21.9%)

Threshold costs 3.9b (2%)

8.0b15%Toniolo and Linder, Equation (13)
6.4b73.2%Toniolo and Linder, Equation (7)
5.4b0%Henrywood and Agarwal, Equation (12)
5.4b40.2%Toniolo and Linder, Equation (10-)
3.9b0%Given's Rotation SVD example

bsearch4.7s (0.4%)

localize4.1s (0.4%)

end1.0ms (0.0%)