Details

prune12.7m (46.5%)

simplify7.6m (27.8%)

sample4.4m (16.0%)

Algorithm
61×intervals
Results
1.1m257647×body80valid
49.5s28008×body1280valid
41.8s160351×body80nan
24.2s19304×body640valid
19.7s8707×body10240exit
14.4s7880×body2560valid
11.4s3435×body5120valid
9.7s9538×body320valid
5.0s8917×body160valid
960.0ms622×body640nan
733.0ms8256×pre80true
664.0ms563×body1280nan
280.0ms362×body320nan
73.0ms191×body160nan

series1.4m (5.3%)

Calls

460 calls:

2.3s
(/ 1 (* (cbrt (sqrt (* 2 (- 1 (* (* (* v v) 9) (* v v)))))) (cbrt (sqrt (* 2 (- 1 (* (* (* v v) 9) (* v v))))))))
2.3s
(sqrt (* U (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))))
2.1s
(sqrt (* U (* (* (cbrt (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))) (cbrt (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))) (cbrt (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))))))
2.0s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
2.0s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

rewrite40.1s (2.4%)

Algorithm
118×rewrite-expression-head
Calls

460 calls:

8.6s
(sqrt (- 1 (/ (/ M (/ d D)) (/ (/ l h) (/ (/ M (/ d D)) 4)))))
1.9s
(* (/ (cbrt 4/3) (- (* PI (* PI PI)) (* (* (* v (* PI v)) (* v (* PI v))) (* v (* PI v))))) (+ (* PI PI) (+ (* (* PI (* v v)) (* PI (* v v))) (* PI (* PI (* v v))))))
1.4s
(* (* (cbrt 4/3) (cbrt 4/3)) (* (/ (cbrt 4/3) (- (* PI (* PI PI)) (* (* (* v (* PI v)) (* v (* PI v))) (* v (* PI v))))) (+ (* PI PI) (+ (* (* PI (* v v)) (* PI (* v v))) (* PI (* PI (* v v)))))))
954.0ms
(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (* (* (cbrt (/ U (* (* (cos (/ K 2)) J) 2))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2)))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2))))) 1)) (cos (/ K 2))))
854.0ms
(- (* (* 1 1) (* 1 1)) (* (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))
Rules
99028×times-frac
42135×add-sqr-sqrt
41148×*-un-lft-identity
40492×add-cube-cbrt
17413×cbrt-prod
7483×add-exp-log
5960×add-cbrt-cube
4103×div-inv
3128×div-exp
2735×sqrt-prod
2495×prod-exp
2420×cbrt-undiv
2099×associate-*l*
1967×cbrt-unprod
1965×pow1
1841×associate-/r/
1825×associate-/l*
1334×tan-quot
1217×associate-*r*
990×sqrt-div
926×frac-times
902×associate-/r*
834×associate-*r/
773×flip-+ flip3-+
579×pow-prod-down
572×add-log-exp
524×associate-*l/
460×insert-posit16
365×unswap-sqr
320×pow-prod-up
265×sqrt-pow1
227×pow1/2
213×distribute-lft-out
206×flip3-- flip--
197×difference-of-squares
190×pow-plus
187×cbrt-div distribute-rgt-in distribute-lft-in
171×*-commutative
155×unpow-prod-down
153×1-exp
144×frac-add
140×sub-neg
128×unpow-prod-up swap-sqr
115×pow-exp
113×frac-2neg clear-num
107×sqr-pow
103×pow-sqr
91×distribute-lft-out--
90×rec-exp
84×associate-/l/
82×rem-sqrt-square
80×pow-unpow
79×pow-to-exp
65×cube-unmult
46×pow1/3
41×pow2
38×sin-mult
35×sum-log
28×+-commutative
26×exp-prod
24×pow-pow
23×pow3
21×diff-log
19×difference-cubes
17×pow-flip
16×un-div-inv pow-sub
15×associate--r+
14×div-sub
12×rem-exp-log
11×log-pow
9×exp-sum inv-pow
7×log-prod
6×sqr-sin associate-+l-
4×exp-diff associate-+r- frac-sub associate-+r+ difference-of-sqr-1 unpow2 cos-sum
3×asin-acos acos-asin
2×distribute-lft1-in remove-posit16 associate--l+ rem-log-exp exp-to-pow cos-diff distribute-rgt-out
1×associate-+l+ sqrt-undiv sqrt-unprod sub-div sqrt-pow2 rem-square-sqrt

regimes21.9s (1.3%)

Accuracy

Total 33.5b remaining (17.1%)

Threshold costs 4.8b (2.4%)

8.3b27.6%Toniolo and Linder, Equation (13)
5.7b-1.1%Henrywood and Agarwal, Equation (13)
5.2b78.2%Toniolo and Linder, Equation (7)
2.2b32.6%Henrywood and Agarwal, Equation (12)
1.9b71.9%Toniolo and Linder, Equation (10+)

localize6.4s (0.4%)

bsearch2.2s (0.1%)

end1.0ms (0.0%)