Details

simplify40.0m

Calls

15703 calls:

Slowest
3.3s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
3.0s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
2.9s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.8s
(/ (* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
2.8s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))

prune4.4m

sample3.4m

Algorithm
54×intervals
Results
55.9s238215×body80valid
41.8s159140×body80nan
28.7s17557×body1280valid
20.1s8541×body10240exit
18.0s13924×body640valid
6.5s2304×body5120valid
6.4s4965×body2560valid
5.8s6834×body320valid
4.4s8095×body160valid
750.0ms649×body1280nan
543.0ms634×body640nan
229.0ms325×body320nan
65.0ms196×body160nan

series1.1m

Calls

404 calls:

Slowest
2.0s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
1.8s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.8s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.7s
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite23.5s

Algorithm
103×rewrite-expression-head
Calls

404 calls:

Slowest
732.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
720.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
701.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (cos (/ K 2))) (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) J)))
609.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) J)))
559.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
Rules
29950×times-frac
14567×add-sqr-sqrt
13597×*-un-lft-identity
13011×add-cube-cbrt
7475×add-exp-log
5845×add-cbrt-cube
5153×sqrt-prod
3142×prod-exp
3132×associate-*r*
2505×div-exp
2288×cbrt-unprod
2034×cbrt-undiv
1634×pow1
1360×associate-/r/
1331×div-inv
1106×associate-*l*
951×associate-/l*
685×associate-/r*
567×pow-prod-down
499×associate-*r/
486×flip-+ flip3-+
485×unpow-prod-down
476×add-log-exp
418×unswap-sqr
404×insert-posit16
384×associate-*l/
363×frac-times
349×sqrt-div
309×pow-exp
296×difference-of-squares
178×sqr-pow
164×*-commutative
161×pow-unpow
160×flip3-- flip--
147×swap-sqr
135×pow-to-exp
126×cbrt-prod
117×exp-prod
116×tan-quot
110×distribute-lft-out--
103×distribute-lft-out
96×frac-2neg clear-num
94×1-exp
93×frac-add
92×pow-prod-up
91×rec-exp
89×sin-mult
86×sqrt-pow1
76×rem-sqrt-square
71×pow1/2
64×distribute-rgt-in distribute-lft-in
62×sub-neg
60×pow-plus
55×associate-/l/ pow-sqr
43×pow2
42×distribute-lft-neg-in distribute-rgt-neg-in
36×unpow2
29×distribute-rgt-out--
26×sum-log
25×pow-pow div-sub
23×pow1/3 cbrt-div
18×pow-flip +-commutative
13×associate-+l+ pow-sub
12×frac-sub inv-pow
11×sqr-sin diff-log
pow3
associate-+r+ exp-sum
remove-posit16 associate-+r- neg-mul-1 cos-sum associate--l+
acos-asin
exp-diff difference-of-sqr-1
log-prod log-pow rem-cbrt-cube
neg-sub0 sqrt-undiv exp-neg distribute-frac-neg sub-div rem-exp-log
sqrt-pow2 un-div-inv exp-to-pow cos-diff rem-log-exp

regimes17.1s

Accuracy

Total 50.0b remaining (31.6%)

9.8b1.7%Henrywood and Agarwal, Equation (13)
8.1b3.9%Maksimov and Kolovsky, Equation (3)
7.8b8.8%Toniolo and Linder, Equation (13)
7.0b31.3%Henrywood and Agarwal, Equation (3)
5.4b0%Henrywood and Agarwal, Equation (12)

localize5.5s

bsearch5.2s

end28.0ms