Details

simplify1.1hr

Calls

24561 calls:

Slowest
2.5s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k)))) (* (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k)))) (* (* t t) t))) (* (* (cos k) (cos k)) (cos k))))
2.3s
(* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (* (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k))) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))))
2.3s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t t) t))) (* (* (cos k) (cos k)) (cos k))))
2.0s
(* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (* (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k))) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))))

prune4.5m

sample4.3m

Algorithm
59×intervals
Results
1.0m251923×body80valid
47.3s25818×body1280valid
42.2s160617×body80nan
23.7s17439×body640valid
19.8s7930×body2560valid
19.5s8613×body10240exit
14.5s3396×body5120valid
7.3s8391×body320valid
4.2s8576×body160valid
1.0s632×body1280nan
562.0ms614×body640nan
465.0ms154×body160nan
367.0ms8256×pre80true
280.0ms332×body320nan

series1.3m

Calls

440 calls:

Slowest
2.6s
(expm1 (log1p (sqrt (* (- t (fma (* (/ 2 (cbrt Om)) (/ l (cbrt Om))) (/ l (cbrt Om)) (* (* (- U U*) (* (/ l Om) n)) (/ l Om)))) (* (* U n) 2)))))
2.0s
(sqrt (pow (* (* (- (fma (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2 t) (* (* (* (/ l Om) (/ l Om)) n) (- U U*))) n) (* U 2)) 1))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))

rewrite25.0s

Algorithm
115×rewrite-expression-head
Calls

440 calls:

Slowest
1.6s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.3s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.2s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.2s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
Rules
52010×times-frac
20222×add-sqr-sqrt
20026×*-un-lft-identity
18743×add-cube-cbrt
4615×add-exp-log
4020×add-cbrt-cube
3687×sqrt-prod
2668×div-inv
2053×cbrt-prod
1786×div-exp
1730×prod-diff
1630×cbrt-undiv
1399×associate-*l*
1392×prod-exp
1312×associate-/l*
1229×pow1
1204×cbrt-unprod
811×difference-of-squares
714×associate-*r*
600×associate-/r*
536×add-log-exp
473×unpow-prod-down
441×log1p-expm1-u
440×expm1-log1p-u insert-posit16
377×distribute-lft-out--
356×distribute-rgt-neg-in
353×pow-prod-down
346×distribute-lft-neg-in
290×associate-/r/
287×exp-prod
269×exp-sum
233×associate-*r/
216×distribute-lft-out unswap-sqr
178×associate-*l/
163×swap-sqr
150×frac-times
147×sqrt-div
146×pow-unpow sqr-pow
133×unpow-prod-up
131×flip-- flip3--
127×*-commutative
120×fma-neg
118×frac-2neg clear-num
93×pow-exp
92×sqrt-pow1 cos-sum
81×distribute-rgt-in distribute-lft-in
65×pow1/2
62×unpow2
60×rem-sqrt-square
57×pow-to-exp
55×associate-/l/
53×pow1/3
47×sub-neg
46×pow-prod-up
42×1-exp
40×diff-log
37×rec-exp
36×div-sub
35×fma-udef
34×neg-mul-1
32×cbrt-div
31×tan-quot
30×fma-def pow-sqr
29×pow-plus
23×associate--l+ pow-pow rem-exp-log
22×pow2 flip-+ associate--r+ flip3-+
21×exp-diff
19×frac-sub
15×log-pow
14×pow-sub
12×associate-+r-
11×neg-sub0
10×pow-flip frac-add
log-prod difference-of-sqr-1 distribute-frac-neg expm1-def
neg-log inv-pow exp-neg
hypot-udef
sum-log +-commutative associate--r-
pow3 asin-acos hypot-def acos-asin cos-diff
expm1-log1p expm1-udef un-div-inv sin-mult
associate--l- distribute-neg-frac rem-cbrt-cube rem-log-exp log1p-udef log-div
cos-mult mul0 cube-unmult log1p-expm1 sqrt-unprod sub-div exp-to-pow sqr-sin rem-square-sqrt e-exp-1

regimes16.6s

Accuracy

Total 38.3b remaining (25.8%)

Threshold costs 3.1b (2.1%)

11.7b10.8%Toniolo and Linder, Equation (13)
7.0b19.9%Henrywood and Agarwal, Equation (13)
5.2b78%Toniolo and Linder, Equation (7)
3.7b0%Maksimov and Kolovsky, Equation (3)
2.6b31.6%Henrywood and Agarwal, Equation (12)

localize6.0s

bsearch3.4s

end1.0ms