Details

simplify51.3m

Calls

18522 calls:

Slowest
2.6s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(/ (* (* (/ 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 t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
2.2s
(/ (* (* (* 2 2) 2) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* 4 4) 4) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))) (* (/ (* (* 4 4) 4) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))) (* (* (/ 4 (- 1 (* v v))) (/ 4 (- 1 (* v v)))) (/ 4 (- 1 (* v v)))))))
2.1s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
2.0s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))

prune4.7m

sample3.1m

Algorithm
53×intervals
Results
52.0s233307×body80valid
36.0s157522×body80nan
25.8s15945×body1280valid
18.9s8541×body10240exit
14.0s12569×body640valid
7.3s4965×body2560valid
5.4s6153×body320valid
5.2s2304×body5120valid
3.9s7746×body160valid
808.0ms649×body1280nan
595.0ms634×body640nan
267.0ms325×body320nan
94.0ms196×body160nan

series1.2m

Calls

390 calls:

Slowest
1.9s
(* (* (* (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))))
1.8s
(* (* (* (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)))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(cbrt (/ (* 2 (sqrt 2)) (* (/ 4 (- 1 (* v v))) (* (/ 4 (- 1 (* v v))) (/ 4 (- 1 (* v v)))))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite21.5s

Algorithm
103×rewrite-expression-head
Calls

390 calls:

Slowest
2.0s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (/ d D) (* (/ d D) (/ c0 h))) w))
1.9s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
899.0ms
(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
675.0ms
(* (* (* (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)))
643.0ms
(* (* (* (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))))
Rules
44272×times-frac
21273×add-sqr-sqrt
20254×*-un-lft-identity
19537×add-cube-cbrt
7562×sqrt-prod
5428×add-exp-log
3654×add-cbrt-cube
3279×cbrt-prod
2008×prod-exp
1958×div-exp
1802×div-inv
1508×pow1
1449×associate-*r*
1339×cbrt-undiv
1213×prod-diff
1190×associate-/l*
1155×cbrt-unprod
963×associate-*l*
921×associate-/r*
790×associate-/r/
691×difference-of-squares
678×unpow-prod-down
451×associate-*l/
444×pow-prod-down
441×add-log-exp
391×expm1-log1p-u
390×insert-posit16 log1p-expm1-u
381×unswap-sqr
372×associate-*r/
317×pow-exp
293×frac-times
254×sqr-pow
167×distribute-rgt-in distribute-lft-in
161×pow-unpow
159×pow-prod-up
154×flip3-- flip--
143×pow-to-exp
131×*-commutative
121×exp-prod
119×1-exp rec-exp
115×sqrt-div
112×swap-sqr
106×sqrt-pow1 frac-2neg clear-num
97×distribute-lft-out
95×pow-sqr
87×pow1/3
85×pow-plus distribute-lft-out--
60×fma-neg
59×pow1/2
58×pow2
55×rem-sqrt-square
52×fma-def
49×sub-neg
48×exp-sum
45×frac-sub
42×distribute-lft-neg-in cbrt-div distribute-rgt-neg-in
35×associate-/l/ fma-udef tan-quot
32×flip-+ flip3-+
29×associate--l+
25×cos-sum
23×pow-flip pow-pow
18×sum-log div-sub
13×pow-sub
12×+-commutative inv-pow
pow3 sub-div frac-add diff-log
unpow2
distribute-rgt-out-- neg-mul-1
rem-cbrt-cube acos-asin
difference-of-sqr-1
associate-+l+ exp-diff hypot-udef cos-diff un-div-inv
neg-sub0 associate-+r- associate-+r+ distribute-frac-neg exp-neg rem-exp-log
expm1-log1p expm1-udef remove-posit16 mul0 cube-unmult log1p-expm1 sqrt-unprod sqr-sin rem-square-sqrt sin-mult log1p-udef

regimes16.1s

Accuracy

Total 45.7b remaining (33.3%)

11.6b7.9%Toniolo and Linder, Equation (13)
7.9b45.5%Henrywood and Agarwal, Equation (3)
6.8b18.8%Henrywood and Agarwal, Equation (13)
5.7b0%Henrywood and Agarwal, Equation (12)
5.0b78.1%Toniolo and Linder, Equation (7)

localize5.5s

bsearch3.0s

end1.0ms