Details

simplify7.2m (40.7%)

sample3.2m (18.4%)

Algorithm
61×intervals
Results
43.4s253519×body80valid
39.2s29653×body1280valid
29.0s160386×body80nan
20.1s20115×body640valid
16.8s8614×body2560valid
9.9s3411×body5120valid
8.5s10106×body320valid
3.3s9107×body160valid
1.1s631×body10240exit
759.0ms625×body640nan
352.0ms595×body1280nan
204.0ms8256×pre80true
108.0ms343×body320nan
68.0ms181×body160nan

prune2.9m (16.7%)

series2.9m (16.7%)

Calls

450 calls:

10.0s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))
9.5s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))
8.9s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))
8.4s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))
6.4s
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))

rewrite40.9s (3.9%)

Algorithm
117×rewrite-expression-head
Calls

450 calls:

4.3s
(* (* (* (* (/ (/ (pow (cbrt t) 3.0) (cbrt l)) (cbrt l)) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.0s
(* (* (* (/ (/ (pow (cbrt t) 3.0) (cbrt l)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.0s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.9s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.9s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
Rules
36703×add-exp-log
22846×prod-exp
15480×times-frac
12895×div-exp
12633×pow-exp
8689×add-sqr-sqrt
8151×*-un-lft-identity
7646×add-cube-cbrt
4556×unpow-prod-down
4227×pow-to-exp
2897×add-cbrt-cube
2432×sqrt-prod
2297×1-exp
2292×rec-exp
2186×pow1
1370×associate-*r*
1236×cbrt-unprod
1021×div-inv
966×associate-*l*
803×sqr-pow
736×associate-*r/
659×pow-prod-down
647×cbrt-undiv
538×associate-/r/
516×tan-quot
504×add-log-exp
502×prod-diff
452×expm1-log1p-u log1p-expm1-u
421×associate-/l* associate-/r*
415×associate-*l/
405×cbrt-prod
367×frac-times
348×pow-unpow
331×pow-prod-up
300×unswap-sqr
224×sqrt-div
176×sqrt-pow1
167×distribute-lft-out
163×difference-of-squares
161×*-commutative
155×pow-sqr
138×pow-plus
128×flip3-- flip--
127×exp-sum
123×distribute-rgt-in distribute-lft-in
121×distribute-lft-out--
97×pow1/2
89×flip-+ flip3-+
86×frac-2neg pow2 clear-num
84×pow1/3
67×rem-sqrt-square
65×swap-sqr
60×exp-prod
53×fma-neg
51×associate-/l/
49×fma-def
40×pow-pow
36×sub-neg
32×frac-add
25×cos-sum
24×associate--l+
23×div-sub
20×fma-udef
19×cube-unmult
16×pow-flip
15×diff-log
13×distribute-lft-neg-in distribute-rgt-neg-in pow-sub
12×pow3 hypot-def
11×sum-log +-commutative
10×pow-div associate-+l-
rem-exp-log
cbrt-div
neg-sub0 pow-neg inv-pow
expm1-log1p difference-cubes un-div-inv
expm1-udef exp-diff log-prod acos-asin
frac-sub hypot-udef unpow2
sin-sum associate-+r+ log1p-def log1p-expm1 sqrt-unprod asin-acos rem-square-sqrt log1p-udef log-div
sqrt-undiv neg-mul-1 sub-div rem-log-exp log-pow cos-diff rem-cbrt-cube distribute-rgt-out

regimes25.9s (2.5%)

Accuracy

Total 56.6b remaining (29.3%)

Threshold costs 5.1b (2.6%)

8.5b43.6%Henrywood and Agarwal, Equation (3)
7.9b-1.7%Henrywood and Agarwal, Equation (13)
7.9b0%Henrywood and Agarwal, Equation (12)
7.3b47.1%Toniolo and Linder, Equation (10+)
6.7b34.9%Toniolo and Linder, Equation (13)

localize8.2s (0.8%)

bsearch4.2s (0.4%)

end1.0ms (0.0%)