Details

prune6.1m (33.2%)

simplify5.0m (27.1%)

sample4.8m (25.8%)

Algorithm
61×intervals
Results
1.1m253450×body80valid
1.0m29676×body1280valid
44.5s160289×body80nan
30.9s19749×body640valid
25.0s8836×body2560valid
17.0s3362×body5120valid
11.4s10000×body320valid
6.1s8882×body160valid
2.4s648×body10240exit
1.2s581×body1280nan
650.0ms582×body640nan
336.0ms366×body320nan
301.0ms8256×pre80true
108.0ms182×body160nan

series1.4m (7.8%)

Calls

423 calls:

2.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om))))
1.7s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.7s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (/ (* h (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d))) (* 2 l))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.7s
(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h)))) (/ (/ (* M D) d) 2))))

rewrite36.5s (3.3%)

Algorithm
114×rewrite-expression-head
Calls

423 calls:

4.3s
(+ (sqrt (- (* (* (* (cbrt (/ c0 h)) (cbrt (/ c0 h))) (* (cbrt (/ c0 h)) (/ (* (/ d D) (/ d D)) w))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
3.3s
(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt (* (cbrt t) (cbrt t))) (* (cbrt (/ l t)) (cbrt (/ l t)))) (* (/ (cbrt (cbrt t)) (cbrt (/ l t))) (sin k)))) (tan k)) (fma (/ k t) (/ k t) 2))
3.2s
(* (/ 2 (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))) (/ l t))
2.2s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.2s
(sqrt (- (* (* (* (cbrt (/ c0 h)) (cbrt (/ c0 h))) (* (cbrt (/ c0 h)) (/ (* (/ d D) (/ d D)) w))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
Rules
79373×times-frac
45196×add-sqr-sqrt
44175×*-un-lft-identity
42834×add-cube-cbrt
25830×unpow-prod-up
25499×prod-diff
12973×sqrt-prod
6902×add-exp-log
5039×add-cbrt-cube
3736×div-inv
2761×div-exp
2492×prod-exp
2122×associate-*l*
1998×associate-*r*
1986×cbrt-undiv
1779×cbrt-unprod
1450×unpow-prod-down
1404×associate-/r*
1304×pow1
1036×associate-/l*
1007×difference-of-squares
859×cbrt-prod
707×sqr-pow
688×sub-neg
463×add-log-exp
460×pow-prod-down
424×expm1-log1p-u
423×log1p-expm1-u insert-posit16
418×associate-*r/
409×unswap-sqr
347×associate-*l/
306×sqrt-div
301×frac-times
295×associate-/r/
263×distribute-lft-out--
229×pow-exp
198×distribute-rgt-in distribute-lft-in
197×1-exp
188×flip3-- flip--
179×cos-sum
137×distribute-lft-out
132×*-commutative
122×frac-2neg clear-num
111×fma-neg
109×tan-quot
108×pow-to-exp
102×pow-unpow
96×rec-exp
80×sqrt-pow1
68×frac-sub
67×pow1/2
64×flip-+ flip3-+ pow-sub
62×exp-prod associate-/l/
58×exp-sum
57×swap-sqr
56×rem-sqrt-square
47×pow1/3
46×associate--l+
44×fma-def
33×cbrt-div
29×unpow2
28×fma-udef
25×pow-prod-up
24×pow-flip
20×pow-plus pow-pow
17×div-sub
16×frac-add
15×log-prod pow-sqr
13×inv-pow
12×pow2 log-pow
10×sum-log +-commutative
9×diff-log
7×rem-log-exp
6×pow-div un-div-inv
5×exp-diff hypot-udef
4×associate-+r+ acos-asin
3×sqr-sin rem-exp-log sin-mult e-exp-1
2×expm1-udef remove-posit16 associate-+r- pow3 associate--r+ asin-acos associate-+l- hypot-def log-div
1×expm1-log1p sqrt-undiv log1p-expm1 sqrt-unprod sub-div rem-square-sqrt cos-diff log1p-udef

regimes20.9s (1.9%)

Accuracy

Total 49.8b remaining (28%)

Threshold costs 4.0b (2.3%)

9.2b19.4%Toniolo and Linder, Equation (13)
5.7b53.2%Henrywood and Agarwal, Equation (3)
5.7b26.7%Henrywood and Agarwal, Equation (13)
5.4b0%Henrywood and Agarwal, Equation (12)
5.3b77.3%Toniolo and Linder, Equation (7)

localize6.6s (0.6%)

bsearch2.8s (0.3%)

end1.0ms (0.0%)