Date:Tuesday, May 5th, 2020
Commit:9fe10098 on separate-biginterval
Hostname:warfa with Racket 7.5
Seed:2020126
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

prune1.8m (34.1%)

Filtered
30097 candidates to 17678 candidates (58.7%)

series1.6m (31.7%)

Calls

438 calls:

4.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

sample1.1m (21.7%)

Algorithm
56×intervals
Results
16.4s221500×body80valid
11.7s140072×body80nan
11.4s22459×body1280valid
5.1s6700×body2560valid
5.0s14434×body640valid
1.7s7145×body320valid
1.4s2357×body5120valid
1.3s7567×body160valid
669.0ms1084×body1280nan
390.0ms879×body640nan
387.0ms2863×body80overflowed
341.0ms563×body5120exit
137.0ms8256×pre80true
131.0ms433×body320nan
40.0ms219×body160nan

simplify16.9s (5.4%)

Algorithm
171×egg-herbie

regimes10.9s (3.5%)

Accuracy

Total 15.5b remaining (11.8%)

Threshold costs 5.0b (3.9%)

4.9b22.1%Henrywood and Agarwal, Equation (12)
2.1b0%Henrywood and Agarwal, Equation (13)
1.3b63%Henrywood and Agarwal, Equation (9a)
1.1b0%Falkner and Boettcher, Appendix B, 1
1.1b0%Henrywood and Agarwal, Equation (3)

rewrite8.7s (2.8%)

Algorithm
116×rewrite-expression-head
Calls

438 calls:

1.0s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
346.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
87.0ms
(/ (/ (/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))) (cbrt (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))) (cbrt (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
82.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
79.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
Rules
37487×times-frac
36564×add-exp-log
24267×prod-exp
18358×add-sqr-sqrt
17051×*-un-lft-identity
16278×add-cube-cbrt
14438×pow-exp
13753×div-exp
9051×unpow-prod-down
7101×pow-to-exp
6826×cbrt-prod
4738×associate-*r*
2378×add-cbrt-cube
2297×1-exp
2126×sqrt-prod
1888×sqr-pow
1699×rec-exp
1237×pow1
972×cbrt-unprod
970×difference-of-squares
909×associate-/l*
799×associate-*l*
731×unpow2
589×div-inv
540×add-log-exp
520×associate-*r/
433×unswap-sqr
397×pow-prod-down
389×cbrt-undiv
378×associate-/r*
341×sqrt-div
309×pow-unpow
293×distribute-lft-out
288×associate-/r/
256×flip3-- flip--
244×exp-prod
222×frac-times
219×associate-*l/
176×flip-+ flip3-+
151×distribute-lft-out--
147×cbrt-div *-commutative
140×sqrt-pow1
119×distribute-rgt-neg-in
107×cube-prod
90×pow1/2
87×frac-2neg clear-num
82×distribute-rgt-in distribute-lft-in
80×distribute-lft-neg-in
70×tan-quot
66×swap-sqr
64×sub-neg
62×pow1/3
59×rem-sqrt-square
48×pow-pow
43×associate-/l/
39×frac-sub
38×log-pow
37×sum-log
35×div-sub
33×exp-diff
27×log-prod
25×+-commutative
24×frac-add associate--l+ log-div
20×pow-prod-up
15×associate-+r+ diff-log
14×pow-sqr
13×neg-sub0 exp-sum
11×rem-cube-cbrt
10×pow-sub unpow3 cube-mult
neg-mul-1
rem-exp-log pow-flip
cube-div associate-+r-
cos-sum unsub-neg pow-neg
inv-pow pow-plus pow2
distribute-neg-in acos-asin
difference-cubes associate-+l+ cos-diff asin-acos rem-log-exp
un-div-inv sqrt-unprod exp-neg rem-square-sqrt distribute-frac-neg rem-cbrt-cube
sqrt-undiv distribute-lft-neg-out neg-log mul0

localize2.3s (0.7%)

bsearch47.0ms (0.0%)

end0.0ms (0.0%)

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