Date:Tuesday, July 14th, 2020
Commit:0946c439 on ival-find-range
Hostname:warfa with Racket 7.5
Seed:2020196
Parameters:256 points for 4 iterations
Flags:
setup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

prune2.6min (44.5%)

Filtered
51358 candidates to 16258 candidates (68.3%)

sample1.3min (21.7%)

Algorithm
61×intervals
Results
17.4s27666×body1280valid
15.0s175241×body80valid
8.2s18443×body640valid
4.9s6474×body2560valid
4.7s50367×body80nan
2.8s9101×body320valid
2.6s4577×body1280nan
2.4s22821×body80invalid
1.7s4146×body640nan
1.7s8642×body160valid
1.5s2369×body5120valid
1.3s2943×body1280invalid
794.0ms2530×body640invalid
609.0ms1965×body320nan
402.0ms588×body5120exit
346.0ms2551×body80overflowed
321.0ms1350×body320invalid
149.0ms8256×pre80true
125.0ms83×body2560invalid
122.0ms697×body160invalid
119.0ms653×body160nan
91.0ms26×body5120invalid

analyze34.1s (9.6%)

Algorithm
31×search
Search
TrueOtherFalseIter
0%98.2%1.8%0
3.2%95%1.8%1
5.6%91%3.4%2
8%84.5%7.4%3
9.8%80.7%9.5%4
13.5%76.9%9.7%5
16%72.8%11.2%6
18.1%68.2%13.7%7
21.2%62.6%16.2%8
24.7%57%18.2%9
26.4%53.6%20%10
28.9%49.8%21.3%11
30.2%47.2%22.5%12
31.9%42.5%25.7%13
32.9%40.8%26.3%14

series26.6s (7.5%)

Calls

448 calls:

2.0s
(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))
2.0s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))
1.9s
(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))))
1.9s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))
345.0ms
(* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))

simplify21.3s (6.0%)

Algorithm
178×egg-herbie

regimes17.9s (5.0%)

Accuracy

Total 45.3b remaining (23.2%)

Threshold costs 5.6b (2.9%)

9.4b-3.8%Henrywood and Agarwal, Equation (13)
8.5b0.2%Toniolo and Linder, Equation (13)
5.6b16.2%Toniolo and Linder, Equation (10+)
5.0b78.5%Toniolo and Linder, Equation (7)
5.0b-21.7%Henrywood and Agarwal, Equation (12)

rewrite16.3s (4.6%)

Algorithm
117×rewrite-expression-head
Calls

448 calls:

687.0ms
(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))
652.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
205.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))
163.0ms
(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
155.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
Rules
237658×add-exp-log
167787×prod-exp
160436×pow-exp
97622×div-exp
50422×pow-to-exp
14061×1-exp
7318×times-frac
6301×add-sqr-sqrt
5131×*-un-lft-identity
4821×sqrt-prod
4668×add-cube-cbrt
2636×add-cbrt-cube
1930×associate-*r*
1361×unpow-prod-down
1250×pow1
1131×cbrt-unprod
1081×associate-*l*
858×cbrt-prod
577×associate-*r/
562×add-log-exp
505×sqr-pow
495×associate-/l*
475×cbrt-undiv
438×unswap-sqr
396×pow-prod-down
365×pow-unpow associate-/r*
285×div-inv
269×associate-/r/
257×sqrt-div
245×difference-of-squares
214×flip-+ flip3-+
190×associate-*l/
175×*-commutative
156×distribute-lft-out
141×rec-exp
139×frac-times
132×flip-- flip3--
124×cbrt-div
104×cube-prod
93×sqrt-pow1
89×distribute-lft-out--
87×clear-num frac-2neg
70×distribute-rgt-in distribute-lft-in
66×pow-pow
65×pow1/2
59×associate-/l/
50×tan-quot
45×log-prod
43×sub-neg
42×rem-sqrt-square
41×sum-log
39×pow1/3
36×distribute-lft-neg-in distribute-rgt-neg-in
35×div-sub
33×+-commutative
25×pow-sub
24×pow-flip
21×frac-add
19×frac-sub diff-log
18×cube-div swap-sqr
14×unpow2
13×sinh-def rem-cube-cbrt
12×neg-mul-1 cube-mult unpow3
11×associate-+r+
10×pow-div
associate-+r- sinh-undef
neg-sub0 inv-pow distribute-frac-neg pow-prod-up pow-neg
cosh-undef
rem-log-exp pow-sqr
exp-prod
unpow-prod-up associate--l+ log-pow rem-cbrt-cube associate--r+
pow2 cosh-def pow-plus asin-acos
acos-asin cos-diff associate-+l+
associate--l- log-div cos-sum sqrt-undiv rem-square-sqrt sqrt-pow2 sqrt-unprod sub-div associate--r- un-div-inv mul0-rgt distribute-rgt-out-- remove-double-div

localize2.2s (0.6%)

bsearch1.5s (0.4%)

end1.0ms (0.0%)

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