Date:Thursday, July 2nd, 2020
Commit:47d1d61e on ival-find-range
Hostname:warfa with Racket 7.5
Seed:2020184
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

simplify1.4min (22.9%)

Algorithm
178×egg-herbie

sample1.3min (22.1%)

Algorithm
61×intervals
Results
17.1s27364×body1280valid
15.3s175211×body80valid
8.2s18678×body640valid
4.9s6565×body2560valid
4.7s51240×body80nan
2.8s23305×body80invalid
2.8s9064×body320valid
2.7s4652×body1280nan
1.7s8738×body160valid
1.7s4043×body640nan
1.4s2316×body5120valid
1.3s2980×body1280invalid
800.0ms2587×body640invalid
610.0ms2007×body320nan
398.0ms619×body5120exit
341.0ms2483×body80overflowed
325.0ms1372×body320invalid
144.0ms8256×pre80true
126.0ms98×body2560invalid
121.0ms714×body160invalid
120.0ms666×body160nan
83.0ms29×body5120invalid

rewrite1.2min (20.9%)

Algorithm
117×rewrite-expression-head
Calls

448 calls:

5.1s
(* l (/ 2.0 (* (* (* (/ (pow (sin k) 2) (* l (cos k))) (pow (/ 1 (pow (pow (/ -1 k) (/ 2.0 2)) 1.0)) 1.0)) (pow (/ 1 (pow (pow (/ -1 k) (/ 2.0 2)) 1.0)) 1.0)) (pow (/ (pow -1 3.0) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
3.0s
(/ 2.0 (* (* (* (/ (pow (sin k) 2) (* l (cos k))) (pow (/ 1 (pow (pow (/ -1 k) (/ 2.0 2)) 1.0)) 1.0)) (pow (/ 1 (pow (pow (/ -1 k) (/ 2.0 2)) 1.0)) 1.0)) (pow (/ (pow -1 3.0) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0)))
1.4s
(* (* (* (/ (pow (sin k) 2) (* l (cos k))) (pow (/ 1 (pow (pow (/ -1 k) (/ 2.0 2)) 1.0)) 1.0)) (pow (/ 1 (pow (pow (/ -1 k) (/ 2.0 2)) 1.0)) 1.0)) (pow (/ (pow -1 3.0) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))
285.0ms
(* l (/ 2.0 (* (* (/ (pow (sin k) 2) (* l (cos k))) (pow (/ 1 (pow (pow (/ -1 k) 2.0) 1.0)) 1.0)) (pow (/ (pow -1 3.0) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
122.0ms
(* (* (/ (pow (sin k) 2) (* l (cos k))) (pow (/ 1 (pow (pow (/ -1 k) 2.0) 1.0)) 1.0)) (pow (/ (pow -1 3.0) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))
Rules
1340339×add-exp-log
1178674×pow-exp
798449×div-exp
766214×prod-exp
317913×pow-to-exp
113351×1-exp rec-exp
4068×add-sqr-sqrt
3634×times-frac
3406×*-un-lft-identity
2926×add-cube-cbrt
2568×add-cbrt-cube
1936×unpow-prod-down
1639×associate-*r*
1381×sqrt-prod
1290×pow1
1093×cbrt-unprod
729×associate-*r/
666×associate-*l*
531×add-log-exp
480×cbrt-prod
433×pow-prod-down
427×sqr-pow
417×cbrt-undiv
334×pow-unpow
320×associate-/l*
270×unswap-sqr
261×sqrt-div
259×difference-of-squares
252×associate-/r/
250×associate-/r*
246×div-inv
240×associate-*l/
193×frac-times
184×flip-+ flip3-+
180×flip-- flip3--
166×*-commutative
164×distribute-lft-out
155×log-prod
98×distribute-lft-out--
87×tan-quot
86×sqrt-pow1
81×pow-pow
77×clear-num frac-2neg
76×exp-prod
63×rem-sqrt-square
58×distribute-rgt-in distribute-lft-in pow1/2 pow1/3
57×sub-neg
56×associate-/l/
54×exp-sum
48×log-pow
35×swap-sqr
33×distribute-lft-neg-in distribute-rgt-neg-in
28×cbrt-div
27×sum-log
25×+-commutative
24×div-sub
22×frac-add
19×cube-prod
17×frac-sub
16×rem-log-exp
15×log-div diff-log
12×pow-sub
11×neg-mul-1
pow-flip
neg-sub0 sinh-def pow-neg unpow2
associate-+r+ associate-+r- distribute-frac-neg asin-acos exp-diff
inv-pow cube-mult unpow3
pow-sqr pow-prod-up rem-cube-cbrt
cos-diff cos-sum associate--l+ un-div-inv rem-exp-log
pow2 unpow-prod-up pow-plus sinh-undef associate--r-
associate--l- acos-asin associate-+l+ sqrt-undiv sum-cubes mul0-rgt associate-+l- rem-cbrt-cube

prune40.8s (11.6%)

Filtered
23295 candidates to 9828 candidates (57.8%)

analyze32.2s (9.1%)

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

series27.2s (7.7%)

Calls

448 calls:

2.2s
(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)))))))))
2.0s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))
1.8s
(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n))))))
1.8s
(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))
473.0ms
(* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n)))

regimes16.8s (4.7%)

Accuracy

Total 33.1b remaining (18%)

Threshold costs 4.5b (2.4%)

5.8b76.1%Toniolo and Linder, Equation (7)
5.7b-6%Henrywood and Agarwal, Equation (12)
5.1b34.3%Toniolo and Linder, Equation (13)
3.6b29.6%Henrywood and Agarwal, Equation (13)
2.2b79.3%Toniolo and Linder, Equation (10+)

localize2.3s (0.6%)

bsearch1.2s (0.3%)

end1.0ms (0.0%)

Profiling

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