Date:Friday, July 3rd, 2020
Commit:8652dc03 on ival-find-range
Hostname:warfa with Racket 7.5
Seed:2020185
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

prune2.5min (47.3%)

Filtered
21212 candidates to 11549 candidates (45.6%)

sample1.8min (32.7%)

Algorithm
99×intervals
Results
45.2s8207×body5120exit
23.2s359614×body80valid
8.0s15657×body1280valid
5.8s11526×body1280invalid
3.5s12334×body640valid
2.9s8772×body640invalid
1.6s7646×body160valid
1.5s86270×pre80true
1.2s6659×body320valid
1.0s18143×body80invalid
947.0ms4162×body320invalid
427.0ms1386×body2560valid
286.0ms1951×body160invalid
220.0ms2378×body80nan
219.0ms602×body5120valid
83.0ms46×body2560invalid
0.0msbody80overflowed

simplify15.0s (4.7%)

Algorithm
256×egg-herbie

analyze14.6s (4.5%)

Algorithm
50×search
Search
TrueOtherFalseIter
0%87.1%12.9%0
2.5%84.6%12.9%1
9.3%75.6%15.1%2
22.1%62.3%15.6%3
27.1%55.4%17.4%4
36.3%45.6%18.1%5
39.7%40.6%19.7%6
44.2%33.4%22.4%7
47.6%29.3%23.1%8
50.7%25.2%24.1%9
53.2%21.6%25.2%10
55.3%18.7%26%11
57.2%16.3%26.5%12
59.1%13.6%27.4%13
60.1%12.2%27.7%14

regimes12.2s (3.8%)

Accuracy

Total 109.2b remaining (44.5%)

Threshold costs 4.8b (2%)

22.3b36.7%math.sqrt on complex, real part
11.7b39.8%math.sqrt on complex, imaginary part, im greater than 0 branch
10.8b57.2%math.log/2 on complex, real part
10.4b58%math.log10 on complex, real part
10.2b58.6%math.log/1 on complex, real part

series11.6s (3.6%)

Calls

458 calls:

386.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
311.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
309.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
304.0ms
(- 1.0 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x)))))))))) (pow (exp (fabs x)) (fabs x)))))
304.0ms
(- 1.0 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (cbrt (pow (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* 1.0 (/ (+ 1.421413741 (- (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (/ 1.453152027 (+ 1.0 (* 0.3275911 (fabs x)))))) (+ 1.0 (* 0.3275911 (fabs x)))))))) 3)) (pow (exp (fabs x)) (fabs x)))))

rewrite7.3s (2.3%)

Algorithm
158×rewrite-expression-head
Calls

458 calls:

234.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
212.0ms
(* (sqrt (* PI 2.0)) (* (* (exp (- z (+ 7.0 0.5))) (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))) (/ PI (sin (* PI z)))))
193.0ms
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))))))))
154.0ms
(* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
140.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
Rules
24696×*-un-lft-identity
23963×times-frac
11006×add-sqr-sqrt
9757×add-cube-cbrt
8561×distribute-lft-out
6683×sqrt-prod
2790×frac-add
2615×add-exp-log
1876×add-cbrt-cube
1649×pow1
1648×associate-*r*
1551×flip-+ flip3-+
1330×associate-*r/
1325×associate-/l*
1163×frac-times
1053×associate-*l*
1041×prod-exp
807×associate-*l/
738×cbrt-prod
685×cbrt-unprod
678×associate-/r/
642×add-log-exp
510×div-exp
497×sqrt-div
425×pow-prod-down
384×div-inv
364×associate-/r*
339×unpow-prod-down
338×cbrt-undiv
317×pow-sub
276×unswap-sqr
269×difference-of-squares
259×exp-diff
233×distribute-lft-out--
199×log-pow
198×cbrt-div
193×associate-/l/
157×sqrt-pow1
147×*-commutative
118×pow-exp
110×pow1/2
107×pow-prod-up
106×sqr-pow
92×pow1/3
85×flip-- flip3--
82×cube-prod
78×log-prod
75×clear-num frac-2neg
74×swap-sqr
71×pow-to-exp pow-sqr
65×distribute-rgt-in pow-unpow distribute-lft-in
63×sum-log 1-exp
61×exp-sum
58×rem-sqrt-square
57×rec-exp
48×+-commutative pow-pow
47×pow-plus
41×sub-neg exp-prod
37×pow2
35×diff-log
30×cube-div
23×div-sub
21×cube-mult unpow2 unpow3
18×log-div
16×associate-+r+
12×un-div-inv
10×pow-flip
rem-log-exp
associate--l+ rem-cube-cbrt
cos-sum associate-+r- inv-pow rem-exp-log
associate--r+
associate-+l+ sqrt-unprod sin-sum
rem-square-sqrt associate-+l-
unpow-prod-up sqrt-undiv frac-sub rem-cbrt-cube
associate--l- associate--r-

localize2.6s (0.8%)

bsearch1.0s (0.3%)

end1.0ms (0.0%)

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