Date:Friday, July 10th, 2020
Commit:40c95423 on ival-perf-with-search
Hostname:warfa with Racket 7.5
Seed:2020192
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 (44.4%)

Filtered
50577 candidates to 16088 candidates (68.2%)

sample1.3min (21.5%)

Algorithm
61×intervals
Results
17.3s27431×body1280valid
14.4s174902×body80valid
8.3s18653×body640valid
5.0s6556×body2560valid
4.9s50985×body80nan
2.9s9372×body320valid
2.7s4515×body1280nan
2.4s23181×body80invalid
1.7s8568×body160valid
1.7s4029×body640nan
1.5s2454×body5120valid
1.2s2883×body1280invalid
808.0ms2553×body640invalid
618.0ms2055×body320nan
383.0ms584×body5120exit
342.0ms1451×body320invalid
333.0ms2473×body80overflowed
147.0ms8256×pre80true
119.0ms84×body2560invalid
117.0ms720×body160invalid
113.0ms625×body160nan
100.0ms28×body5120invalid

analyze33.6s (9.5%)

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

series29.5s (8.3%)

Calls

453 calls:

1.9s
(sqrt (* 2.0 (* n (* (* (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))
1.9s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))
1.9s
(sqrt (* 2.0 (* (* (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 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)))))))))
404.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify21.9s (6.2%)

Algorithm
181×egg-herbie

rewrite16.6s (4.7%)

Algorithm
120×rewrite-expression-head
Calls

453 calls:

912.0ms
(+ 1.0 (/ (/ (/ x (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
713.0ms
(* 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))))
659.0ms
(* 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))))
216.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
208.0ms
(* (* (/ (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))
Rules
241685×add-exp-log
170311×prod-exp
162789×pow-exp
99134×div-exp
50993×pow-to-exp
14210×1-exp
4649×add-sqr-sqrt
4271×times-frac
3866×*-un-lft-identity
3217×add-cube-cbrt
2505×add-cbrt-cube
1506×sqrt-prod
1405×unpow-prod-down
1293×pow1
1224×associate-*l*
1139×associate-*r*
1057×cbrt-unprod
716×cbrt-prod
715×associate-*r/
556×add-log-exp
481×sqr-pow
455×pow-prod-down
424×cbrt-undiv
410×unswap-sqr
339×associate-/r*
331×associate-/l*
320×sqrt-div
290×rec-exp
275×distribute-lft-out
272×pow-unpow
261×flip-+ flip3-+ associate-*l/
253×frac-times
238×div-inv
234×cbrt-div
206×associate-/r/
195×difference-of-squares
166×*-commutative
135×flip-- flip3--
131×sqrt-pow1
103×log-pow
102×exp-prod
85×distribute-lft-out--
84×clear-num frac-2neg
80×rem-sqrt-square
65×pow1/3
64×log-prod
63×distribute-rgt-in distribute-lft-in
62×pow1/2
59×tan-quot
57×associate-/l/
50×cube-prod
49×sub-neg
39×pow-pow
36×distribute-lft-neg-in sum-log distribute-rgt-neg-in
30×+-commutative frac-sub
26×log-div exp-diff
24×frac-add
20×diff-log div-sub
16×swap-sqr
14×unpow2
12×associate-+r- neg-mul-1
11×associate-+r+ distribute-frac-neg pow-neg pow-sub
10×sinh-def
neg-sub0 sinh-undef
rem-log-exp exp-sum cosh-undef
cube-div cube-mult pow-flip unpow3
inv-pow un-div-inv associate--r+
acos-asin cosh-def associate--l+ pow-sqr pow-prod-up rem-cube-cbrt
cos-diff cos-sum sqrt-undiv rem-cbrt-cube
associate--l- pow2 unpow-prod-up pow-plus asin-acos rem-exp-log
mul0-rgt

regimes15.9s (4.5%)

Accuracy

Total 42.5b remaining (21.4%)

Threshold costs 6.0b (3%)

8.0b8.3%Henrywood and Agarwal, Equation (13)
6.6b28.4%Toniolo and Linder, Equation (10+)
6.4b0%Henrywood and Agarwal, Equation (12)
6.1b29%Toniolo and Linder, Equation (13)
5.3b77.3%Toniolo and Linder, Equation (7)

localize2.4s (0.7%)

bsearch775.0ms (0.2%)

end1.0ms (0.0%)

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