Date:Friday, July 10th, 2020
Commit:a8193a33 on movability-off
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 (44.3%)

Filtered
50404 candidates to 15965 candidates (68.3%)

sample1.3min (21.5%)

Algorithm
61×intervals
Results
16.9s27431×body1280valid
14.2s174902×body80valid
8.1s18653×body640valid
4.9s6556×body2560valid
4.6s50985×body80nan
3.2s5538×body1280nan
2.9s9372×body320valid
2.4s23181×body80invalid
2.1s4857×body640nan
1.7s8568×body160valid
1.5s2454×body5120valid
1.2s2883×body1280invalid
801.0ms2553×body640invalid
755.0ms2478×body320nan
376.0ms584×body5120exit
343.0ms1451×body320invalid
155.0ms824×body160nan
143.0ms8256×pre80true
128.0ms84×body2560invalid
117.0ms720×body160invalid
94.0ms28×body5120invalid

analyze33.4s (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

series29.6s (8.4%)

Calls

446 calls:

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 (* (* (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 (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))
1.7s
(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)))))))))))
681.0ms
(* (* (* (/ (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))

simplify21.0s (6.0%)

Algorithm
180×egg-herbie

rewrite17.4s (4.9%)

Algorithm
119×rewrite-expression-head
Calls

446 calls:

900.0ms
(+ 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))))))
723.0ms
(* 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))))
695.0ms
(* 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))))
217.0ms
(* (* (/ (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))
169.0ms
(* (* (* (/ (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))
Rules
241663×add-exp-log
170298×prod-exp
162789×pow-exp
99139×div-exp
50993×pow-to-exp
14210×1-exp
4631×add-sqr-sqrt
4287×times-frac
3854×*-un-lft-identity
3205×add-cube-cbrt
2482×add-cbrt-cube
1503×sqrt-prod
1405×unpow-prod-down
1250×pow1
1213×associate-*l*
1123×associate-*r*
1044×cbrt-unprod
716×cbrt-prod
679×associate-*r/
549×add-log-exp
481×sqr-pow
433×pow-prod-down
429×cbrt-undiv
407×unswap-sqr
338×associate-/l*
335×associate-/r*
308×sqrt-div
290×rec-exp
275×distribute-lft-out
272×pow-unpow
261×flip-+ flip3-+
257×associate-*l/
245×frac-times
239×div-inv
234×cbrt-div
204×associate-/r/
193×difference-of-squares
161×*-commutative
131×sqrt-pow1
119×flip-- flip3--
99×log-pow
95×exp-prod
85×distribute-lft-out--
83×clear-num frac-2neg
80×rem-sqrt-square
65×pow1/3
62×pow1/2
59×log-prod tan-quot
58×associate-/l/
57×distribute-rgt-in distribute-lft-in
50×cube-prod
41×sub-neg
39×pow-pow
36×distribute-lft-neg-in sum-log distribute-rgt-neg-in
30×+-commutative frac-sub
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×log-div sinh-def exp-diff
9×neg-sub0 sinh-undef
7×rem-log-exp cosh-undef
6×cube-div cube-mult pow-flip unpow3
5×inv-pow un-div-inv associate--r+
4×acos-asin cosh-def associate--l+ pow-sqr pow-prod-up rem-cube-cbrt
3×cos-diff cos-sum sqrt-undiv rem-cbrt-cube
2×associate--l- pow2 exp-sum unpow-prod-up pow-plus asin-acos
1×mul0-rgt rem-exp-log

regimes16.1s (4.6%)

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)

localize2.5s (0.7%)

bsearch750.0ms (0.2%)

end1.0ms (0.0%)

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