Date:Saturday, May 2nd, 2020
Commit:37107503 on gh-actions
Hostname:warfa with Racket 7.5
Seed:2020123
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

series1.7m (36.4%)

Calls

443 calls:

6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.6m (34.9%)

Algorithm
61×intervals
Results
19.5s249315×body80valid
18.4s31170×body1280valid
13.9s167167×body80nan
9.5s8854×body2560valid
8.7s20867×body640valid
5.5s3467×body5120valid
2.9s10415×body320valid
1.7s9374×body160valid
840.0ms1662×body1280nan
536.0ms1467×body640nan
369.0ms581×body5120exit
367.0ms2904×body80overflowed
203.0ms780×body320nan
149.0ms8256×pre80true
62.0ms407×body160nan

prune44.9s (16.2%)

Filtered
21269 candidates to 9829 candidates (46.2%)

simplify12.8s (4.6%)

Algorithm
176×egg-herbie

regimes10.6s (3.8%)

Accuracy

Total 43.2b remaining (21.2%)

Threshold costs 4.6b (2.2%)

10.0b-19.6%Toniolo and Linder, Equation (10+)
7.1b25.8%Toniolo and Linder, Equation (13)
6.2b0%Henrywood and Agarwal, Equation (12)
5.6b76.4%Toniolo and Linder, Equation (7)
3.6b50.1%Toniolo and Linder, Equation (10-)

rewrite6.3s (2.3%)

Algorithm
116×rewrite-expression-head
Calls

443 calls:

271.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
76.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
73.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
60.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
41.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))
Rules
38120×add-exp-log
26655×prod-exp
12621×pow-exp
11239×div-exp
5720×pow-to-exp
4422×times-frac
4218×add-sqr-sqrt
3898×*-un-lft-identity
3205×add-cube-cbrt
2968×add-cbrt-cube
1971×1-exp
1482×sqrt-prod
1374×cbrt-unprod
1347×rec-exp
1310×pow1
1203×associate-*r/
1050×unpow-prod-down
979×associate-*r*
859×associate-*l*
738×cbrt-prod
729×frac-times
648×sqrt-div
574×associate-*l/
567×cbrt-undiv
549×add-log-exp
449×flip3-- flip--
448×pow-prod-down
425×associate-/r/
405×cbrt-div
393×associate-/r*
358×associate-/l*
313×unswap-sqr
312×div-inv
293×flip-+ flip3-+
290×pow-unpow
278×sqr-pow
264×distribute-lft-out
169×difference-of-squares
159×*-commutative
136×cube-prod
120×distribute-lft-out--
114×frac-sub
112×tan-quot
97×clear-num frac-2neg
92×distribute-rgt-neg-in
86×distribute-rgt-in distribute-lft-in
81×sqrt-pow1
80×distribute-lft-neg-in
76×sub-neg
69×pow1/3
58×pow1/2
48×rem-sqrt-square swap-sqr
43×unpow2
41×sum-log pow-pow
39×associate--l+
30×associate-/l/
29×frac-add
27×+-commutative
26×exp-diff log-div
21×pow-prod-up
20×unpow3 cube-mult
19×pow-sqr
17×diff-log
13×div-sub
12×pow-sub exp-prod
11×associate-+r+ log-pow neg-sub0 log-prod
10×pow-neg
pow-plus
cos-sum inv-pow pow-flip neg-mul-1
pow2
cube-div rem-cube-cbrt asin-acos
exp-sum
cos-diff
un-div-inv rem-cbrt-cube
acos-asin associate--r- distribute-neg-frac rem-log-exp
sqrt-undiv associate-+l+ rem-exp-log sqrt-unprod unsub-neg rem-square-sqrt distribute-frac-neg distribute-rgt-out associate-+r- sub-div mul0

bsearch2.6s (1.0%)

localize2.2s (0.8%)

end1.0ms (0.0%)

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