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:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

series2.0m (39.5%)

Calls

432 calls:

6.7s
(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*)))))
5.6s
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
4.9s
(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*)))))
4.7s
(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*)))))

sample1.6m (32.4%)

Algorithm
61×intervals
Results
19.6s249315×body80valid
18.5s31170×body1280valid
14.0s167167×body80nan
9.5s8854×body2560valid
8.5s20867×body640valid
5.5s3467×body5120valid
2.9s10415×body320valid
1.7s9374×body160valid
862.0ms1662×body1280nan
549.0ms1467×body640nan
374.0ms581×body5120exit
373.0ms2904×body80overflowed
208.0ms780×body320nan
160.0ms8256×pre80true
63.0ms407×body160nan

prune50.7s (17.0%)

Filtered
21631 candidates to 10612 candidates (49.1%)

simplify12.8s (4.3%)

Algorithm
176×egg-herbie

regimes10.3s (3.4%)

Accuracy

Total 40.6b remaining (22.9%)

Threshold costs 4.6b (2.6%)

8.4b0.4%Toniolo and Linder, Equation (10+)
7.1b25.8%Toniolo and Linder, Equation (13)
6.7b0%Henrywood and Agarwal, Equation (12)
5.6b76.4%Toniolo and Linder, Equation (7)
3.6b50.1%Toniolo and Linder, Equation (10-)

rewrite5.4s (1.8%)

Algorithm
116×rewrite-expression-head
Calls

432 calls:

74.0ms
(* (* (* (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)))))
74.0ms
(* (* (* (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))
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))
43.0ms
(* (* (/ (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))
Rules
38060×add-exp-log
26614×prod-exp
12578×pow-exp
11269×div-exp
5682×pow-to-exp
4112×add-sqr-sqrt
3701×*-un-lft-identity
3531×times-frac
3066×add-cube-cbrt
2878×add-cbrt-cube
1971×1-exp
1350×cbrt-unprod
1347×rec-exp
1235×sqrt-prod
1209×pow1
901×unpow-prod-down
871×associate-*r*
865×associate-*r/
755×associate-*l*
707×cbrt-prod
663×frac-times
598×cbrt-undiv
571×prod-diff
536×sqrt-div
519×associate-*l/
502×add-log-exp
432×log1p-expm1-u expm1-log1p-u
412×pow-prod-down
390×cbrt-div
386×associate-/r*
379×flip3-- flip--
360×associate-/l*
348×associate-/r/
313×div-inv
291×sqr-pow
281×pow-unpow
262×unswap-sqr
238×distribute-lft-out
232×difference-of-squares
217×flip-+ flip3-+
199×cube-prod
174×distribute-rgt-in distribute-lft-in
143×*-commutative
135×distribute-lft-out--
115×tan-quot
101×clear-num frac-2neg
92×distribute-rgt-neg-in
88×fma-def
86×pow1/3
80×distribute-lft-neg-in
70×sqrt-pow1
58×swap-sqr
52×sub-neg
50×pow-pow
48×pow1/2
45×fma-neg
43×associate--l+
38×fma-udef
36×frac-sub
35×rem-sqrt-square
33×unpow3 cube-mult
30×associate-/l/
29×sum-log
26×cos-sum
25×unpow2
18×+-commutative
17×pow-prod-up
15×pow-sqr
14×log-pow div-sub hypot-def
13×frac-add
11×exp-prod
10×diff-log cube-div log-prod
rem-cube-cbrt
neg-mul-1
pow-plus pow2 pow-sub neg-sub0
inv-pow pow-flip
difference-cubes
sqrt-pow2 pow-neg asin-acos
associate-+r+ hypot-udef acos-asin rem-log-exp
un-div-inv associate-+r- unsub-neg distribute-neg-frac
neg-log exp-diff sqrt-undiv associate-+l+ sqrt-unprod cos-diff expm1-log1p rem-square-sqrt distribute-frac-neg distribute-rgt-out associate--r- exp-sum mul0 rem-cbrt-cube expm1-udef log-div

bsearch2.3s (0.8%)

localize2.2s (0.7%)

end1.0ms (0.0%)

Profiling

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