Date:Friday, March 6th, 2020
Commit:044801c1 on master
Hostname:warfa with Racket 7.5
Seed:2020066
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

series1.8m (38.9%)

Calls

443 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* 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 (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (29.8%)

Algorithm
61×intervals
Results
15.1s248501×body80valid
15.1s30344×body1280valid
10.8s167382×body80nan
8.7s8923×body2560valid
7.1s21205×body640valid
5.4s3407×body5120valid
2.3s10028×body320valid
1.3s9322×body160valid
843.0ms2648×body1280nan
570.0ms2338×body640nan
428.0ms904×body10240exit
218.0ms1245×body320nan
116.0ms8256×pre80true
72.0ms634×body160nan

prune55.2s (20.1%)

Filtered
21318 candidates to 10392 candidates (48.7%)

simplify11.7s (4.3%)

Algorithm
178×egg-herbie

regimes10.0s (3.7%)

Accuracy

Total 49.5b remaining (26%)

Threshold costs 4.9b (2.6%)

9.5b30.8%Henrywood and Agarwal, Equation (3)
7.7b15.8%Toniolo and Linder, Equation (13)
5.9b0%Henrywood and Agarwal, Equation (12)
5.6b24.8%Toniolo and Linder, Equation (10+)
5.3b77.6%Toniolo and Linder, Equation (7)

rewrite5.4s (2.0%)

Algorithm
118×rewrite-expression-head
Calls

443 calls:

79.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
78.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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) (/ 1 l))))
64.0ms
(* (* (* (* (/ (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))
57.0ms
(* (* (* (/ (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))
46.0ms
(* (/ (/ 1 PI) (* (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 (* v v)) (* 3.0 (* v v)))))) (fma 1.0 1.0 (pow v 4)))) (/ (/ (- 1.0 (* 5.0 (* v v))) t) (- (* 1.0 1.0) (* (* v v) (* v v)))))
Rules
38745×add-exp-log
26771×prod-exp
12353×pow-exp
11150×div-exp
5634×pow-to-exp
3702×add-sqr-sqrt
3461×*-un-lft-identity
3227×add-cbrt-cube
3083×times-frac
2823×add-cube-cbrt
1452×cbrt-unprod
1326×rec-exp 1-exp
1289×pow1
960×associate-*r*
825×associate-*l*
821×sqrt-prod
810×unpow-prod-down
699×cbrt-undiv
509×add-log-exp
496×cbrt-prod
459×associate-*r/
444×log1p-expm1-u
443×expm1-log1p-u
439×pow-prod-down
385×prod-diff
368×associate-*l/
367×associate-/r*
338×frac-times
330×associate-/l*
296×unswap-sqr
288×div-inv
286×exp-prod
264×sqrt-div
263×pow-unpow
224×sqr-pow
223×distribute-lft-out
195×distribute-rgt-in distribute-lft-in
166×*-commutative
164×distribute-lft-out--
163×flip-+ flip3-+
160×flip3-- flip--
158×associate-/r/
139×difference-of-squares
138×distribute-rgt-neg-in
121×log-pow
109×tan-quot
107×sqrt-pow1
102×distribute-lft-neg-in
100×clear-num frac-2neg
89×cube-prod
66×pow1/2
59×sub-neg
56×fma-def
53×rem-sqrt-square
42×associate--l+
38×pow-pow
33×associate-/l/
32×frac-sub
29×fma-udef
28×unpow2
27×log-prod
26×pow1/3
24×cos-sum
23×div-sub
22×fma-neg sum-log
18×frac-add +-commutative
17×swap-sqr cbrt-div
15×hypot-def
14×pow-prod-up
13×pow-flip unpow3 cube-mult
12×neg-mul-1
pow-sqr neg-sub0 diff-log
cube-div inv-pow
rem-exp-log un-div-inv pow-sub
exp-diff exp-sum rem-log-exp associate-+r-
hypot-udef asin-acos
pow-plus exp-neg pow2 unsub-neg distribute-frac-neg rem-cbrt-cube pow-neg
associate-+l+ associate-+r+ acos-asin exp-to-pow
pow-div rem-cube-cbrt sqrt-undiv log1p-udef sqrt-unprod sin-sum log1p-expm1 cos-diff expm1-log1p rem-square-sqrt mul0 expm1-udef

localize2.3s (0.8%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)