Date:Saturday, February 22nd, 2020
Commit:72c1b946 on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020053
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

series1.9m (32.9%)

Calls

432 calls:

4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- 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 (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
2.7s
(/ (hypot (pow (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) 3) (pow 1.0 3/2)) (sqrt (+ (* 1.0 1.0) (- (* (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (* 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))))

prune1.6m (28.4%)

Filtered
29305 candidates to 14093 candidates (48.1%)

sample1.3m (22.9%)

Algorithm
61×intervals
Results
15.5s29334×body1280valid
15.5s252270×body80valid
9.6s160524×body80nan
8.8s8782×body2560valid
7.1s20088×body640valid
5.1s3325×body5120valid
2.3s9646×body320valid
1.3s9085×body160valid
389.0ms684×body10240exit
155.0ms627×body1280nan
122.0ms645×body640nan
105.0ms8256×pre80true
52.0ms354×body320nan
19.0ms186×body160nan

rewrite24.7s (7.1%)

Algorithm
117×rewrite-expression-head
Calls

432 calls:

3.7s
(sqrt (+ (* 1.0 1.0) (- (* (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (* 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
3.1s
(/ (hypot (pow (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) 3) (pow 1.0 3/2)) (sqrt (+ (* 1.0 1.0) (- (* (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (* 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))))
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ 1 (cbrt (* (cbrt h) (cbrt h)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt h))) (/ 1.0 2.0)))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.1s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
1.1s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
Rules
79780×add-exp-log
59281×prod-exp
32470×pow-exp
22304×div-exp
11791×pow-to-exp
5869×times-frac
5792×add-sqr-sqrt
5231×*-un-lft-identity
4474×associate-*r/
4209×add-cube-cbrt
3539×1-exp
3524×rec-exp
3169×sqrt-div
2731×add-cbrt-cube
2511×sqrt-prod
1835×cbrt-prod
1688×frac-times
1525×flip-+ flip3-+
1186×associate-*r*
1136×pow1
1067×cbrt-unprod
992×unpow-prod-down
887×prod-diff
865×associate-*l*
695×associate-*l/
672×frac-sub
609×cbrt-undiv
563×pow-unpow
522×add-log-exp
456×associate-/l*
433×expm1-log1p-u
432×log1p-expm1-u
430×distribute-rgt-neg-in
367×sqr-pow
361×distribute-lft-neg-in
354×unswap-sqr
349×pow-prod-down
341×associate-/r*
340×div-inv
304×distribute-lft-out
303×distribute-lft-out--
253×difference-of-squares
249×exp-sum
220×flip3-- flip--
184×cos-sum
182×distribute-rgt-in distribute-lft-in
164×associate-/r/
146×*-commutative
133×sqrt-pow1
96×clear-num frac-2neg
95×pow1/2
88×exp-prod
70×sub-neg
65×rem-sqrt-square fma-def
62×hypot-def
48×fma-neg
42×associate-/l/ associate--l+
40×sub-div div-sub pow-pow
38×unpow2
37×neg-mul-1
36×swap-sqr
27×pow-sub pow1/3
25×fma-udef
24×diff-log
23×sum-log tan-quot
19×+-commutative
18×neg-sub0
17×pow-prod-up
14×frac-add
13×log-pow
12×rem-exp-log pow-neg distribute-frac-neg log-prod
11×pow-sqr associate--r+
8×exp-diff cos-diff
6×cbrt-div neg-log distribute-neg-frac
5×sqrt-unprod asin-acos
4×un-div-inv inv-pow pow2 pow-flip associate--r-
3×pow-plus associate-+l+ e-exp-1 hypot-udef unsub-neg associate-+r- rem-log-exp
2×expm1-log1p associate-+r+ expm1-udef rem-square-sqrt
1×sqrt-undiv log1p-udef associate--l- log1p-expm1 acos-asin mul0 distribute-rgt-out--

simplify16.0s (4.6%)

Algorithm
177×egg-herbie

regimes10.0s (2.9%)

Accuracy

Total 40.7b remaining (19.8%)

Threshold costs 4.5b (2.2%)

9.5b36%Henrywood and Agarwal, Equation (3)
6.8b25.5%Toniolo and Linder, Equation (13)
6.2b73.7%Toniolo and Linder, Equation (7)
5.1b29.3%Henrywood and Agarwal, Equation (12)
2.6b39.5%Toniolo and Linder, Equation (10-)

localize2.2s (0.6%)

bsearch1.8s (0.5%)

end1.0ms (0.0%)