Date:Tuesday, March 31st, 2020
Commit:2cac45bc on simpler-alts
Hostname:warfa with Racket 7.5
Seed:2020091
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 (41.2%)

Calls

428 calls:

9.9s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))
5.5s
(/ (- (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*)))))
4.8s
(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*)))))

sample1.4m (30.6%)

Algorithm
59×intervals
Results
16.1s30920×body1280valid
15.3s237948×body80valid
10.8s162180×body80nan
8.8s8782×body2560valid
7.5s21032×body640valid
5.4s3425×body5120valid
2.4s10184×body320valid
1.4s9126×body160valid
913.0ms2674×body1280nan
624.0ms2313×body640nan
361.0ms699×body10240exit
214.0ms1177×body320nan
113.0ms8256×pre80true
65.0ms573×body160nan

prune46.4s (17.0%)

Filtered
19648 candidates to 9576 candidates (48.7%)

simplify12.3s (4.5%)

Algorithm
170×egg-herbie

regimes9.9s (3.6%)

Accuracy

Total 42.4b remaining (22.8%)

Threshold costs 4.3b (2.3%)

8.5b25.3%Toniolo and Linder, Equation (13)
7.5b1.7%Toniolo and Linder, Equation (10+)
5.6b35.9%Henrywood and Agarwal, Equation (12)
5.6b75.8%Toniolo and Linder, Equation (7)
5.3b58.9%Henrywood and Agarwal, Equation (3)

rewrite5.1s (1.9%)

Algorithm
112×rewrite-expression-head
Calls

428 calls:

248.0ms
(* (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)))
90.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
90.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
46.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (pow 1.0 3) (pow (* v v) 3))))
45.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
32683×add-exp-log
24007×prod-exp
12960×pow-exp
8977×div-exp
5440×pow-to-exp
3416×add-sqr-sqrt
3034×*-un-lft-identity
2410×add-cube-cbrt
2277×add-cbrt-cube
2051×times-frac
2041×1-exp rec-exp
1223×pow1
922×cbrt-unprod
921×unpow-prod-down
716×prod-diff
654×associate-*r*
613×sqrt-prod
593×associate-*l*
543×associate-*r/
530×associate-*l/
508×add-log-exp frac-times
429×expm1-log1p-u
428×log1p-expm1-u
419×cbrt-prod
370×pow-prod-down
359×cbrt-undiv
347×sqrt-div
328×associate-/l*
311×difference-of-squares
305×pow-unpow
296×associate-/r*
270×flip-- flip3--
262×sqr-pow
259×distribute-rgt-neg-in
250×distribute-lft-out--
242×distribute-lft-neg-in
209×div-inv
183×cube-prod
178×unswap-sqr
176×cbrt-div
162×distribute-rgt-in distribute-lft-in
133×associate-/r/
131×*-commutative
111×flip-+ flip3-+
110×tan-quot
105×distribute-lft-out
88×clear-num frac-2neg
84×fma-neg
80×fma-def
72×sqrt-pow1
70×pow1/3
68×log-prod
58×pow-pow
56×sub-neg
48×associate-/l/
47×log-pow
45×pow1/2
43×pow-prod-up
40×cube-div
39×rem-sqrt-square
38×unpow3 cube-mult
32×associate--l+
31×fma-udef
29×pow-sqr swap-sqr
27×neg-mul-1
26×exp-prod
25×cos-sum frac-sub
23×unpow2
22×pow-plus sum-log associate--r+
20×div-sub exp-sum
19×diff-log pow-neg neg-sub0
18×+-commutative
17×pow2
16×hypot-def
15×pow-sub
13×rem-log-exp
11×un-div-inv
10×frac-add
rem-cube-cbrt
exp-neg distribute-rgt-neg-out distribute-neg-frac
hypot-udef
neg-log
difference-cubes asin-acos
mul-1-neg inv-pow pow-flip log-rec
sqrt-undiv acos-asin associate--r- rem-cbrt-cube exp-to-pow
associate--l- sin-sum expm1-log1p expm1-udef distribute-frac-neg associate-+l- log-div
rem-exp-log exp-diff sqrt-pow2 associate-+l+ distribute-lft-neg-out associate-+r- log1p-expm1 cos-diff log1p-udef unsub-neg mul0

localize2.3s (0.8%)

bsearch851.0ms (0.3%)

end1.0ms (0.0%)