Date:Tuesday, May 19th, 2020
Commit:6de45b16 on cleanup
Hostname:warfa with Racket 7.5
Seed:2020140
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 (36.1%)

Calls

441 calls:

9.6s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))
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*)))))
4.6s
(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*)))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.6m (34.7%)

Algorithm
61×intervals
Results
19.6s249238×body80valid
18.5s31088×body1280valid
13.9s166169×body80nan
9.6s8884×body2560valid
8.7s21116×body640valid
5.9s3405×body5120valid
2.8s9978×body320valid
1.7s9166×body160valid
851.0ms1670×body1280nan
567.0ms1493×body640nan
399.0ms634×body5120exit
355.0ms2578×body80overflowed
201.0ms781×body320nan
157.0ms8256×pre80true
64.0ms394×body160nan

prune44.9s (16.0%)

Filtered
26119 candidates to 9671 candidates (37.0%)

simplify14.1s (5.0%)

Algorithm
176×egg-herbie

regimes10.7s (3.8%)

Accuracy

Total 43.4b remaining (20.8%)

Threshold costs 3.3b (1.6%)

10.0b14%Toniolo and Linder, Equation (13)
6.9b-0%Henrywood and Agarwal, Equation (12)
6.5b17.7%Toniolo and Linder, Equation (10+)
5.3b77.8%Toniolo and Linder, Equation (7)
3.1b0%Henrywood and Agarwal, Equation (13)

rewrite7.2s (2.6%)

Algorithm
116×rewrite-expression-head
Calls

441 calls:

98.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
86.0ms
(* (* (* (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))))
83.0ms
(* (* (* (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))))
75.0ms
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
61.0ms
(* (* (* (* (/ (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))
Rules
62242×add-exp-log
45838×prod-exp
29571×pow-exp
21372×div-exp
13284×pow-to-exp
4784×rec-exp 1-exp
4233×add-sqr-sqrt
3754×times-frac
3746×*-un-lft-identity
3085×add-cube-cbrt
2901×add-cbrt-cube
1924×sqrt-prod
1344×cbrt-unprod
1246×pow1
1055×associate-*r*
1004×unpow-prod-down
909×associate-*l*
576×add-log-exp
540×cbrt-undiv
474×cbrt-prod
471×associate-*l/
460×associate-*r/
445×frac-times
411×pow-prod-down
396×unswap-sqr
389×associate-/l*
374×associate-/r*
365×sqrt-div
320×sqr-pow
310×pow-unpow
295×distribute-lft-out
250×div-inv
189×flip-+ flip3-+
180×flip3-- flip--
174×associate-/r/
164×difference-of-squares
152×*-commutative
134×tan-quot
122×sqrt-pow1
101×distribute-rgt-neg-in
100×clear-num frac-2neg
86×pow1/2 exp-prod
83×unpow2
82×distribute-lft-out--
68×pow1/3 sub-neg
67×swap-sqr
66×distribute-rgt-in cube-prod distribute-lft-in
60×rem-sqrt-square
53×distribute-lft-neg-in
49×pow-pow
42×associate-/l/
41×cbrt-div
38×frac-sub
37×sum-log
36×diff-log
29×div-sub associate--l+
24×pow-prod-up
23×+-commutative
18×pow-sqr log-pow
17×pow-sub neg-sub0
16×frac-add associate-+r+
13×rem-exp-log
12×exp-diff log-prod pow-neg
10×cube-div cos-sum
exp-sum
log-div
neg-log pow-plus pow2
unsub-neg associate-+r-
sqrt-unprod inv-pow cos-diff pow-flip unpow3 cube-mult neg-mul-1
difference-cubes distribute-neg-in asin-acos associate--r-
rem-cube-cbrt unpow-prod-up acos-asin
un-div-inv rem-square-sqrt associate--r+ rem-log-exp
sqrt-undiv associate-+l+ e-exp-1 associate--l- distribute-lft-neg-out sum-cubes mul0 rem-cbrt-cube exp-to-pow

bsearch3.1s (1.1%)

localize2.3s (0.8%)

end1.0ms (0.0%)

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