Date:Tuesday, February 25th, 2020
Commit:61e80a61 on faster-rr
Hostname:warfa with Racket 7.5
Seed:2020056
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 (38.0%)

Calls

452 calls:

5.0s
(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*)))))
4.9s
(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 (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* 1 (* (* (* 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*))))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.3m (29.1%)

Algorithm
61×intervals
Results
15.9s29517×body1280valid
15.2s253719×body80valid
9.6s159891×body80nan
9.0s8828×body2560valid
7.1s20160×body640valid
5.3s3336×body5120valid
2.3s9513×body320valid
1.2s8943×body160valid
466.0ms741×body10240exit
158.0ms676×body1280nan
107.0ms586×body640nan
102.0ms8256×pre80true
46.0ms342×body320nan
18.0ms197×body160nan

prune55.5s (20.2%)

simplify13.3s (4.9%)

Algorithm
177×egg-herbie

regimes11.2s (4.1%)

Accuracy

Total 42.2b remaining (20.4%)

Threshold costs 5.1b (2.5%)

8.9b3.1%Toniolo and Linder, Equation (13)
6.3b0%Henrywood and Agarwal, Equation (12)
5.7b76.2%Toniolo and Linder, Equation (7)
5.7b15.7%Toniolo and Linder, Equation (10+)
3.9b44.4%Toniolo and Linder, Equation (10-)

rewrite6.1s (2.2%)

Algorithm
117×rewrite-expression-head
Calls

452 calls:

92.0ms
(* (* (* (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)))
91.0ms
(* (* (* (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))))
65.0ms
(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
58.0ms
(/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))
49.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
Rules
36062×add-exp-log
25558×prod-exp
13453×pow-exp
10523×div-exp
6717×times-frac
5682×add-sqr-sqrt
5672×pow-to-exp
5225×*-un-lft-identity
4428×add-cube-cbrt
3740×sqrt-prod
2626×add-cbrt-cube
2080×1-exp
2069×rec-exp
1626×associate-*l*
1296×unpow-prod-down
1193×pow1
1037×cbrt-unprod
767×associate-*r*
573×associate-*r/
561×add-log-exp
515×cbrt-prod
507×associate-/l*
487×cbrt-undiv
417×sqr-pow
393×pow-prod-down
375×pow-unpow
372×associate-/r*
369×sqrt-div
310×difference-of-squares
294×frac-times
292×div-inv
287×unswap-sqr
273×associate-*l/
267×distribute-lft-out
241×flip3-- flip--
208×flip-+ flip3-+
202×distribute-lft-out--
200×cube-prod
165×associate-/r/
145×*-commutative
116×distribute-rgt-neg-in
111×distribute-rgt-in distribute-lft-in
92×frac-2neg clear-num
82×sub-neg
80×sqrt-pow1
79×tan-quot
75×pow1/3
72×cbrt-div
69×distribute-lft-neg-in exp-prod
60×frac-add
58×pow1/2
54×rem-sqrt-square
51×pow-pow
50×frac-sub
38×associate-/l/
36×div-sub
34×sum-log
33×unpow2
28×+-commutative log-prod
22×diff-log associate--l+
15×log-pow neg-sub0
14×pow-sub
12×cube-div
11×unpow3 swap-sqr
10×rem-cube-cbrt cube-mult
neg-mul-1
cos-sum exp-diff difference-cubes inv-pow pow-flip neg-log distribute-neg-frac associate--r+
associate-+r+ asin-acos
associate-+l-
rem-log-exp
pow-neg associate-+r- cos-diff unsub-neg
pow-sqr pow-prod-up associate--r-
rem-exp-log associate--l- pow2 distribute-frac-neg rem-cbrt-cube log-div
sqrt-undiv un-div-inv quot-tan sqrt-unprod pow-plus acos-asin exp-sum mul0

localize2.3s (0.9%)

bsearch1.6s (0.6%)

end1.0ms (0.0%)