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: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 (36.6%)

Calls

455 calls:

5.1s
(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 (31.1%)

Algorithm
61×intervals
Results
15.7s248501×body80valid
15.6s30344×body1280valid
11.1s167382×body80nan
8.9s8923×body2560valid
7.4s21205×body640valid
5.6s3407×body5120valid
2.4s10028×body320valid
1.4s9322×body160valid
884.0ms2648×body1280nan
586.0ms2338×body640nan
433.0ms904×body10240exit
232.0ms1245×body320nan
122.0ms8256×pre80true
69.0ms634×body160nan

prune55.1s (20.3%)

Filtered
21808 candidates to 10071 candidates (46.2%)

simplify12.1s (4.5%)

Algorithm
178×egg-herbie

regimes10.3s (3.8%)

Accuracy

Total 50.6b remaining (23.7%)

Threshold costs 5.5b (2.6%)

9.5b30.8%Henrywood and Agarwal, Equation (3)
7.7b15.8%Toniolo and Linder, Equation (13)
5.7b0%Henrywood and Agarwal, Equation (12)
5.6b24.9%Toniolo and Linder, Equation (10+)
5.4b77.6%Toniolo and Linder, Equation (7)

rewrite6.5s (2.4%)

Algorithm
118×rewrite-expression-head
Calls

455 calls:

77.0ms
(* (* (* (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))))
75.0ms
(* (* (* (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))
63.0ms
(* (* (* (* (/ (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))
50.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
Rules
38333×add-exp-log
26660×prod-exp
12398×pow-exp
10907×div-exp
5678×pow-to-exp
5013×times-frac
4788×add-sqr-sqrt
4498×*-un-lft-identity
3763×add-cube-cbrt
3362×sqrt-prod
2954×add-cbrt-cube
1387×pow1
1377×cbrt-unprod
1296×rec-exp 1-exp
1246×associate-*l*
1015×associate-*r/
1006×associate-*r*
909×unpow-prod-down
784×sqrt-div
755×cbrt-prod
632×frac-times
583×add-log-exp
550×cbrt-undiv
485×associate-*l/
445×pow-prod-down
417×flip3-- flip--
388×associate-/l*
384×unswap-sqr
347×associate-/r*
290×exp-prod
275×cbrt-div distribute-lft-out
267×associate-/r/
262×div-inv
261×pow-unpow
250×sqr-pow
175×flip-+ flip3-+
160×*-commutative
159×distribute-lft-out--
129×distribute-rgt-neg-in
117×log-pow
112×difference-of-squares
108×tan-quot
103×cube-prod
99×sqrt-pow1
94×clear-num frac-2neg
89×distribute-lft-neg-in
80×unpow2
68×pow1/2
67×distribute-rgt-in distribute-lft-in
64×rem-sqrt-square
63×pow1/3 sub-neg
50×sum-log
48×pow-pow
45×pow-prod-up
40×frac-sub
32×associate--l+
31×associate-/l/ pow-sqr +-commutative
29×swap-sqr
25×exp-diff
23×pow-plus frac-add log-prod
22×div-sub log-div
20×cube-div
18×pow2
16×diff-log
15×associate-+r+ unpow3 cube-mult
14×neg-sub0
13×exp-sum
11×pow-flip neg-mul-1
rem-exp-log pow-sub
rem-cube-cbrt
inv-pow associate-+r- pow-neg
un-div-inv rem-cbrt-cube rem-log-exp
cos-sum
associate-+l+ exp-neg distribute-neg-frac unsub-neg distribute-frac-neg neg-log asin-acos associate-+l-
cos-diff acos-asin exp-to-pow
pow-div sqrt-undiv mul0

localize2.4s (0.9%)

bsearch1.2s (0.5%)

end1.0ms (0.0%)