Date:Wednesday, April 1st, 2020
Commit:71d48594 on master
Hostname:warfa with Racket 7.5
Seed:2020092
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

series1.6m (37.4%)

Calls

440 calls:

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*)))))
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.7s
(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*))))

sample1.4m (32.1%)

Algorithm
61×intervals
Results
15.5s30777×body1280valid
15.3s248736×body80valid
10.8s165823×body80nan
8.9s8852×body2560valid
7.3s21159×body640valid
5.2s3300×body5120valid
2.4s10281×body320valid
1.3s9179×body160valid
897.0ms2617×body1280nan
588.0ms2363×body640nan
361.0ms722×body10240exit
220.0ms1210×body320nan
109.0ms8256×pre80true
74.0ms664×body160nan

prune45.3s (17.6%)

Filtered
20671 candidates to 9880 candidates (47.8%)

simplify12.3s (4.8%)

Algorithm
175×egg-herbie

regimes11.1s (4.3%)

Accuracy

Total 39.9b remaining (20.1%)

Threshold costs 5.7b (2.8%)

9.8b20.6%Toniolo and Linder, Equation (13)
5.9b20.3%Toniolo and Linder, Equation (10+)
5.2b78.1%Toniolo and Linder, Equation (7)
4.9b7%Henrywood and Agarwal, Equation (12)
4.6b35.4%Toniolo and Linder, Equation (10-)

rewrite5.8s (2.2%)

Algorithm
115×rewrite-expression-head
Calls

440 calls:

81.0ms
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
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))))
51.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
48.0ms
(* (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (* PI t)) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (pow (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) 3)))
44.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
34777×add-exp-log
24782×prod-exp
11902×pow-exp
9387×div-exp
5431×pow-to-exp
4083×add-sqr-sqrt
3580×*-un-lft-identity
3468×times-frac
2951×add-cube-cbrt
2897×add-cbrt-cube
1434×pow1
1364×cbrt-unprod
1363×1-exp rec-exp
1248×associate-*r*
1170×associate-*r/
1130×unpow-prod-down
970×associate-*l*
911×sqrt-prod
720×cbrt-prod
713×sqrt-div
689×frac-times
553×add-log-exp
518×associate-*l/
500×pow-prod-down
475×cbrt-undiv
410×flip3-- flip-+ flip3-+ flip--
397×associate-/l*
357×unswap-sqr
326×sqr-pow
317×pow-unpow
314×associate-/r*
302×cube-prod
292×cbrt-div
230×div-inv
215×associate-/r/
207×difference-of-squares
202×distribute-lft-out
172×*-commutative
165×distribute-lft-out--
150×frac-add
136×distribute-rgt-neg-in
132×distribute-neg-frac
115×associate-/l/
108×distribute-lft-neg-in
101×distribute-rgt-in distribute-lft-in
91×frac-2neg clear-num
89×sqrt-pow1
85×tan-quot
79×unpow2
71×sub-neg
64×pow1/2
57×pow1/3
50×rem-sqrt-square
49×pow-prod-up
46×frac-sub pow-pow
39×sum-log
36×swap-sqr
33×pow-sqr
29×+-commutative
26×associate--l+
24×unpow3 cube-mult
23×pow-plus div-sub
22×diff-log
19×associate-+r+
18×pow2
17×neg-sub0
15×log-pow pow-sub
13×cube-div
12×exp-prod neg-mul-1
10×pow-neg
rem-cube-cbrt
log-prod
pow-flip asin-acos
cos-sum associate--r+
inv-pow associate-+l+ neg-log
difference-cubes un-div-inv distribute-neg-in associate-+l-
associate-+r- cos-diff associate--r-
associate--l- sqrt-unprod unsub-neg distribute-frac-neg exp-sum rem-cbrt-cube rem-log-exp
sqrt-undiv rem-square-sqrt acos-asin sub-div mul0 sum-cubes

bsearch2.2s (0.9%)

localize2.1s (0.8%)

end0.0ms (0.0%)