Date:Wednesday, March 18th, 2020
Commit:1a959946 on master
Hostname:warfa with Racket 7.5
Seed:2020078
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 (36.2%)

Calls

446 calls:

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)) (- 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 (/ Om l)))) (* (* (* 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 (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (30.6%)

Algorithm
61×intervals
Results
16.0s31110×body1280valid
15.9s250036×body80valid
11.1s167152×body80nan
9.0s8964×body2560valid
7.2s20903×body640valid
5.6s3294×body5120valid
2.4s10184×body320valid
1.4s8996×body160valid
946.0ms2722×body1280nan
623.0ms2386×body640nan
328.0ms609×body10240exit
217.0ms1209×body320nan
113.0ms8256×pre80true
77.0ms637×body160nan

prune58.1s (21.0%)

Filtered
22670 candidates to 10411 candidates (45.9%)

simplify12.8s (4.6%)

Algorithm
177×egg-herbie

regimes10.7s (3.9%)

Accuracy

Total 50.2b remaining (23.3%)

Threshold costs 4.2b (1.9%)

8.5b29.6%Toniolo and Linder, Equation (13)
7.8b47%Henrywood and Agarwal, Equation (3)
6.5b10.9%Toniolo and Linder, Equation (10+)
5.9b75.1%Toniolo and Linder, Equation (7)
4.7b21.5%Henrywood and Agarwal, Equation (12)

rewrite6.7s (2.4%)

Algorithm
117×rewrite-expression-head
Calls

446 calls:

88.0ms
(* (* (* (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)))
85.0ms
(* (* (* (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))))
68.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
63.0ms
(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x))))))
61.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
40404×add-exp-log
28008×prod-exp
15103×pow-exp
12395×div-exp
7264×pow-to-exp
5373×times-frac
5199×add-sqr-sqrt
5116×*-un-lft-identity
3902×add-cube-cbrt
3449×sqrt-prod
2915×add-cbrt-cube
1655×associate-*l*
1360×cbrt-unprod
1235×cbrt-prod
1207×pow1
1146×associate-*r/
1069×1-exp rec-exp
977×unpow-prod-down
968×associate-*r*
635×frac-times
586×sqrt-div
539×cbrt-undiv
537×add-log-exp
529×associate-*l/
482×distribute-lft-out--
420×unswap-sqr
399×associate-/l*
394×pow-prod-down
369×flip-- flip3--
334×cbrt-div
307×associate-/r*
303×exp-prod
287×distribute-rgt-neg-in
277×sqr-pow
260×pow-unpow
259×distribute-lft-neg-in
258×div-inv
240×distribute-lft-out
233×associate-/r/
217×flip-+ flip3-+
184×difference-of-squares
159×*-commutative
110×distribute-rgt-in distribute-lft-in
108×div-sub
105×tan-quot
100×sqrt-pow1
95×cube-prod
93×pow1/3
89×clear-num frac-2neg
87×pow-sub
77×rem-sqrt-square
74×sub-neg
72×pow1/2
62×swap-sqr
60×unpow2
47×frac-sub
42×log-prod
41×pow-pow
38×associate-/l/
37×neg-mul-1
30×frac-add associate--l+
25×sum-log
23×cube-div
21×+-commutative diff-log
18×distribute-neg-frac
17×rem-cube-cbrt neg-sub0
16×log-pow
14×pow-prod-up pow-sqr
13×pow-flip
10×unpow3 cube-mult distribute-frac-neg
associate--r+
inv-pow pow2 pow-plus
cos-sum associate-+r+
exp-diff rem-exp-log exp-neg
pow-neg distribute-neg-in neg-log rem-log-exp
distribute-rgt-out-- cos-diff sum-cubes log-div
pow-div difference-cubes associate-+l+ un-div-inv unsub-neg associate--l- associate-+r- acos-asin associate--r-
sub-div asin-acos mul0 rem-cbrt-cube distribute-rgt-neg-out

localize2.4s (0.8%)

bsearch1.3s (0.5%)

end1.0ms (0.0%)