Date:Saturday, April 11th, 2020
Commit:a26a9b61 on overflow-detection-both-ends
Hostname:warfa with Racket 7.5
Seed:2020102
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 (35.8%)

Calls

444 calls:

4.8s
(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 (* (* (* 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 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*)))))

sample1.6m (34.3%)

Algorithm
61×intervals
Results
19.6s247959×body80valid
17.6s31001×body1280valid
13.8s167437×body80nan
9.5s8828×body2560valid
8.3s20885×body640valid
5.1s3333×body5120valid
2.8s10422×body320valid
1.7s9387×body160valid
1.1s2790×body1280nan
718.0ms2326×body640nan
381.0ms599×body5120exit
280.0ms1262×body320nan
162.0ms8256×pre80true
86.0ms626×body160nan
57.0ms703×body80overflowed

prune49.7s (17.7%)

Filtered
20639 candidates to 10593 candidates (51.3%)

simplify13.0s (4.6%)

Algorithm
177×egg-herbie

regimes10.7s (3.8%)

Accuracy

Total 38.1b remaining (20.3%)

Threshold costs 4.8b (2.6%)

11.3b5.2%Toniolo and Linder, Equation (13)
6.2b73.6%Toniolo and Linder, Equation (7)
4.2b41.9%Henrywood and Agarwal, Equation (12)
3.3b61.1%Toniolo and Linder, Equation (10+)
2.6b49.9%Toniolo and Linder, Equation (10-)

rewrite5.9s (2.1%)

Algorithm
117×rewrite-expression-head
Calls

444 calls:

164.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))
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 (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 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 (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt 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 (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
65.0ms
(/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
Rules
30614×add-exp-log
21176×prod-exp
10491×pow-exp
8945×div-exp
8014×times-frac
5783×add-sqr-sqrt
5506×*-un-lft-identity
5386×pow-to-exp
4841×add-cube-cbrt
2525×add-cbrt-cube
2202×sqrt-prod
1200×associate-*r*
1183×pow1
1157×associate-*l*
987×cbrt-unprod
776×1-exp rec-exp
712×unpow-prod-down
573×associate-/l*
544×add-log-exp
518×associate-*r/
487×cbrt-prod
466×cbrt-undiv
400×div-inv
396×sqrt-div
378×associate-/r*
357×pow-prod-down
315×unswap-sqr
274×frac-times
273×associate-*l/
262×pow-unpow
230×associate-/r/
212×flip3-- flip--
202×flip-+ flip3-+
195×sqr-pow
194×distribute-lft-out--
175×distribute-lft-out
148×exp-prod
145×*-commutative
133×difference-of-squares
107×sqrt-pow1
102×clear-num frac-2neg
89×distribute-rgt-in distribute-lft-in
86×log-pow
83×tan-quot
80×pow1/3
79×sub-neg
72×pow1/2 cbrt-div
67×swap-sqr
62×distribute-lft-neg-in div-sub distribute-rgt-neg-in
54×pow-sub
52×rem-sqrt-square frac-sub
47×unpow2
45×associate--l+
43×log-prod
38×cube-prod
36×pow-flip
35×pow-pow
32×frac-add
28×associate-/l/
27×diff-log
25×pow-prod-up sum-log
19×pow-sqr
18×+-commutative
12×cos-sum associate--r+
10×exp-sum log-div
rem-log-exp
inv-pow neg-mul-1 associate-+r+
pow-plus pow2
exp-diff cos-diff
rem-cube-cbrt neg-sub0
unpow3 pow-neg cube-mult unpow-prod-up exp-to-pow
associate--l- acos-asin asin-acos
cube-div rem-exp-log associate-+r- sqrt-unprod rem-square-sqrt distribute-frac-neg distribute-neg-frac
associate-+l+ e-exp-1 un-div-inv exp-neg sub-div mul0 rem-cbrt-cube

bsearch2.2s (0.8%)

localize2.2s (0.8%)

end1.0ms (0.0%)