Date:Tuesday, April 14th, 2020
Commit:681051fe on overflow-detection-both-ends
Hostname:warfa with Racket 7.5
Seed:2020105
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 (31.9%)

Calls

446 calls:

5.0s
(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*)))))
4.6s
(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*)))))
4.5s
(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*))))

sample1.6m (31.2%)

Algorithm
61×intervals
Results
19.7s248900×body80valid
17.8s30618×body1280valid
13.8s167260×body80nan
9.1s8723×body2560valid
8.6s21181×body640valid
5.4s3312×body5120valid
2.9s10232×body320valid
1.7s9204×body160valid
817.0ms1609×body1280nan
542.0ms1462×body640nan
387.0ms3108×body80overflowed
373.0ms595×body5120exit
206.0ms779×body320nan
145.0ms8256×pre80true
62.0ms388×body160nan

prune1.2m (24.4%)

Filtered
27741 candidates to 13869 candidates (50.0%)

simplify14.4s (4.7%)

Algorithm
176×egg-herbie

regimes11.3s (3.7%)

Accuracy

Total 51.7b remaining (25.2%)

Threshold costs 4.9b (2.4%)

9.0b33.1%Toniolo and Linder, Equation (13)
8.0b0.4%Toniolo and Linder, Equation (10+)
7.3b48.5%Henrywood and Agarwal, Equation (3)
5.8b75.8%Toniolo and Linder, Equation (7)
5.7b-17.5%Toniolo and Linder, Equation (10-)

rewrite8.4s (2.7%)

Algorithm
116×rewrite-expression-head
Calls

446 calls:

1.2s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
77.0ms
(/ 2.0 (* (* (* (/ (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)))
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)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
74.0ms
(* (* (* (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)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
69.0ms
(* (* (* (/ (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))
Rules
45691×add-exp-log
29333×prod-exp
21579×times-frac
16635×div-exp
14677×pow-exp
12035×add-sqr-sqrt
11120×*-un-lft-identity
10254×add-cube-cbrt
7481×pow-to-exp
4821×unpow-prod-down
4567×sqrt-prod
4529×associate-*r*
3195×add-cbrt-cube
2164×cbrt-prod
1767×1-exp
1457×cbrt-unprod
1303×rec-exp
1249×associate-*l*
1228×pow1
1045×sqr-pow
634×cbrt-undiv
616×associate-*r/
568×add-log-exp
566×associate-/l*
505×frac-times
488×unswap-sqr
487×associate-*l/
454×div-inv
417×pow-prod-down
414×unpow2
413×associate-/r*
360×pow-unpow
317×sqrt-div
316×distribute-lft-out
288×difference-of-squares
232×flip3-- flip--
207×flip-+ flip3-+
200×associate-/r/
199×exp-prod
190×distribute-lft-out--
163×cube-prod
161×*-commutative
151×distribute-rgt-neg-in
137×tan-quot
122×sqrt-pow1
109×log-pow
108×distribute-rgt-in distribute-lft-in
101×clear-num frac-2neg
98×cbrt-div
96×distribute-lft-neg-in
93×sub-neg
54×pow-pow
50×rem-sqrt-square
48×pow1/2
45×frac-sub
44×exp-diff frac-add
43×associate-/l/ sum-log
42×div-sub
37×log-div
31×+-commutative
30×associate--l+
29×log-prod
28×pow-sub pow1/3
23×cube-div
22×diff-log
17×neg-sub0
16×rem-cube-cbrt associate-+r+
15×unpow3 cube-mult
12×neg-mul-1
11×pow-neg
10×cos-sum
inv-pow pow-flip
un-div-inv asin-acos exp-sum rem-log-exp
difference-cubes rem-exp-log
associate-+r- cos-diff unsub-neg
neg-log distribute-neg-frac associate--r+
associate-+l+ associate--r-
associate--l- distribute-frac-neg sqrt-undiv associate-+l-
pow-div acos-asin mul0 rem-cbrt-cube distribute-rgt-neg-out

localize2.3s (0.7%)

bsearch2.0s (0.7%)

end0.0ms (0.0%)