Date:Tuesday, February 25th, 2020
Commit:61e80a61 on faster-rr
Hostname:warfa with Racket 7.5
Seed:2020056
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

series2.0m (41.3%)

Calls

447 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*)))))
4.8s
(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 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 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.7s
(sqrt (* (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*))))) (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*)))))))

sample1.3m (26.9%)

Algorithm
61×intervals
Results
15.6s29517×body1280valid
15.4s253719×body80valid
9.6s159891×body80nan
8.9s8828×body2560valid
7.1s20160×body640valid
5.2s3336×body5120valid
2.4s9513×body320valid
1.3s8943×body160valid
446.0ms741×body10240exit
158.0ms676×body1280nan
111.0ms586×body640nan
104.0ms8256×pre80true
46.0ms342×body320nan
20.0ms197×body160nan

prune1.0m (20.8%)

simplify12.7s (4.3%)

Algorithm
178×egg-herbie

regimes10.6s (3.6%)

Accuracy

Total 36.8b remaining (19.3%)

Threshold costs 4.4b (2.3%)

8.9b3.1%Toniolo and Linder, Equation (13)
6.3b0%Henrywood and Agarwal, Equation (12)
5.6b76.6%Toniolo and Linder, Equation (7)
3.9b44.4%Toniolo and Linder, Equation (10-)
2.7b0%Toniolo and Linder, Equation (10+)

rewrite5.8s (2.0%)

Algorithm
118×rewrite-expression-head
Calls

447 calls:

234.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
97.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
93.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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)))
47.0ms
(/ a (/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow (cbrt k) m)) (pow (* (cbrt k) (cbrt k)) m)))
40.0ms
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
Rules
32904×add-exp-log
23736×prod-exp
12902×pow-exp
9336×div-exp
7493×times-frac
6746×add-sqr-sqrt
5784×*-un-lft-identity
5343×pow-to-exp
4860×add-cube-cbrt
3357×sqrt-prod
2591×add-cbrt-cube
2096×1-exp
2068×rec-exp
1483×unpow-prod-down
1343×pow1
1138×prod-diff
1111×associate-*r*
989×cbrt-unprod
832×associate-*l*
661×cbrt-prod
574×associate-/r*
551×difference-of-squares
550×cbrt-undiv
546×associate-*r/
519×add-log-exp
518×sqr-pow
494×pow-prod-down
448×log1p-expm1-u
447×expm1-log1p-u
418×pow-unpow
416×div-inv
413×sqrt-div
373×associate-/l*
369×flip3-- flip--
327×unswap-sqr
303×distribute-lft-out--
274×distribute-rgt-neg-in
267×associate-/r/
236×sqrt-pow1
228×distribute-lft-neg-in
225×distribute-lft-out
215×frac-times
172×distribute-rgt-in distribute-lft-in
141×*-commutative
124×fma-neg
117×associate-*l/
97×frac-2neg clear-num
94×frac-sub
91×unpow2
73×fma-def
70×flip-+ exp-prod flip3-+
61×pow1/2
59×pow1/3
57×sub-neg
52×hypot-def
50×rem-sqrt-square
45×pow-pow
42×associate--l+
35×associate-/l/ div-sub
31×fma-udef
30×pow-prod-up log-prod
25×cos-sum
24×neg-mul-1
22×pow-sqr swap-sqr tan-quot associate--r+
21×cube-prod
20×diff-log
17×+-commutative sum-log
16×frac-add
15×pow-sub
13×log-pow pow-flip
12×neg-sub0
inv-pow
unpow1/3
cbrt-div
exp-diff
expm1-log1p expm1-udef
pow-neg associate-+r- pow2 unsub-neg neg-log asin-acos distribute-neg-frac rem-log-exp
rem-exp-log unpow3 unpow-prod-up hypot-udef cube-mult acos-asin exp-sum
un-div-inv associate--l- sin-sum pow-plus distribute-frac-neg associate--r-
rem-cube-cbrt sqrt-undiv associate-+l+ e-exp-1 log1p-udef log1p-expm1 cos-diff mul0 rem-cbrt-cube

localize2.3s (0.8%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)