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: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 (42.3%)

Calls

421 calls:

14.2s
(pow E (log (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
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*)))))
4.6s
(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*)))))

sample1.4m (29.7%)

Algorithm
61×intervals
Results
15.9s30777×body1280valid
15.7s248736×body80valid
10.9s165823×body80nan
8.9s8852×body2560valid
7.4s21159×body640valid
5.2s3300×body5120valid
2.4s10281×body320valid
1.4s9179×body160valid
884.0ms2617×body1280nan
599.0ms2363×body640nan
361.0ms722×body10240exit
218.0ms1210×body320nan
114.0ms8256×pre80true
74.0ms664×body160nan

prune46.5s (16.5%)

Filtered
20698 candidates to 10180 candidates (49.2%)

simplify11.9s (4.2%)

Algorithm
175×egg-herbie

regimes10.6s (3.8%)

Accuracy

Total 39.6b remaining (22.7%)

Threshold costs 4.2b (2.4%)

9.8b20.6%Toniolo and Linder, Equation (13)
6.0b20.2%Toniolo and Linder, Equation (10+)
5.2b78%Toniolo and Linder, Equation (7)
5.1b6.7%Henrywood and Agarwal, Equation (12)
4.6b35.4%Toniolo and Linder, Equation (10-)

rewrite5.2s (1.8%)

Algorithm
115×rewrite-expression-head
Calls

421 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))))
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 (/ 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))))
57.0ms
(* (* (* (* (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))
51.0ms
(* (/ (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
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))
Rules
34326×add-exp-log
24518×prod-exp
11852×pow-exp
9319×div-exp
5381×pow-to-exp
4124×add-sqr-sqrt
3800×*-un-lft-identity
3311×times-frac
3086×add-cube-cbrt
2581×add-cbrt-cube
1363×rec-exp 1-exp
1300×pow1
1205×cbrt-unprod
1062×associate-*r*
1000×unpow-prod-down
881×sqrt-prod
816×associate-*r/
768×associate-*l*
721×sqrt-div
682×prod-diff
645×cbrt-prod
498×frac-times
479×add-log-exp
475×pow-prod-down
423×cbrt-undiv
421×log1p-expm1-u expm1-log1p-u
388×flip3-- flip--
379×associate-*l/
367×associate-/l*
325×pow-unpow
311×associate-/r*
262×div-inv
256×distribute-rgt-neg-in
249×cbrt-div
248×sqr-pow
241×unswap-sqr
238×distribute-rgt-in distribute-lft-in
228×distribute-lft-neg-in
225×difference-of-squares
221×distribute-lft-out--
187×distribute-lft-out
171×associate-/r/
155×*-commutative
144×cube-prod
101×sqrt-pow1
90×frac-2neg clear-num
87×flip-+ flip3-+
73×tan-quot
71×fma-neg sub-neg
69×cos-sum
62×pow1/2
52×associate--l+
50×fma-udef
49×fma-def pow-pow
44×log-prod
38×associate-/l/ rem-sqrt-square
32×frac-sub
31×swap-sqr
30×unpow2
24×neg-mul-1
23×pow1/3
22×div-sub associate--r+
20×unpow3 cube-mult exp-sum
18×diff-log unpow-prod-up
17×pow-prod-up log-pow
16×exp-prod
14×sum-log
13×hypot-def
12×pow-sub
11×pow-sqr +-commutative neg-sub0 associate-+r+
7×pow-flip
5×pow-neg un-div-inv inv-pow asin-acos
4×cube-div frac-add hypot-udef neg-log distribute-neg-frac
3×rem-cube-cbrt sqrt-unprod associate-+r- cos-diff pow-plus associate--r- rem-cbrt-cube pow2
2×associate--l- unsub-neg rem-square-sqrt distribute-frac-neg acos-asin rem-log-exp log-div
1×rem-exp-log exp-diff sqrt-undiv associate-+l+ e-exp-1 sum-cubes mul0

bsearch2.5s (0.9%)

localize2.0s (0.7%)

end0.0ms (0.0%)