Date:Monday, March 2nd, 2020
Commit:76ce2b17 on master
Hostname:warfa with Racket 7.5
Seed:2020062
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

series11.8m (81.2%)

Calls

406 calls:

5.0s
(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 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 (* (* (cbrt (* (* (* 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*))))) (cbrt (* (* (* 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*)))))) (cbrt (* (* (* 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*)))))))
1.4s
(* (* (* 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 (9.3%)

Algorithm
60×intervals
Results
15.1s240550×body80valid
14.7s28144×body1280valid
11.1s166976×body80nan
9.1s8968×body2560valid
6.5s18476×body640valid
5.1s3369×body5120valid
2.1s8546×body320valid
1.3s8546×body160valid
871.0ms2579×body1280nan
587.0ms2375×body640nan
333.0ms660×body10240exit
219.0ms1190×body320nan
114.0ms8256×pre80true
66.0ms600×body160nan

prune51.6s (5.9%)

simplify11.4s (1.3%)

Algorithm
170×egg-herbie

regimes9.5s (1.1%)

Accuracy

Total 40.8b remaining (22.7%)

Threshold costs 4.6b (2.6%)

8.0b9.2%Toniolo and Linder, Equation (13)
6.3b-9.3%Toniolo and Linder, Equation (10+)
6.1b73.9%Toniolo and Linder, Equation (7)
6.1b-4.8%Henrywood and Agarwal, Equation (12)
4.6b50.7%Henrywood and Agarwal, Equation (3)

rewrite5.0s (0.6%)

Algorithm
112×rewrite-expression-head
Calls

410 calls:

79.0ms
(* (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0))))))
78.0ms
(* (* (* (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)))
77.0ms
(* (* (* (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))))
66.0ms
(* (* (* (* (/ (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))
63.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
Rules
21864×add-exp-log
14014×prod-exp
6559×pow-exp
6479×div-exp
3892×add-sqr-sqrt
3306×*-un-lft-identity
3025×times-frac
2697×add-cube-cbrt
2657×add-cbrt-cube
2628×pow-to-exp
1916×associate-*r/
1122×associate-*r*
1081×pow1 cbrt-unprod
1041×sqrt-prod
944×cbrt-div
911×unpow-prod-down
908×flip3-- flip--
856×cbrt-prod
817×1-exp
763×frac-times
700×associate-*l*
624×frac-sub
616×cbrt-undiv
607×prod-diff
593×sqrt-div
458×add-log-exp
410×log1p-expm1-u expm1-log1p-u
353×rec-exp
349×associate-*l/
335×pow-prod-down
321×unswap-sqr
306×div-inv
299×associate-/r*
290×associate-/l*
272×sqr-pow
216×pow-unpow
195×distribute-rgt-neg-in
193×distribute-lft-out--
181×difference-of-squares
172×distribute-lft-neg-in
145×distribute-rgt-in distribute-lft-in
143×distribute-lft-out
135×*-commutative
125×associate-/r/
123×exp-sum
121×sqrt-pow1
108×exp-prod
89×flip-+ clear-num flip3-+ frac-2neg
71×tan-quot
70×pow1/3
69×cos-sum
66×pow1/2
65×rem-sqrt-square
60×fma-neg
50×cube-prod
48×sub-neg
41×fma-def
37×pow-pow
32×associate--l+
31×hypot-def
27×log-pow
25×fma-udef
24×associate-/l/ unpow2
23×pow-flip
21×pow-prod-up
19×div-sub neg-mul-1
15×swap-sqr
12×diff-log
11×pow-sqr +-commutative sum-log associate--r+
pow-plus
unpow3 cube-mult neg-sub0 asin-acos
inv-pow
rem-cube-cbrt pow-sub log-prod
exp-diff pow2
pow-div pow-neg un-div-inv frac-add associate--r-
cos-diff hypot-udef
cube-div rem-exp-log associate-+r- unsub-neg associate-+r+ distribute-frac-neg neg-log rem-cbrt-cube distribute-neg-frac exp-to-pow rem-log-exp
associate-+l+ associate--l- sqrt-unprod pow3 exp-neg rem-square-sqrt acos-asin mul0

bsearch3.3s (0.4%)

localize2.2s (0.2%)

end1.0ms (0.0%)