Time: 19.7m
Passed: 13/18
Tests: 29
Bits: 199/348
Date:Tuesday, January 22nd, 2019
Commit:45d4082dea7f80b56c44622251112721670e87cb on develop
Hostname:warfa
Points:256
Fuel:4
Seed:2019022
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
TestStartResult ?Target ?∞ ↔ ℝTime
VandenBroeck and Keller, Equation (6)8.57.634.2s»
VandenBroeck and Keller, Equation (24)0.20.222.0s»
VandenBroeck and Keller, Equation (23)13.613.633.4s»
VandenBroeck and Keller, Equation (20)548.0ms»
Toniolo and Linder, Equation (7)42.99.837.4s»
Toniolo and Linder, Equation (3b), real12.69.032.1s»
Toniolo and Linder, Equation (3a)1.61.642.9s»
Toniolo and Linder, Equation (2)10.15.645.3s»
Toniolo and Linder, Equation (13)33.228.71.1m»
Toniolo and Linder, Equation (10-)47.41.82.1m»
Toniolo and Linder, Equation (10+)32.38.11.6m»
Migdal et al, Equation (64)0.50.522.0s»
Migdal et al, Equation (51)0.30.41.2m»
Maksimov and Kolovsky, Equation (4)17.70.431.2s»
Maksimov and Kolovsky, Equation (32)15.31.51.8m»
Maksimov and Kolovsky, Equation (3)17.27.536.8s»
Henrywood and Agarwal, Equation (9a)13.68.327.5s»
Henrywood and Agarwal, Equation (3)18.310.411.0s»
Henrywood and Agarwal, Equation (13)58.033.449.6s»
Henrywood and Agarwal, Equation (12)34.4s»
Falkner and Boettcher, Equation (22+)1.00.043.2s»
Falkner and Boettcher, Equation (20:1,3)0.50.132.8s»
Falkner and Boettcher, Appendix B, 20.00.031.3s»
Falkner and Boettcher, Appendix B, 10.50.527.7s»
Falkner and Boettcher, Appendix A2.00.127.5s»
Bulmash initializePoisson0.00.042.9s»
Bouland and Aaronson, Equation (26)0.20.015.4s»
Bouland and Aaronson, Equation (25)0.20.023.5s»
Bouland and Aaronson, Equation (24)0.20.015.8s»

Details

simplify11.4m

Calls

7286 calls:

Slowest
1.4s
(* (* (* (pow t 3) (sin k)) (sin k)) (- (+ 1 (pow (/ k t) 2)) 1))
1.2s
(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
1.2s
(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
1.1s
(* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v))))))
982.0ms
(sqrt (- (+ 1 (pow (/ k t) 2)) 1))

sample3.9m

Algorithm
55×intervals
Results
51.5s234696×body80valid
50.8s24220×body1280valid
26.7s122320×body80nan
25.9s18293×body640valid
19.7s7127×body2560valid
19.6s8468×body10240exit
13.5s3406×body5120valid
9.5s9018×body320valid
5.1s8636×body160valid
1.0s626×body1280nan
581.0ms637×body640nan
177.0ms335×body320nan
71.0ms205×body160nan

prune2.6m

series47.0s

Calls

391 calls:

Slowest
974.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
698.0ms
(* (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))
617.0ms
(/ x (tan B))
584.0ms
(pow (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (* (cbrt (* (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))))) 1/2)
584.0ms
(pow (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) 1/2)

regimes16.6s

Accuracy

Total 29.6b remaining (19.8%)

6.0b75.1%Toniolo and Linder, Equation (7)
3.7b0%Maksimov and Kolovsky, Equation (3)
3.6b55.6%Toniolo and Linder, Equation (13)
3.1b71.6%Henrywood and Agarwal, Equation (3)
3.0b0%Henrywood and Agarwal, Equation (13)

rewrite4.3s

Algorithm
107×rewrite-expression-head
Calls

391 calls:

Slowest
762.0ms
(pow (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (* (cbrt (* (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))))) 1/2)
186.0ms
(pow (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) 1/2)
128.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
116.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
96.0ms
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
Rules
1904×times-frac
1882×add-sqr-sqrt
1833×*-un-lft-identity
1800×add-cube-cbrt
1211×add-exp-log
948×add-cbrt-cube
804×pow1
538×sqrt-prod
427×add-log-exp
406×div-inv
399×associate-*r*
393×expm1-log1p-u
391×log1p-expm1-u
354×prod-exp
354×associate-*r/
347×associate-/r*
341×unpow-prod-down
282×associate-/l*
279×associate-*l*
235×cbrt-unprod
210×pow-prod-down
204×associate-*l/
200×prod-diff
197×sub-neg
195×frac-times
188×unpow-prod-up
179×div-exp
171×cbrt-prod
160×associate-/r/
156×distribute-rgt-in
156×distribute-lft-in
145×sqrt-div
135×flip3--
135×flip--
130×flip-+
130×flip3-+
118×*-commutative
110×pow-to-exp
107×cbrt-undiv
96×exp-sum
96×frac-2neg
96×clear-num
89×cbrt-div
77×pow-exp
75×unpow2
67×distribute-rgt-neg-in
65×distribute-lft-neg-in
61×rem-sqrt-square
59×tan-quot
57×fma-neg
55×pow1/2
54×fma-udef
50×pow-unpow
42×associate-/l/
40×frac-sub
38×pow-pow
37×fma-def
34×pow1/3
32×pow-sub
24×neg-mul-1
16×div-sub
16×pow-prod-up
15×rec-exp
13×pow-plus
13×distribute-lft-out--
11×pow-flip
11×neg-sub0
11×associate--l+
11×pow2
10×+-commutative
9×sum-log
9×inv-pow
9×diff-log
8×associate-+r+
7×difference-of-squares
7×distribute-frac-neg
7×un-div-inv
6×distribute-lft-out
6×cos-sum
6×distribute-neg-frac
6×hypot-udef
5×unpow3
5×associate--r+
5×cube-mult
4×acos-asin
3×associate-+l+
3×associate-+r-
3×unpow1/2
3×pow3
3×cos-diff
3×unsub-neg
2×expm1-log1p
2×expm1-udef
2×distribute-rgt-neg-out
2×log1p-expm1
2×neg-log
2×difference-of-sqr-1
2×associate--l-
2×asin-acos
2×rem-cbrt-cube
2×frac-add
2×associate--r-
2×sin-mult
2×log1p-udef
1×sqrt-undiv
1×mul0
1×sqrt-unprod
1×hypot-def
1×rem-square-sqrt
1×expm1-def

bsearch3.2s

localize2.9s

end23.0ms