Time: 31.6m
Passed: 13/19
Tests: 29
Bits: 209/348
Date:Tuesday, January 22nd, 2019
Commit:45d4082dea7f80b56c44622251112721670e87cb on develop
Hostname:warfa
Points:256
Fuel:4
Seed:2019022
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
TestStartResult ?Target ?∞ ↔ ℝTime
VandenBroeck and Keller, Equation (6)8.50.828.5s»
VandenBroeck and Keller, Equation (24)0.20.216.8s»
VandenBroeck and Keller, Equation (23)13.60.229.0s»
VandenBroeck and Keller, Equation (20)503.0ms»
Toniolo and Linder, Equation (7)42.97.637.7s»
Toniolo and Linder, Equation (3b), real12.612.732.2s»
Toniolo and Linder, Equation (3a)1.61.642.7s»
Toniolo and Linder, Equation (2)10.15.645.7s»
Toniolo and Linder, Equation (13)33.228.52.0m»
Toniolo and Linder, Equation (10-)47.41.82.1m»
Toniolo and Linder, Equation (10+)32.38.71.8m»
Migdal et al, Equation (64)0.50.526.7s»
Migdal et al, Equation (51)0.30.41.1m»
Maksimov and Kolovsky, Equation (4)17.70.445.9s»
Maksimov and Kolovsky, Equation (32)15.31.51.3m»
Maksimov and Kolovsky, Equation (3)17.213.241.5s»
Henrywood and Agarwal, Equation (9a)13.68.327.8s»
Henrywood and Agarwal, Equation (3)18.310.48.5s»
Henrywood and Agarwal, Equation (13)58.033.41.2m»
Henrywood and Agarwal, Equation (12)31.2s»
Falkner and Boettcher, Equation (22+)1.00.01.0m»
Falkner and Boettcher, Equation (20:1,3)10.0m»
Falkner and Boettcher, Appendix B, 20.00.017.9s»
Falkner and Boettcher, Appendix B, 10.50.51.6m»
Falkner and Boettcher, Appendix A2.01.913.9s»
Bulmash initializePoisson0.00.045.5s»
Bouland and Aaronson, Equation (26)0.20.013.1s»
Bouland and Aaronson, Equation (25)0.20.029.5s»
Bouland and Aaronson, Equation (24)0.20.034.8s»

Details

simplify15.4m

Calls

9090 calls:

Slowest
1.2s
(* (* (* K (- (* m m) (* n n))) (* K (- (* m m) (* n n)))) (* K (- (* m m) (* n n))))
1.2s
(* (* (* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) 1)) (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) 1))) (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) 1))) (* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2))))
1.2s
(/ (* (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
967.0ms
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
943.0ms
(* (* (* (/ (* (* (pow t 3) (pow t 3)) (pow t 3)) (* (* (* l l) (* l l)) (* l l))) (* (* (sin k) (sin k)) (sin k))) (* (* (tan k) (tan k)) (tan k))) (* (* (+ (+ 1 (pow (/ k t) 2)) 1) (+ (+ 1 (pow (/ k t) 2)) 1)) (+ (+ 1 (pow (/ k t) 2)) 1)))

sample3.9m

Algorithm
54×intervals
Results
55.0s226695×body80valid
50.2s24220×body1280valid
27.3s18293×body640valid
24.0s114323×body80nan
19.9s8468×body10240exit
16.5s7127×body2560valid
13.8s3406×body5120valid
9.5s9018×body320valid
4.8s8636×body160valid
1.0s626×body1280nan
862.0ms637×body640nan
198.0ms335×body320nan
105.0ms205×body160nan

prune2.8m

series47.2s

Calls

398 calls:

Slowest
1.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))
813.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes17.9s

Accuracy

Total 29.7b remaining (21.5%)

8.4b10.5%Toniolo and Linder, Equation (13)
4.7b80.9%Toniolo and Linder, Equation (7)
3.1b0%Henrywood and Agarwal, Equation (13)
3.1b71.6%Henrywood and Agarwal, Equation (3)
2.5b68%Toniolo and Linder, Equation (10+)

rewrite5.2s

Algorithm
105×rewrite-expression-head
Calls

398 calls:

Slowest
316.0ms
(cbrt (* (* (* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2))) (* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2)))) (* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2)))))
145.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
131.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
126.0ms
(* (* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2))) (* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2))))
94.0ms
(* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
Rules
19284×times-frac
8576×add-sqr-sqrt
8556×*-un-lft-identity
7517×add-cube-cbrt
6437×sqrt-prod
3984×cbrt-prod
1407×associate-/r/
1170×add-exp-log
1098×associate-*r/
1068×pow1
1058×cbrt-div
953×div-inv
925×add-cbrt-cube
867×flip3--
867×flip--
715×sqrt-div
625×frac-times
562×associate-*r*
562×associate-*l/
496×distribute-lft-out--
490×difference-of-squares
481×flip-+
481×difference-cubes
481×flip3-+
468×add-log-exp
457×associate-/r*
359×associate-/l*
335×prod-exp
318×associate-*l*
299×pow-prod-down
298×unpow-prod-down
234×cbrt-unprod
211×sub-neg
200×frac-sub
188×pow-prod-up
188×unpow-prod-up
173×div-exp
162×frac-add
135×*-commutative
133×distribute-rgt-in
133×distribute-lft-in
124×pow-to-exp
105×associate-/l/
105×cbrt-undiv
99×pow1/2
96×exp-sum
93×frac-2neg
93×clear-num
91×pow-plus
90×tan-quot
80×unpow2
64×pow-exp
64×rem-sqrt-square
50×pow-unpow
49×pow2
47×pow1/3
33×pow-pow
32×pow-sub
27×sum-log
26×distribute-lft-out
25×associate--l+
23×rec-exp
19×+-commutative
16×associate--r+
13×pow-flip
12×inv-pow
11×diff-log
10×associate-+r+
9×div-sub
8×sqrt-unprod
7×unpow3
7×un-div-inv
7×cube-mult
6×cos-sum
6×difference-of-sqr-1
5×pow3
4×associate--l-
3×rem-square-sqrt
3×acos-asin
3×cos-diff
3×rem-cbrt-cube
3×associate-+l-
2×associate-+l+
2×neg-sub0
2×asin-acos
2×associate--r-
2×sqrt-undiv
2×neg-log
2×distribute-rgt-neg-in
1×mul0

localize3.3s

bsearch2.8s

end1.0ms