Time: 25.7m
Passed: 13/18
Tests: 29
Bits: 190/373
Date:Wednesday, January 16th, 2019
Commit:4ad0fa0d8ea811155e6236e8b72b9505c4bb3dd0 on develop
Hostname:warfa
Points:256
Fuel:4
Seed:2019016
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)8.58.132.9s»
VandenBroeck and Keller, Equation (24)0.20.220.6s»
VandenBroeck and Keller, Equation (23)13.313.233.2s»
VandenBroeck and Keller, Equation (20)8.7s»
Toniolo and Linder, Equation (7)42.710.139.5s»
Toniolo and Linder, Equation (3b), real12.18.534.7s»
Toniolo and Linder, Equation (3a)1.71.724.7s»
Toniolo and Linder, Equation (2)10.210.258.0s»
Toniolo and Linder, Equation (13)33.427.71.3m»
Toniolo and Linder, Equation (10-)47.218.51.6m»
Toniolo and Linder, Equation (10+)32.58.11.8m»
Migdal et al, Equation (64)0.50.523.8s»
Migdal et al, Equation (51)0.40.41.0m»
Maksimov and Kolovsky, Equation (4)17.40.633.8s»
Maksimov and Kolovsky, Equation (32)14.91.31.4m»
Maksimov and Kolovsky, Equation (3)17.69.225.6s»
Henrywood and Agarwal, Equation (9a)13.68.831.4s»
Henrywood and Agarwal, Equation (3)18.16.216.2s»
Henrywood and Agarwal, Equation (13)58.133.753.1s»
Henrywood and Agarwal, Equation (12)25.714.71.3m»
Falkner and Boettcher, Equation (22+)1.00.04.5m»
Falkner and Boettcher, Equation (20:1,3)0.40.11.1m»
Falkner and Boettcher, Appendix B, 20.00.01.2m»
Falkner and Boettcher, Appendix B, 10.60.634.9s»
Falkner and Boettcher, Appendix A2.00.143.9s»
Bulmash initializePoisson0.00.050.2s»
Bouland and Aaronson, Equation (26)0.20.012.9s»
Bouland and Aaronson, Equation (25)0.20.030.5s»
Bouland and Aaronson, Equation (24)0.20.020.1s»

Details

simplify15.8m

Calls

8938 calls:

Slowest
1.3s
(* (* (* (pow t 3) (sin k)) (sin k)) (- (+ 1 (pow (/ k t) 2)) 1))
1.3s
(/ (cbrt (/ (/ (sqrt (/ (/ 64/27 PI) (* PI PI))) (- 1 (* v v))) (- 1 (* v v)))) (sqrt (fma -6 (* v v) 2)))
1.3s
(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
1.3s
(/ (cbrt (/ (/ (cbrt (/ (/ 64/27 PI) (* PI PI))) (- 1 (* v v))) (- 1 (* v v)))) (sqrt (fma -6 (* v v) 2)))
1.3s
(* (* (* (* a a) (* a a)) (* a a)) (* (* (+ 1 a) (+ 1 a)) (+ 1 a)))

sample4.7m

Algorithm
56×intervals
Results
489776×(pre true 80)
247320×(body real 80)
160964×(body nan 80)
24307×(body real 1280)
18264×(body real 640)
9206×(body real 320)
8861×(body real 160)
8579×(body exit 10240)
7116×(body real 2560)
3347×(body real 5120)
643×(body nan 640)
626×(body nan 1280)
351×(body nan 320)
192×(body nan 160)

prune2.9m

series48.3s

Calls

401 calls:

Slowest
1.6s
(sqrt (pow (* (* 2 (* U n)) (- t (fma (* (/ l Om) (- U U*)) (* n (/ l Om)) (* (* 2 l) (/ l Om))))) 1))
1.3s
(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 (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
887.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
653.0ms
(/ (sqrt (/ (/ (fma v (* v -5) 1) PI) (sqrt (fma v (* v -6) 2)))) t)

regimes17.5s

Accuracy

Total 50.2b remaining (27.4%)

9.8b5.3%Toniolo and Linder, Equation (13)
6.6b17.8%Toniolo and Linder, Equation (10-)
6.5b56.5%Henrywood and Agarwal, Equation (12)
6.2b73.7%Toniolo and Linder, Equation (7)
5.3b-41.4%Maksimov and Kolovsky, Equation (3)

bsearch14.6s

rewrite4.5s

Algorithm
108×rewrite-expression-head
Calls

401 calls:

Slowest
185.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
159.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
92.0ms
(/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)
87.0ms
(/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)
81.0ms
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
Rules
4148×times-frac
2770×add-sqr-sqrt
2704×*-un-lft-identity
2671×add-cube-cbrt
1450×sqrt-prod
1220×add-exp-log
984×add-cbrt-cube
765×pow1
642×div-inv
522×cbrt-prod
499×associate-*r*
449×add-log-exp
411×associate-/l*
402×log1p-expm1-u
401×expm1-log1p-u
356×associate-*r/
336×associate-*l*
328×prod-exp
324×associate-/r/
320×associate-/r*
301×associate-*l/
297×frac-times
260×flip--
260×flip3--
225×cbrt-unprod
215×sqrt-div
205×prod-diff
196×div-exp
193×unpow-prod-down
183×pow-prod-down
125×cbrt-undiv
124×*-commutative
121×sub-neg
111×flip-+
111×flip3-+
106×distribute-rgt-in
106×distribute-lft-in
98×frac-2neg
98×clear-num
95×pow-to-exp
82×unpow-prod-up
76×distribute-rgt-neg-in
74×distribute-lft-neg-in
68×tan-quot
66×fma-neg
64×pow-exp
64×frac-sub
64×rem-sqrt-square
62×pow1/2
49×associate-/l/
48×fma-def
38×unpow2
35×cbrt-div
34×pow-unpow
33×pow1/3
30×rec-exp
26×div-sub
26×fma-udef
25×exp-prod
24×pow-sub
22×pow-pow
22×neg-mul-1
18×pow-prod-up
16×cos-sum
15×neg-sub0
15×pow2
15×associate--l+
14×exp-diff
14×distribute-lft-out--
14×+-commutative
14×distribute-neg-frac
11×sum-log
11×difference-of-squares
11×pow-plus
10×associate-+r+
10×diff-log
9×distribute-frac-neg
8×pow-flip
8×asin-acos
8×cos-diff
7×inv-pow
6×unpow3
6×cube-mult
6×rem-exp-log
4×associate-+r-
4×associate--r+
4×unsub-neg
4×associate--r-
3×associate-+l+
3×distribute-lft-out
3×expm1-udef
3×log-prod
3×hypot-udef
3×un-div-inv
2×expm1-log1p
2×neg-log
2×difference-of-sqr-1
2×associate--l-
2×log-pow
2×frac-add
2×sin-mult
1×mul0
1×exp-neg
1×pow3
1×sqrt-unprod
1×sub-div
1×rem-log-exp
1×associate-+l-
1×hypot-def
1×rem-square-sqrt
1×acos-asin
1×expm1-def

localize3.0s

end1.0ms