Date:Sunday, March 15th, 2020
Commit:1a959946 on master
Hostname:warfa with Racket 7.5
Seed:2020075
Parameters:256 points for 4 iterations
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

Details

prune1.9m (33.2%)

Filtered
41473 candidates to 18777 candidates (45.3%)

series1.7m (29.7%)

Calls

441 calls:

5.1s
(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*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- 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*))))))
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*)))))

sample1.4m (24.6%)

Algorithm
61×intervals
Results
16.0s30740×body1280valid
15.7s250029×body80valid
10.8s168017×body80nan
9.1s8908×body2560valid
7.5s20910×body640valid
5.4s3269×body5120valid
2.5s10686×body320valid
1.4s9084×body160valid
886.0ms2672×body1280nan
574.0ms2320×body640nan
353.0ms683×body10240exit
225.0ms1282×body320nan
112.0ms8256×pre80true
69.0ms620×body160nan

simplify17.2s (5.0%)

Algorithm
173×egg-herbie

rewrite11.4s (3.3%)

Algorithm
113×rewrite-expression-head
Calls

441 calls:

1.3s
(* (/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
238.0ms
(/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
89.0ms
(/ (sqrt 2.0) (/ (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (sqrt 2.0)))
82.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
81.0ms
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
Rules
72826×times-frac
52833×sqrt-prod
46096×add-exp-log
33499×add-sqr-sqrt
32777×*-un-lft-identity
31771×add-cube-cbrt
31720×prod-exp
17326×pow-exp
15475×div-exp
9905×associate-*l*
8714×pow-to-exp
3185×add-cbrt-cube
1810×1-exp rec-exp
1534×cbrt-unprod
1512×div-inv
1227×unpow-prod-down
1164×pow1
868×cbrt-prod
801×associate-*r*
670×cbrt-undiv
641×associate-/r*
565×associate-*r/
531×add-log-exp
455×associate-*l/
435×associate-/l*
434×unswap-sqr
422×frac-times
377×pow-prod-down
351×distribute-lft-out
324×sqr-pow
261×associate-/r/
255×sqrt-div
244×pow-unpow
233×difference-of-squares
221×cube-prod
198×flip-+ flip3-+
178×flip3-- flip--
152×distribute-lft-out--
142×*-commutative
127×tan-quot
103×sqrt-pow1
97×pow1/3
88×clear-num frac-2neg
85×distribute-rgt-in distribute-lft-in
75×distribute-rgt-neg-in
72×pow1/2
70×sub-neg
67×rem-sqrt-square exp-prod
63×distribute-lft-neg-in
59×unpow3 cube-mult
57×unpow2
50×cbrt-div
46×swap-sqr
42×frac-sub
41×pow-pow
32×sum-log
31×associate--l+
27×associate-/l/
26×div-sub
24×frac-add
22×+-commutative
19×pow-sub pow-flip
16×diff-log
13×pow-prod-up associate-+r+
11×pow-sqr
10×distribute-neg-frac
neg-mul-1
inv-pow
neg-sub0
pow-plus pow2 log-pow associate-+r-
cube-div rem-cube-cbrt associate-+l+ pow-neg distribute-neg-in exp-sum
asin-acos rem-cbrt-cube log-prod
pow-div cos-sum exp-diff distribute-frac-neg acos-asin
un-div-inv rem-exp-log sqrt-unprod exp-neg cos-diff unsub-neg rem-square-sqrt sub-div mul0 distribute-rgt-neg-out rem-log-exp

regimes10.6s (3.1%)

Accuracy

Total 39.9b remaining (19.7%)

Threshold costs 3.6b (1.8%)

7.3b17.9%Toniolo and Linder, Equation (13)
6.9b7.6%Toniolo and Linder, Equation (10+)
5.9b75.5%Toniolo and Linder, Equation (7)
5.1b0%Henrywood and Agarwal, Equation (12)
3.0b36%Toniolo and Linder, Equation (10-)

localize2.3s (0.7%)

bsearch1.6s (0.5%)

end1.0ms (0.0%)