Date:Tuesday, February 18th, 2020
Commit:5d186d9c on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020049
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

series1.8m (36.3%)

Calls

431 calls:

4.9s
(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)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.8s
(sqrt (+ (* (* (* 2.0 n) U) (fma (* (cbrt (- t (* 2.0 (* l (/ l Om))))) (cbrt (- t (* 2.0 (* l (/ l Om)))))) (cbrt (- t (* 2.0 (* l (/ l Om))))) (- (* (- U U*) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))))) (* (* (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (+ (- (- U U*)) (- U U*))) 2.0) (* U n))))
1.8s
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

sample1.3m (27.5%)

Algorithm
61×intervals
Results
15.7s29179×body1280valid
15.5s252801×body80valid
9.9s161396×body80nan
8.8s8842×body2560valid
7.3s20532×body640valid
5.6s3369×body5120valid
2.4s9820×body320valid
1.3s9079×body160valid
457.0ms792×body10240exit
160.0ms658×body1280nan
123.0ms647×body640nan
100.0ms8256×pre80true
53.0ms371×body320nan
18.0ms194×body160nan

prune1.0m (21.2%)

rewrite17.3s (5.9%)

Algorithm
117×rewrite-expression-head
Calls

431 calls:

747.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))) (* M M))))
683.0ms
(/ (+ (pow 1.0 3) (pow (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) 3)) (fma (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (- (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) 1.0) (* 1.0 1.0)))
668.0ms
(* (/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
663.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
662.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
50810×add-exp-log
36229×prod-exp
25764×pow-exp
19027×div-exp
11864×pow-to-exp
8564×times-frac
6198×add-sqr-sqrt
5993×*-un-lft-identity
4871×add-cube-cbrt
3936×rec-exp 1-exp
2812×add-cbrt-cube
1888×sqrt-prod
1499×associate-*l*
1179×unpow-prod-down
1144×cbrt-unprod
1113×associate-*r*
1101×pow1
714×cbrt-prod
697×associate-*r/
644×cbrt-undiv
634×prod-diff
502×add-log-exp
453×sqrt-div div-inv
431×log1p-expm1-u expm1-log1p-u
420×distribute-lft-out--
412×associate-/r*
365×exp-prod
348×distribute-rgt-neg-in
340×pow-prod-down
333×unswap-sqr
317×associate-/l*
308×distribute-lft-neg-in flip3-- flip--
301×sqr-pow
284×pow-unpow
268×frac-times
256×cbrt-div
242×associate-/r/
236×difference-of-squares
233×distribute-lft-out
173×cos-sum
156×associate-*l/
154×distribute-rgt-in distribute-lft-in
150×*-commutative
101×pow-pow
88×clear-num frac-2neg
78×flip-+ flip3-+
67×fma-neg
62×pow1/3 sqrt-pow1
57×sub-neg
55×fma-def cube-prod
45×pow1/2 rem-sqrt-square
38×neg-mul-1
35×fma-udef div-sub
32×associate--l+
30×associate-/l/ unpow2
25×tan-quot
24×frac-sub
22×swap-sqr associate--r+
19×diff-log
17×exp-diff
15×neg-sub0 hypot-def sum-log
13×log-pow unpow3 cube-mult +-commutative
12×pow-sub pow-flip
11×log-prod
10×un-div-inv
inv-pow pow-sqr pow-prod-up
rem-exp-log
distribute-frac-neg
exp-neg
cube-div pow-neg associate-+r+ associate-+r- pow2 sum-cubes neg-log frac-add hypot-udef unsub-neg pow-plus acos-asin
associate-+l+ expm1-log1p asin-acos expm1-udef rem-log-exp
rem-cube-cbrt cos-diff associate--l- associate--r- exp-sum rem-cbrt-cube distribute-neg-frac
sin-sum log1p-udef log1p-expm1 mul0 exp-to-pow

simplify13.4s (4.6%)

Algorithm
177×egg-herbie

regimes10.0s (3.4%)

Accuracy

Total 42.5b remaining (20.7%)

Threshold costs 6.1b (3%)

11.3b-9.8%Toniolo and Linder, Equation (13)
6.4b0%Toniolo and Linder, Equation (10-)
6.1b75%Toniolo and Linder, Equation (7)
4.9b0%Henrywood and Agarwal, Equation (12)
2.5b0%Toniolo and Linder, Equation (10+)

localize2.2s (0.8%)

bsearch1.1s (0.4%)

end1.0ms (0.0%)