Date:Thursday, April 23rd, 2020
Commit:38368d1c on better-rr
Hostname:warfa with Racket 7.5
Seed:2020114
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

rewrite23.8m (56.2%)

Algorithm
109×rewrite-expression-head
Calls

409 calls:

1.5m
(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l))))))
4.7s
(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))))))
3.3s
(* (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
1.2s
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
727.0ms
(sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l)))
Rules
2845090×add-sqr-sqrt
2390541×cbrt-prod
1664743×unswap-sqr
941923×times-frac
616598×sqrt-prod
343205×associate-*r*
279352×*-un-lft-identity
212840×associate-*r/
208648×sqrt-div
204040×frac-times
191976×swap-sqr
177366×associate-/l*
149978×unpow-prod-down
120688×add-cube-cbrt
114557×associate-/r*
96528×associate-*l*
70210×*-commutative
69625×sqr-pow
36422×add-exp-log
24164×prod-exp
16056×unpow2
15724×pow-exp
14683×div-exp
9057×clear-num
8911×frac-2neg
7282×difference-of-squares
6698×pow-to-exp
6507×prod-diff
6479×associate-*l/
3416×distribute-lft-out
2993×rec-exp 1-exp
2690×distribute-rgt-in distribute-lft-in
2541×distribute-lft-out--
2028×add-cbrt-cube
1194×pow1
934×associate-/l/
927×div-inv
744×distribute-rgt-neg-in
742×cbrt-unprod
717×distribute-lft-neg-in
695×rem-sqrt-square
553×associate-/r/
525×cos-sum
455×add-log-exp
438×flip3-- flip--
408×log1p-expm1-u
407×expm1-log1p-u
394×cbrt-undiv
386×associate--l+
384×associate-+r+
346×pow-prod-down
341×un-div-inv
277×flip-+ flip3-+
243×pow-unpow
211×neg-mul-1
166×hypot-def
148×sqrt-pow1
129×fma-neg
118×div-sub
110×fma-def pow-sub
84×pow1/2
69×pow1/3
68×difference-cubes
60×pow-prod-up
59×tan-quot
52×associate-+l+
49×sub-neg
44×+-commutative
36×pow-sqr
31×pow-pow
28×fma-udef
25×pow-plus
20×pow2
19×neg-sub0
16×frac-sub
14×sum-log
13×cbrt-div
12×pow-neg
11×diff-log associate--r+
pow-flip remove-double-div
distribute-frac-neg
inv-pow
cos-diff acos-asin distribute-neg-frac
sqrt-unprod hypot-udef
rem-cube-cbrt associate-+r- pow3 distribute-lft-neg-out expm1-log1p unsub-neg sqrt-undiv neg-log
unpow3 expm1-udef associate--l- rem-square-sqrt asin-acos associate--r- distribute-rgt-neg-out

prune10.5m (24.9%)

Filtered
489915 candidates to 255446 candidates (47.9%)

simplify4.0m (9.4%)

Algorithm
164×egg-herbie

series2.5m (6.0%)

Calls

407 calls:

50.2s
(/ (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
10.4s
(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.9s
(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.9s
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

sample1.3m (3.0%)

Algorithm
58×intervals
Results
15.2s228395×body80valid
14.1s27646×body1280valid
10.4s143679×body80nan
8.5s7054×body2560valid
6.5s19304×body640valid
3.9s1026×body5120valid
2.1s9099×body320valid
1.3s8639×body160valid
921.0ms2647×body1280nan
628.0ms2378×body640nan
227.0ms1223×body320nan
118.0ms8256×pre80true
77.0ms619×body160nan
22.0ms47×body10240exit

regimes8.7s (0.3%)

Accuracy

Total 35.3b remaining (30.2%)

Threshold costs 5.0b (4.3%)

12.0b10%Toniolo and Linder, Equation (13)
7.3b-4.6%Henrywood and Agarwal, Equation (12)
5.3b78%Toniolo and Linder, Equation (7)
4.2b12.9%Toniolo and Linder, Equation (10-)
1.6b0%Given's Rotation SVD example

localize2.2s (0.1%)

bsearch1.9s (0.1%)

end1.0ms (0.0%)