Date:Thursday, February 27th, 2020
Commit:17a4275c on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020058
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

rewrite10.4m (70.4%)

Algorithm
159×rewrite-expression-head
Calls

480 calls:

6.7s
(* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
3.9s
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
3.9s
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
803.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
415.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
Rules
44294×times-frac
35113×*-un-lft-identity
18994×add-sqr-sqrt
18020×add-cube-cbrt
9903×distribute-lft-out
3602×sqrt-prod
2467×add-exp-log
1814×add-cbrt-cube
1710×prod-diff
1511×pow1
1335×associate-/r/
1294×div-inv
872×associate-/l*
832×prod-exp
750×associate-*r*
744×add-log-exp
686×associate-*l*
657×flip-+ flip3-+
642×div-exp
529×cbrt-unprod
523×associate-/r*
481×log1p-expm1-u
479×expm1-log1p-u
465×cbrt-prod
394×pow-prod-down
381×distribute-rgt-in distribute-lft-in
354×cbrt-undiv
343×log-pow
300×unpow-prod-down
261×log-prod
236×fma-neg
229×difference-of-squares
228×distribute-lft-out--
206×unswap-sqr
189×exp-sum
187×associate--l+
177×cube-prod
170×distribute-rgt-neg-in 1-exp
162×distribute-lft-neg-in
153×fma-def
152×flip3-- flip--
149×sqrt-pow1
123×*-commutative
116×exp-prod
115×associate-*r/
114×swap-sqr
104×pow1/2 rec-exp
95×sub-neg
90×pow1/3
88×clear-num frac-2neg
84×associate-*l/
82×diff-log
81×associate-/l/
79×pow-unpow
78×sqr-pow
77×frac-times
74×frac-add
72×pow-prod-up pow-exp
65×sqrt-div
58×fma-udef
57×exp-neg
55×exp-diff
54×neg-sub0
50×pow-to-exp
47×neg-mul-1
46×associate-+l+
44×pow-sqr
43×sum-log
42×cbrt-div exp-to-pow
37×pow-pow
29×+-commutative
28×rem-sqrt-square
25×unpow3 cube-mult
24×pow-plus
23×distribute-rgt-out
21×rem-log-exp
20×rem-cube-cbrt pow2 pow-flip
19×distribute-neg-in div-sub associate--l-
17×associate-+r+
16×inv-pow
14×un-div-inv
13×distribute-rgt1-in
12×hypot-udef hypot-def
11×cube-div
10×rem-exp-log
8×neg-log associate--r+ log-div
6×sqrt-unprod unpow2
5×distribute-lft1-in rem-square-sqrt
4×log1p-udef sin-sum log1p-expm1 expm1-log1p expm1-udef
3×rem-cbrt-cube associate-+l-
2×sqrt-pow2 distribute-rgt-out-- pow3 distribute-lft-neg-out frac-sub distribute-rgt-neg-out
1×unpow-prod-up pow-sub unsub-neg distribute-frac-neg log-rec cos-sum associate--r- associate-+r-

sample1.7m (11.4%)

Algorithm
99×intervals
Results
42.8s11886×body10240exit
19.2s460328×body80valid
11.9s27581×body1280valid
5.0s20733×body640valid
2.5s69453×body80nan
1.7s1627×body1280nan
1.6s10624×body320valid
1.0s9394×body160valid
896.0ms1261×body640nan
661.0ms49536×pre80true
344.0ms677×body320nan
342.0ms1462×body2560valid
149.0ms627×body5120valid
102.0ms301×body160nan

prune1.3m (8.6%)

Filtered
26529 candidates to 14659 candidates (55.3%)

series59.5s (6.7%)

Calls

478 calls:

2.0s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
1.9s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
822.0ms
(log (/ (pow (* -2.0 (log u1)) 0.5) 6.0))
781.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
761.0ms
(* (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))

simplify17.2s (1.9%)

Algorithm
257×egg-herbie

regimes5.1s (0.6%)

Accuracy

Total 46.5b remaining (41.8%)

Threshold costs 4.5b (4%)

8.1b33.8%_divideComplex, imaginary part
7.8b32.2%_divideComplex, real part
5.8b16.1%Octave 3.8, jcobi/2
4.8b54.2%Octave 3.8, jcobi/4
4.4b67.8%Octave 3.8, jcobi/1

localize2.5s (0.3%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)