Date:Thursday, April 30th, 2020
Commit:56fb38c9 on gh-actions
Hostname:warfa with Racket 7.5
Seed:2020121
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

sample2.2m (46.1%)

Algorithm
100×intervals
Results
46.4s8007×body5120exit
28.9s506880×body80valid
15.9s30496×body1280valid
7.7s23509×body640valid
4.1s3024×body1280nan
3.4s70430×body80nan
2.6s11864×body320valid
2.4s2590×body640nan
1.4s9884×body160valid
913.0ms49536×pre80true
885.0ms1308×body320nan
833.0ms8002×body80overflowed
478.0ms1471×body2560valid
285.0ms674×body160nan
208.0ms612×body5120valid

prune1.0m (22.1%)

Filtered
20344 candidates to 12783 candidates (62.8%)

series1.0m (21.3%)

Calls

468 calls:

2.6s
(fma (/ (/ 1 (/ 1 (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (cbrt (- beta alpha)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.0s
(/ (* (- (* (+ (+ 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))))
1.8s
(/ (* (* (- (* (+ (+ 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))))
859.0ms
(exp (log1p (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))
852.0ms
(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))

simplify15.3s (5.4%)

Algorithm
258×egg-herbie

rewrite5.7s (2.0%)

Algorithm
158×rewrite-expression-head
Calls

468 calls:

394.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
190.0ms
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
153.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
84.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
73.0ms
(* (/ 1 (sqrt (+ (+ (+ (+ (+ (+ 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)))))) (/ (fma 0.0001789971 (* (pow x 2) (* (pow x 2) (* (pow x 2) (* x (pow x 3))))) (fma 0.0005064034 (pow x 8) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* 0.1049934947 x) x 1.0))))) (* (sqrt (+ (+ (+ (+ (+ (+ 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))))) 1)))
Rules
15923×times-frac
13293×*-un-lft-identity
10453×add-sqr-sqrt
8030×add-cube-cbrt
2713×add-exp-log
1928×add-cbrt-cube
1913×distribute-lft-out
1479×pow1
1421×prod-diff
1352×fma-def
1041×sqrt-prod
992×prod-exp
931×associate-*l*
923×associate-/l*
808×difference-of-squares
763×distribute-lft-out-- associate-/r/
756×unpow-prod-down
693×add-log-exp
670×associate-*r*
654×div-exp
643×cbrt-unprod
568×associate-/r*
535×div-inv
470×expm1-log1p-u
469×log1p-expm1-u
460×flip-+ flip3-+
446×pow-prod-down
404×frac-add
345×cbrt-undiv
341×unswap-sqr
287×cbrt-prod
253×associate-*r/
211×log-pow
201×fma-neg
195×frac-times
194×distribute-rgt-in distribute-lft-in
190×sqr-pow
174×flip3-- flip--
172×1-exp
165×pow-exp
150×associate-*l/ exp-sum
148×sqrt-div
144×sqrt-pow1
136×associate--l+
129×cube-prod log-prod
127×*-commutative
117×rec-exp
99×frac-2neg clear-num
96×pow1/2
90×swap-sqr
88×pow1/3
82×sub-neg
78×pow-to-exp
75×diff-log
73×associate-/l/ cbrt-div
72×exp-prod
71×associate--r+
70×pow-unpow
62×pow-prod-up
61×fma-udef
57×associate-+l-
55×pow-sub
54×exp-neg
48×distribute-rgt-neg-in distribute-lft-neg-in
46×sum-log
40×neg-sub0
38×exp-diff
34×pow-pow
32×pow-sqr
28×unpow3 cube-mult neg-mul-1
27×rem-sqrt-square
26×+-commutative
25×associate-+l+
22×un-div-inv
19×pow-flip
17×rem-exp-log
16×div-sub
15×rem-log-exp
14×associate--l- inv-pow hypot-udef
13×pow2 pow-plus hypot-def
12×rem-cube-cbrt
10×neg-log
9×frac-sub
6×cube-div
5×sqrt-unprod log-div
4×log1p-udef sin-sum
3×expm1-def log1p-expm1 difference-of-sqr-1 exp-to-pow
2×sqrt-pow2 distribute-neg-in unpow-prod-up expm1-log1p rem-square-sqrt rem-cbrt-cube distribute-rgt-neg-out expm1-udef
1×distribute-lft-neg-out distribute-frac-neg cos-sum associate--r-

regimes5.1s (1.8%)

Accuracy

Total 48.5b remaining (44.8%)

Threshold costs 4.2b (3.9%)

8.3b33.9%_divideComplex, imaginary part
8.3b46%Octave 3.8, jcobi/4
8.1b27.3%_divideComplex, real part
5.9b9.1%Octave 3.8, jcobi/2
4.4b29%math.sqrt on complex, real part

localize2.6s (0.9%)

bsearch937.0ms (0.3%)

end1.0ms (0.0%)