Date:Thursday, March 5th, 2020
Commit:a3b4d238 on findroot
Hostname:warfa with Racket 7.5
Seed:2020065
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

series3.4m (47.0%)

Calls

484 calls:

1.8m
(- (pow 1.0 3) (/ (pow (* (* 1.0 (* (- 1.0 (* 0.3275911 (fabs x))) (- (* 0.254829592 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))))) (exp (- (* (fabs x) (fabs x))))) 3) (pow (* (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))) (- 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) 3)))
21.7s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
2.3s
(- 1.0 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))))
2.2s
(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
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))))

sample2.0m (28.0%)

Algorithm
100×intervals
Results
49.2s16071×body10240exit
23.4s513131×body80valid
14.2s30418×body1280valid
6.8s23657×body640valid
2.9s3105×body1280nan
2.6s71370×body80nan
2.2s12029×body320valid
1.8s2629×body640nan
1.2s10037×body160valid
805.0ms49536×pre80true
639.0ms1278×body320nan
350.0ms1410×body2560valid
216.0ms677×body160nan
138.0ms597×body5120valid

prune1.2m (16.8%)

simplify19.7s (4.6%)

Algorithm
257×egg-herbie

rewrite6.3s (1.5%)

Algorithm
157×rewrite-expression-head
Calls

484 calls:

152.0ms
(* (* (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)))))
150.0ms
(* (* (* (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 1.0) 1.0))) (/ -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))))
146.0ms
(* (* (* (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))))
143.0ms
(/ (* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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))))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
132.0ms
(* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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)))))
Rules
7110×*-un-lft-identity
6526×times-frac
6348×add-sqr-sqrt
4930×add-cube-cbrt
3016×add-exp-log
2284×prod-diff
1975×add-cbrt-cube
1636×frac-add
1527×pow1
1370×sqrt-prod
1154×associate-*r*
1122×prod-exp
940×associate-*l*
905×distribute-lft-out
888×unpow-prod-down
827×div-exp
774×frac-times associate-*r/
717×cube-prod
709×add-log-exp
588×associate-/r*
568×cbrt-unprod
533×flip-+ flip3-+
485×log1p-expm1-u expm1-log1p-u
450×associate-/l*
422×cbrt-undiv
416×sqr-pow
381×associate-/r/
361×pow-prod-down
340×difference-of-squares
317×unpow3 cube-mult
316×div-inv
302×cbrt-prod
298×unswap-sqr
287×flip3-- flip--
283×distribute-lft-out--
262×associate-*l/
249×fma-def
247×distribute-rgt-in distribute-lft-in
244×sqrt-div
240×1-exp
225×exp-sum
213×associate-+l-
207×pow-sub
197×log-pow pow-exp
191×fma-neg
189×swap-sqr
176×sqrt-pow1
173×exp-neg
156×cube-div
148×*-commutative
143×exp-diff
142×rec-exp
140×neg-sub0
116×associate-/l/ pow-to-exp
108×pow1/2
104×log-prod
97×frac-2neg clear-num
95×associate--l+
91×cbrt-div sub-neg
83×pow-prod-up pow1/3
75×diff-log
70×pow-unpow
60×exp-prod
58×pow-sqr
50×fma-udef
48×sum-log
44×rem-sqrt-square
38×un-div-inv
35×pow-plus
34×pow-pow
30×distribute-rgt-neg-in distribute-lft-neg-in pow2
27×+-commutative
23×neg-mul-1
21×pow-flip
18×hypot-def
17×rem-cube-cbrt associate-+l+ inv-pow
16×div-sub
15×hypot-udef
11×rem-exp-log associate--l-
8×sqrt-unprod
7×rem-log-exp
6×neg-log frac-sub associate--r+
5×unpow2
4×sin-sum unpow-prod-up associate-+r+ rem-square-sqrt
2×sqrt-pow2 log1p-udef log1p-expm1 distribute-neg-in expm1-log1p distribute-rgt-neg-out expm1-udef log-div
1×difference-cubes sum-cubes associate--r- cos-sum

regimes5.9s (1.4%)

Accuracy

Total 41.7b remaining (31.8%)

Threshold costs 5.8b (4.5%)

8.2b32%_divideComplex, imaginary part
8.2b35%_divideComplex, real part
5.9b9.1%Octave 3.8, jcobi/2
4.4b23%math.sqrt on complex, imaginary part, im greater than 0 branch
4.4b33.2%math.sqrt on complex, real part

localize2.6s (0.6%)

bsearch974.0ms (0.2%)

end1.0ms (0.0%)