Date:Tuesday, February 25th, 2020
Commit:4d1e59da on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020056
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 (71.0%)

Algorithm
152×rewrite-expression-head
Calls

448 calls:

9.5m
(/ (* (* (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)))
7.1s
(* (/ (+ (+ (+ (+ (+ 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)
4.1s
(/ (+ (+ (+ (+ (+ 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)))))
1.1s
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
1.1s
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
Rules
6893×*-un-lft-identity
6568×times-frac
5912×add-sqr-sqrt
4837×add-cube-cbrt
2691×add-exp-log
1965×add-cbrt-cube
1535×prod-diff
1497×pow1
1313×sqrt-prod
1072×prod-exp
871×distribute-lft-out
851×associate-*r*
789×associate-*l*
705×cbrt-unprod
660×add-log-exp
616×div-exp
595×associate-/l*
506×pow-prod-down
449×log1p-expm1-u
446×expm1-log1p-u
389×associate-/r*
373×associate-/r/
347×div-inv
334×cbrt-undiv
333×flip-+ flip3-+
289×unpow-prod-down
253×cbrt-prod
243×difference-of-squares
242×unswap-sqr
234×distribute-lft-out--
232×fma-neg
225×distribute-rgt-in distribute-lft-in
218×associate-*r/
215×fma-def
194×log-pow
182×sqrt-div
169×exp-sum
148×1-exp
136×associate--l+
127×sqr-pow associate-*l/
125×*-commutative flip3-- flip--
112×cube-prod frac-times
92×log-prod
91×clear-num frac-2neg
90×sub-neg
89×pow-exp
79×associate-/l/
76×frac-add diff-log
75×sqrt-pow1
72×cbrt-div
71×associate--r+
70×swap-sqr
67×rec-exp
66×fma-udef
63×pow-to-exp
61×pow1/3
54×exp-prod
53×pow1/2
52×pow-unpow
41×sum-log
39×pow-prod-up
34×unpow3 cube-mult
30×+-commutative
27×rem-sqrt-square
25×pow-sqr pow-plus div-sub
24×distribute-rgt-neg-in distribute-lft-neg-in
22×neg-mul-1
18×pow-pow
17×associate-+l+ hypot-udef
16×pow2
15×pow-flip
14×associate--l-
12×associate-+r+ hypot-def
11×inv-pow
rem-cube-cbrt
rem-exp-log
log1p-udef sqrt-unprod log1p-expm1 rem-log-exp
exp-diff rem-cbrt-cube distribute-rgt-neg-out associate-+l-
sqrt-undiv sin-sum distribute-neg-in expm1-log1p frac-sub expm1-udef unpow2
sqrt-pow2 un-div-inv pow3 rem-square-sqrt neg-sub0 neg-log log-div
distribute-lft-neg-out unpow-prod-up pow-sub unsub-neg cos-sum associate--r-

sample1.7m (11.5%)

Algorithm
98×intervals
Results
44.1s11865×body10240exit
18.1s438149×body80valid
11.3s27353×body1280valid
5.2s21229×body640valid
2.6s69933×body80nan
1.7s1629×body1280nan
1.6s10546×body320valid
1.1s9479×body160valid
952.0ms1344×body640nan
680.0ms49536×pre80true
350.0ms1394×body2560valid
335.0ms659×body320nan
152.0ms593×body5120valid
109.0ms326×body160nan

series1.2m (8.3%)

Calls

445 calls:

2.4s
(cbrt (- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))
2.3s
(cbrt (- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))
1.9s
(/ (* (* (- (* (+ (+ 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))))
1.5s
(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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))))))
1.4s
(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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))))))

prune58.2s (6.6%)

Filtered
16674 candidates to 10645 candidates (63.8%)

simplify14.2s (1.6%)

Algorithm
248×egg-herbie

regimes5.1s (0.6%)

Accuracy

Total 40.8b remaining (29%)

Threshold costs 6.2b (4.4%)

9.0b31.9%_divideComplex, imaginary part
7.4b33.4%_divideComplex, real part
5.9b9.9%Octave 3.8, jcobi/2
4.1b26.8%math.sqrt on complex, imaginary part, im greater than 0 branch
3.9b38.1%math.sqrt on complex, real part

localize2.6s (0.3%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)