Date:Tuesday, April 14th, 2020
Commit:681051fe on overflow-detection-both-ends
Hostname:warfa with Racket 7.5
Seed:2020105
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

sample2.0m (40.7%)

Algorithm
100×intervals
Results
44.7s7688×body5120exit
23.1s446568×body80valid
16.2s30655×body1280valid
8.1s23731×body640valid
3.9s3019×body1280nan
3.4s70246×body80nan
2.7s11963×body320valid
2.4s2558×body640nan
1.5s10126×body160valid
933.0ms49536×pre80true
866.0ms7910×body80overflowed
810.0ms1218×body320nan
468.0ms1470×body2560valid
286.0ms681×body160nan
202.0ms579×body5120valid

prune1.3m (25.0%)

Filtered
22570 candidates to 14445 candidates (64.0%)

series1.2m (23.4%)

Calls

456 calls:

5.4s
(+ (pow 1.0 3) (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))
2.3s
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
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))))
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))))
939.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))

simplify16.7s (5.5%)

Algorithm
255×egg-herbie

rewrite6.4s (2.1%)

Algorithm
155×rewrite-expression-head
Calls

456 calls:

304.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
190.0ms
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
159.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
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)))))
151.0ms
(* (* (* (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))))
Rules
23437×times-frac
16881×*-un-lft-identity
13026×add-sqr-sqrt
11104×add-cube-cbrt
3132×distribute-lft-out
2814×add-exp-log
2099×add-cbrt-cube
1992×prod-diff
1690×pow1
1430×sqrt-prod
1086×associate-*r*
1048×prod-exp
1024×frac-add
1021×associate-/r/
970×div-inv
952×difference-of-squares
901×associate-*l*
837×unpow-prod-down
702×cbrt-unprod
695×div-exp
685×add-log-exp
660×cube-prod
655×associate-/l*
543×pow-prod-down flip-+ flip3-+
533×associate-/r*
532×cbrt-prod
457×log1p-expm1-u
456×expm1-log1p-u
423×cbrt-undiv
420×associate-*r/
386×frac-times
286×unswap-sqr
275×exp-sum
257×fma-neg
236×distribute-lft-out--
233×associate-*l/
209×distribute-rgt-in distribute-lft-in
198×log-pow
181×sqr-pow
178×sqrt-pow1
163×fma-def
158×associate--l+
142×flip3-- flip--
138×*-commutative
134×1-exp
132×log-prod
118×associate--r+
117×associate-+l-
114×exp-diff
109×pow-sub
108×sqrt-div exp-neg
106×pow-exp
105×sub-neg
104×swap-sqr
96×unpow3 cube-mult
94×frac-2neg clear-num
93×pow-prod-up
90×associate-/l/ neg-sub0
89×diff-log
86×rec-exp
85×pow1/2
84×pow-to-exp
77×exp-prod
74×pow1/3
73×pow-unpow
56×pow-plus
51×distribute-rgt-neg-in distribute-lft-neg-in
50×fma-udef
45×pow-sqr
38×sum-log
36×cbrt-div
31×pow-pow
29×neg-mul-1
27×rem-sqrt-square
22×un-div-inv pow2
19×rem-log-exp
18×pow-flip +-commutative
17×cube-div associate--l-
16×rem-exp-log rem-cube-cbrt associate-+l+ div-sub
14×unpow-prod-up hypot-def
13×inv-pow
12×hypot-udef
11×neg-log
10×log-div
9×rem-cbrt-cube
6×associate-+r+ distribute-neg-in associate--r-
5×sqrt-unprod
4×pow3 sin-sum frac-sub distribute-neg-frac mul-1-neg unpow2
3×rem-square-sqrt distribute-rgt-neg-out exp-to-pow
2×expm1-log1p expm1-udef
1×difference-cubes sqrt-pow2 distribute-lft-neg-out sum-cubes log1p-udef log1p-expm1 distribute-frac-neg log-rec cos-sum distribute-rgt-out--

regimes5.9s (2.0%)

Accuracy

Total 50.7b remaining (46.5%)

Threshold costs 6.3b (5.7%)

9.0b44.6%Octave 3.8, jcobi/4
8.2b31.9%_divideComplex, imaginary part
7.3b35.5%_divideComplex, real part
5.1b19.2%Octave 3.8, jcobi/2
4.4b24.4%math.sqrt on complex, real part

localize2.8s (0.9%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)