Details

simplify15.8m (40.2%)

series11.1m (28.3%)

Calls

460 calls:

1.6s
(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
1.2s
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
1.2s
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
1.1s
(* (* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (* (/ (pow (+ (- 7 z) 0.5) (/ (- (- 1 z) (- 1 0.5)) 2)) 1) (/ (pow (+ (- 7 z) 0.5) (/ (- (- 1 z) (- 1 0.5)) 2)) (exp (+ (- 7 z) 0.5))))) (+ (+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (+ (/ -176.6150291621406 (- 4 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (+ 2 (- 1 z))) (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))))
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))

sample5.3m (13.6%)

Algorithm
99×intervals
Results
1.7m16272×body10240exit
1.3m442304×body80valid
48.2s29549×body1280valid
25.2s23233×body640valid
11.2s69965×body80nan
10.6s3119×body1280nan
7.9s11721×body320valid
6.6s2645×body640nan
5.0s9944×body160valid
2.7s1328×body320nan
2.2s41536×pre80true
1.7s1443×body2560valid
1.1s618×body5120valid
808.0ms657×body160nan

prune3.5m (9.0%)

rewrite3.2m (8.1%)

Algorithm
156×rewrite-expression-head
Calls

464 calls:

1.1m
(* (* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (* (/ (pow (+ (- 7 z) 0.5) (/ (- (- 1 z) (- 1 0.5)) 2)) 1) (/ (pow (+ (- 7 z) 0.5) (/ (- (- 1 z) (- 1 0.5)) 2)) (exp (+ (- 7 z) 0.5))))) (+ (+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (+ (/ -176.6150291621406 (- 4 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (+ 2 (- 1 z))) (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))))
21.7s
(/ (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))) (sqrt (exp (+ (- z -6) 0.5))))
18.4s
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (sqrt (exp (+ (- z -6) 0.5)))) (/ (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))) (sqrt (exp (+ (- z -6) 0.5)))))
18.1s
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
15.3s
(* (* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
Rules
55916×*-un-lft-identity
49344×times-frac
22246×add-sqr-sqrt
21879×distribute-lft-out
19006×add-cube-cbrt
13231×sqrt-prod
5945×add-exp-log
5409×pow1
4145×frac-add
4093×frac-times
3615×flip-+ flip3-+
3367×associate-*r*
3072×prod-diff
2685×add-cbrt-cube
2532×prod-exp
2147×div-exp
2058×pow-prod-up
1959×associate-*r/
1906×associate-*l*
1577×associate-*l/
1411×associate-/r/
1263×div-inv
1042×exp-sum
1006×cbrt-div
1003×pow-plus
976×pow-prod-down
967×cbrt-unprod
858×log-prod
839×associate-/l*
783×sqrt-div
706×associate-/r*
680×unswap-sqr
664×sqrt-pow1
634×cbrt-undiv
587×add-log-exp
575×pow-sqr
465×log1p-expm1-u
464×expm1-log1p-u insert-posit16
450×1-exp
424×swap-sqr
423×difference-of-squares
394×rec-exp
390×distribute-lft-out--
379×pow2
360×cbrt-prod
333×distribute-rgt-in distribute-lft-in
316×log-pow
277×associate-/l/
260×unpow-prod-up
232×pow-exp
190×pow-div
175×*-commutative
166×frac-sub
165×flip3-- flip--
163×pow1/2
159×fma-neg
157×associate-+l-
156×pow-to-exp
153×pow-flip
149×unpow-prod-down
148×inv-pow
143×pow-sub
133×fma-def
104×pow1/3
87×associate-+l+
86×frac-2neg clear-num
80×sub-neg
72×associate--r+
68×exp-prod
60×associate--l+
59×cube-unmult
57×sqr-pow
51×associate-+r+
49×fma-udef
42×pow3
36×distribute-rgt-out
35×sum-log
31×cube-prod
30×diff-log
29×+-commutative
28×distribute-rgt1-in
24×rem-sqrt-square
19×exp-diff
17×distribute-rgt-neg-in
16×distribute-lft-neg-in
15×cube-div
12×un-div-inv
10×hypot-def rem-log-exp
9×pow-unpow
8×div-sub
7×sqrt-unprod associate--r- log-div
6×rem-square-sqrt
4×sin-sum sqrt-undiv pow-pow hypot-udef cos-sum rem-cbrt-cube count-2
3×rem-cube-cbrt distribute-lft1-in
2×distribute-lft-neg-out associate-+r- unpow3 neg-mul-1 distribute-neg-frac rem-exp-log cube-mult
1×expm1-log1p expm1-udef neg-sub0 log1p-expm1 neg-log distribute-rgt-out-- log1p-udef unsub-neg

regimes10.6s (0.4%)

Accuracy

Total 26.4b remaining (19.4%)

Threshold costs 6.4b (4.7%)

8.0b30.6%_divideComplex, real part
3.4b73.1%Octave 3.8, jcobi/1
2.8b0%Octave 3.8, jcobi/4
2.6b0%_divideComplex, imaginary part
1.2b53.9%Octave 3.8, jcobi/3

localize8.3s (0.4%)

bsearch1.4s (0.1%)

end1.0ms (0.0%)