Details

rewrite12.7m (30.5%)

Algorithm
155×rewrite-expression-head
Calls

452 calls:

2.2m
(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
2.0m
(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
1.5m
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (* (* (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))) (pow (+ 0.5 (- z -6)) (- z 1))) (pow (+ 0.5 (- z -6)) 0.5)))
58.7s
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
56.4s
(* (* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
Rules
153210×times-frac
88107×add-sqr-sqrt
72422×*-un-lft-identity
67314×sqrt-prod
50655×add-cube-cbrt
18406×difference-of-squares
16832×frac-add
11628×frac-times
10128×flip-+ flip3-+
9362×distribute-lft-out--
8313×associate-/r/
7049×associate-*l/
6061×associate-*r/
4886×add-exp-log
4747×frac-sub
4697×div-inv
2819×pow1
2473×prod-exp
2373×add-cbrt-cube
1872×flip3-- flip--
1826×distribute-lft-out
1610×prod-diff
1405×div-exp
1369×associate-*r*
1006×associate-*l*
953×associate-/l*
863×cbrt-unprod
860×add-log-exp
754×pow-sub
663×pow-prod-down
646×associate-/r*
583×pow-prod-up
521×pow-exp
465×unpow-prod-down
453×expm1-log1p-u
452×cbrt-undiv insert-posit16 1-exp rec-exp log1p-expm1-u
437×distribute-rgt-in distribute-lft-in
349×log-pow
324×cube-prod
302×pow-plus
301×unswap-sqr
270×sub-div
249×sum-log
243×pow-to-exp
221×sqrt-div
186×fma-neg
175×sqr-pow
168×*-commutative
167×fma-def
151×pow-sqr
144×exp-sum
123×unpow-prod-up
113×sqrt-pow1
111×pow-flip
109×cbrt-prod
102×frac-2neg clear-num swap-sqr
98×pow2
88×cube-mult
87×unpow3
86×associate-/l/
84×un-div-inv
82×inv-pow
76×sub-neg
75×pow1/2
74×fma-udef
50×pow1/3
48×log-prod
46×cbrt-div
39×diff-log
33×distribute-rgt-out
28×distribute-rgt1-in
27×+-commutative pow-unpow
26×rem-cube-cbrt cube-unmult
24×rem-sqrt-square
22×pow-div
19×div-sub
18×pow3 exp-prod
17×pow-pow
14×associate-+l+
12×sqrt-unprod exp-to-pow
9×hypot-udef hypot-def
7×cube-div rem-log-exp
6×distribute-lft-neg-in associate--l+ associate--r+ distribute-rgt-neg-in
4×expm1-udef sin-sum associate-+r+ cos-sum associate-+l- associate--r-
3×exp-diff associate-+r- rem-cbrt-cube
2×expm1-log1p distribute-lft1-in difference-cubes neg-mul-1 sub0-neg distribute-neg-in count-2
1×distribute-lft-neg-out associate--l- distribute-rgt-neg-out log1p-expm1 distribute-rgt-out-- rem-square-sqrt remove-posit16 log1p-udef unsub-neg log-div

prune9.9m (23.8%)

simplify9.7m (23.4%)

series6.2m (14.9%)

Calls

452 calls:

4.8m
(- (pow (pow 1 3) 3) (pow (* (sqrt (pow (* (/ (/ 1 (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) 3)) (sqrt (pow (* (/ (/ 1 (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) 3))) 3))
3.4s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))))
2.8s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
1.7s
(* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5))
1.3s
(/ 1 (* (pow -2 1.0) (pow (log u1) 1.0)))

sample2.8m (6.7%)

Algorithm
100×intervals
Results
51.0s441618×body80valid
32.3s30975×body1280valid
27.3s13048×body10240exit
17.4s23328×body640valid
7.4s69380×body80nan
5.4s11920×body320valid
3.4s2028×body1280nan
2.4s9830×body160valid
1.9s49536×pre80true
1.7s1684×body640nan
1.4s1464×body2560valid
785.0ms632×body5120valid
574.0ms835×body320nan
204.0ms412×body160nan

regimes8.9s (0.4%)

Accuracy

Total 29.7b remaining (21.6%)

Threshold costs 5.3b (3.8%)

8.9b18.7%_divideComplex, real part
6.6b39%_divideComplex, imaginary part
3.5b72%Octave 3.8, jcobi/1
2.0b24%Octave 3.8, jcobi/4
1.2b0%Jmat.Real.gamma, branch z greater than 0.5

localize7.2s (0.3%)

bsearch938.0ms (0.0%)

end1.0ms (0.0%)