Details

simplify34.7m

Calls

10611 calls:

Slowest
2.3s
(/ (/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)))
2.3s
(/ (/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)))
2.0s
(/ (/ (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)))
1.9s
(* 1 (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (pow (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ z 1))) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (+ (/ -176.6150291621406 (+ z 3)) (+ (/ -0.13857109526572012 (- z -5)) (/ 12.507343278686905 (+ z 4))))) 3) (pow (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) 3))))
1.9s
(/ (/ (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)))

sample9.0m

Algorithm
89×intervals
Results
6.4m99178×body10240exit
1.2m402276×body80valid
26.2s22952×body1280valid
13.2s17867×body640valid
10.0s69421×body80nan
6.6s1573×body1280nan
4.3s9643×body320valid
3.9s1305×body640nan
2.5s49536×pre80true
1.9s1383×body2560valid
1.7s673×body320nan
1.6s5012×body160valid
539.0ms631×body5120valid
418.0ms325×body160nan

prune3.6m

series53.7s

Calls

416 calls:

Slowest
6.0s
(- (pow 1 3) (pow (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))) 3))
3.8s
(+ (* (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))) (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))) (* 1 (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))))
1.5s
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
1.5s
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
926.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite21.1s

Algorithm
143×rewrite-expression-head
Calls

416 calls:

Slowest
3.0s
(* (* (sqrt (* PI 2)) (pow (+ (- z -6) 0.5) z)) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ -1259.1392167224028 (+ z 1)) (+ (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ 12.507343278686905 (+ 4 z))) (+ (/ -0.13857109526572012 (+ z 5)) (/ -176.6150291621406 (+ z 3)))) (/ 771.3234287776531 (+ z 2))))))
1.7s
(* (exp (- (+ (- z -6) 0.5))) (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ z 1))) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (+ (/ -176.6150291621406 (+ z 3)) (+ (/ -0.13857109526572012 (- z -5)) (/ 12.507343278686905 (+ z 4))))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
1.6s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.5s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.5s
(/ (* (* (sqrt (* PI 2)) (pow (+ (- z -6) 0.5) z)) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ -1259.1392167224028 (+ z 1)) (+ (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ 12.507343278686905 (+ 4 z))) (+ (/ -0.13857109526572012 (+ z 5)) (/ -176.6150291621406 (+ z 3)))) (/ 771.3234287776531 (+ z 2)))))) (* (exp (+ (- z -6) 0.5)) (pow (+ (- z -6) 0.5) (- 1 0.5))))
Rules
4844×times-frac
3586×*-un-lft-identity
3539×add-sqr-sqrt
3537×frac-add
3460×add-cube-cbrt
1575×add-exp-log
1529×frac-times
1508×flip-+ flip3-+
1177×associate-*r/
1080×add-cbrt-cube
1048×pow1
983×associate-*l/
827×sqrt-prod
648×associate-*l*
611×prod-diff
561×associate-*r*
514×add-log-exp
489×prod-exp
486×associate-/r*
454×div-inv
426×associate-/l*
416×expm1-log1p-u insert-posit16 log1p-expm1-u
395×associate-+l-
392×pow-sub
346×associate-/r/
332×div-exp
322×cbrt-div
314×unpow-prod-down
285×cube-prod
271×exp-diff
268×exp-neg neg-sub0
233×cbrt-prod
231×cbrt-unprod
199×cbrt-undiv
195×pow-prod-down
155×pow-prod-up
141×rec-exp
134×flip3-- associate-/l/ flip--
132×fma-def
120×*-commutative
118×cube-mult
117×unpow3
104×pow-div
99×fma-neg
89×frac-2neg clear-num
86×sub-neg
79×sqrt-div
74×distribute-rgt-in distribute-lft-in
73×pow-flip inv-pow
72×pow1/3
71×pow-exp
68×distribute-lft-out
64×log-pow
62×pow1/2 fma-udef
61×pow-to-exp
55×pow-plus
43×pow2
35×difference-of-squares
34×+-commutative
32×log-prod
30×exp-prod
29×associate--l+
28×exp-sum
27×sum-log
26×diff-log
22×frac-sub
19×rem-sqrt-square
18×un-div-inv
16×distribute-lft-out-- div-sub
14×distribute-rgt-out
13×associate-+l+ pow-pow
12×associate--l- sin-sum
11×distribute-rgt1-in difference-of-sqr-1 expm1-def
hypot-def
cube-unmult pow3 sqrt-unprod
rem-cube-cbrt difference-cubes
neg-mul-1 cube-div
associate-+r+ rem-log-exp rem-cbrt-cube
unpow-prod-up associate-+r- associate--r+ rem-square-sqrt
sum-cubes rem-exp-log unsub-neg
remove-posit16 distribute-lft1-in hypot-udef cos-sum distribute-neg-in associate--r- distribute-rgt-out-- log-div

regimes6.8s

Accuracy

Total 28.9b remaining (21.9%)

8.9b20.3%_divideComplex, imaginary part
5.9b3.7%Octave 3.8, jcobi/2
2.9b77.8%Octave 3.8, jcobi/1
2.9b2.9%Octave 3.8, jcobi/4
2.6b0%_divideComplex, real part

localize3.9s

bsearch1.1s

end1.0ms