Details

simplify48.9m

Calls

19685 calls:

Slowest
2.3s
(* (* (/ (* (* (* 0.5 0.5) 0.5) (* (* (cos re) (cos re)) (cos re))) (* (* (exp im) (exp im)) (exp im))) (/ (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp im) (exp im)) (exp im)))) (/ (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp im) (exp im)) (exp im))))
2.2s
(/ (* (* (* (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)))))
2.0s
(* (+ (* (* x.re x.re) (* x.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (- (* x.re x.im) (* x.im x.re)))
1.9s
(* (* (/ (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp im) (exp im)) (exp im))) (/ (* (* (* 0.5 0.5) 0.5) (* (* (cos re) (cos re)) (cos re))) (* (* (exp im) (exp im)) (exp im)))) (/ (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp im) (exp im)) (exp im))))
1.8s
(* (* (/ (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp im) (exp im)) (exp im))) (* (* (/ (* 0.5 (cos re)) (exp im)) (/ (* 0.5 (cos re)) (exp im))) (/ (* 0.5 (cos re)) (exp im)))) (/ (* (* (* 0.5 0.5) 0.5) (* (* (cos re) (cos re)) (cos re))) (* (* (exp im) (exp im)) (exp im))))

sample9.3m

Algorithm
88×intervals
Results
6.5m100747×body10240exit
1.1m390535×body80valid
27.3s22569×body1280valid
13.4s18278×body640valid
12.7s70229×body80nan
6.7s1534×body1280nan
5.2s9699×body320valid
4.4s8963×body160valid
4.0s1394×body640nan
1.4s683×body320nan
1.4s33536×pre80true
1.1s1394×body2560valid
637.0ms586×body5120valid
485.0ms316×body160nan

prune4.5m

series1.2m

Calls

412 calls:

Slowest
3.2s
(* (/ 1 (/ (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
1.6s
(pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5)
1.1s
(/ (pow (* -2 (log u1)) 0.5) 6)
1.0s
(- 1 (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (+ 0.254829592 (+ (- (/ 1.421413741 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (* (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.453152027 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 0.284496736))) (/ 1.061405429 (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))))) (exp (* (fabs x) (fabs x)))))
1.0s
(- 1 (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (+ 0.254829592 (+ (- (/ 1.421413741 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (* (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.453152027 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 0.284496736))) (/ 1.061405429 (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))))) (exp (* (fabs x) (fabs x)))))

rewrite38.3s

Algorithm
142×rewrite-expression-head
Calls

412 calls:

Slowest
3.6s
(+ (log (exp (+ (+ (/ -1259.1392167224028 (- 2 z)) (/ 676.5203681218851 (- 1 z))) 0.9999999999998099))) (/ -176.6150291621406 (- 5 (+ z 1))))
3.5s
(+ (log (exp (+ (+ (/ -1259.1392167224028 (- 2 z)) (/ 676.5203681218851 (- 1 z))) 0.9999999999998099))) (/ -176.6150291621406 (- 5 (+ z 1))))
2.8s
(+ (+ (+ (/ -1259.1392167224028 (+ (- 1 z) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (/ -176.6150291621406 (- 5 (+ z 1))))
2.7s
(+ (+ (+ (/ -1259.1392167224028 (+ (- 1 z) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.2s
(/ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (+ (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (exp (* (fabs x) (fabs x)))))
Rules
19153×*-un-lft-identity
17586×times-frac
10506×add-sqr-sqrt
8233×add-cube-cbrt
5356×distribute-lft-out
3140×sqrt-prod
2887×pow1
2747×add-exp-log
2030×add-cbrt-cube
1764×prod-diff
1189×associate-*l*
1124×exp-sum
1047×associate-*r*
988×prod-exp
871×associate-/r*
831×distribute-lft-out--
808×unpow-prod-down
789×pow-prod-up
786×div-exp
733×associate-/l*
682×cbrt-unprod
675×sqrt-pow1
638×div-inv
628×fma-def
614×pow-prod-down
594×add-log-exp
554×swap-sqr
532×difference-of-squares
430×cbrt-undiv
412×expm1-log1p-u insert-posit16 log1p-expm1-u
397×log-pow
388×associate-/r/
381×unswap-sqr
354×pow1/2
353×flip-+ flip3-+
352×cbrt-prod
339×associate-*l/
291×pow-plus
251×pow-sqr
195×sqr-pow
167×fma-neg
155×distribute-rgt-in distribute-lft-in
146×sqrt-div
140×frac-times
136×*-commutative
128×associate-*r/
125×sub-neg
117×1-exp
115×flip3-- flip--
113×unpow-prod-up
111×rec-exp
109×pow2
106×pow-exp
95×frac-2neg clear-num
94×cbrt-div
86×frac-add
79×associate-/l/
70×associate--l+ fma-udef
66×sum-log
64×log-prod
62×pow-flip
60×pow-to-exp
58×pow1/3
51×exp-prod
37×inv-pow
35×+-commutative
34×diff-log
33×rem-sqrt-square distribute-rgt-out
32×pow-div
28×distribute-rgt1-in
24×cube-unmult
19×pow-unpow div-sub
18×cube-prod
16×associate-+l+ distribute-lft1-in
15×sqrt-unprod
14×pow3
12×sin-sum
10×associate--r+ pow-sub
9×hypot-def
7×rem-exp-log
6×associate-+r- unpow3 cube-mult pow-pow associate-+l-
5×frac-sub un-div-inv rem-log-exp rem-square-sqrt
4×rem-cbrt-cube
2×associate--r- e-exp-1
1×exp-diff associate-+r+ distribute-rgt-out-- remove-double-div cos-sum

regimes8.9s

Accuracy

Total 20.4b remaining (23.4%)

5.3b16.4%Octave 3.8, jcobi/2
3.5b73.4%Octave 3.8, jcobi/1
2.5b0%_divideComplex, imaginary part
2.4b0%_divideComplex, real part
1.9b0%Jmat.Real.lambertw, newton loop step

localize6.8s

bsearch1.5s

end1.0ms