Details

simplify13.7m (38.2%)

prune11.4m (31.9%)

sample4.7m (13.2%)

Algorithm
100×intervals
Results
1.4m474276×body80valid
1.2m15765×body10240exit
43.0s30461×body1280valid
21.9s23826×body640valid
11.9s70532×body80nan
8.2s3115×body1280nan
7.4s11700×body320valid
6.1s2621×body640nan
4.4s10003×body160valid
2.5s49536×pre80true
1.5s1241×body320nan
1.5s1439×body2560valid
1.0s592×body5120valid
487.0ms615×body160nan

rewrite4.0m (11.1%)

Algorithm
163×rewrite-expression-head
Calls

505 calls:

59.9s
(* (* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (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)))))
27.7s
(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)
17.3s
(* (/ (sqrt (* PI 2)) (exp 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)))))
17.0s
(* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
16.7s
(* (/ (sqrt (* PI 2)) (exp 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
40406×*-un-lft-identity
28641×times-frac
15856×add-sqr-sqrt
14405×distribute-lft-out
12375×add-cube-cbrt
5543×pow1
5294×frac-add
4779×add-exp-log
4490×sqrt-prod
4367×prod-diff
3899×associate-*r*
3437×unpow-prod-up
2942×add-cbrt-cube
2593×cbrt-prod
2587×pow-prod-up
2459×associate-*l*
2269×flip-+ flip3-+
2093×prod-exp
1817×frac-times
1634×associate-*r/
1434×div-exp
1376×unpow-prod-down
1317×distribute-lft-out--
1287×swap-sqr
1252×pow-plus
1212×difference-of-squares cbrt-unprod
1131×associate-/l*
900×pow-prod-down
821×exp-sum
798×associate-/r/
705×distribute-lft-neg-in distribute-rgt-neg-in
661×add-log-exp
646×div-inv
635×cbrt-undiv
511×associate-*l/
510×log1p-expm1-u
508×sqrt-pow1
506×expm1-log1p-u
505×insert-posit16 unswap-sqr
503×associate-/r*
443×pow-sqr
330×pow2
322×distribute-rgt-in distribute-lft-in
313×1-exp
292×log-pow
291×sqr-pow
239×rec-exp
235×neg-mul-1
222×cbrt-div
190×sub-neg
170×*-commutative
156×fma-def
145×pow-exp fma-neg
136×pow1/3
115×pow1/2
110×pow-to-exp
104×pow-flip
96×inv-pow
93×flip3-- flip--
88×cube-unmult
84×frac-2neg clear-num
77×log-prod
70×associate--r+
68×associate-/l/
62×associate--l+ fma-udef
61×sqrt-div
52×sum-log
46×associate--r-
43×pow3
37×exp-prod
34×+-commutative diff-log
32×rem-sqrt-square
30×frac-sub
25×pow-unpow
22×exp-diff
21×cube-prod
20×un-div-inv
16×associate-+l- distribute-rgt-out
15×hypot-udef
14×log-div
13×distribute-rgt1-in
12×div-sub
10×pow-sub
9×pow-pow
8×associate-+l+
7×expm1-log1p expm1-udef sqrt-unprod cos-sum hypot-def rem-log-exp
6×associate-+r+ log1p-expm1 log1p-udef exp-neg
5×rem-square-sqrt
4×sin-sum sub0-neg distribute-rgt-out-- rem-cbrt-cube
3×rem-exp-log count-2
2×neg-sub0 rem-cube-cbrt
1×distribute-lft-neg-out associate--l- associate-+r- unpow3 remove-posit16 cube-div cube-mult

series1.7m (4.7%)

Calls

505 calls:

3.4s
(* (/ (/ (* 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))))
3.3s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) 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))))
1.2s
(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
1.2s
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.2s
(fma (- (exp (- (* (fabs x) (fabs x))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 0.254829592) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (* (exp (- (* (fabs x) (fabs x)))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 0.254829592) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))))))

regimes10.8s (0.5%)

Accuracy

Total 44.5b remaining (39.3%)

Threshold costs 5.7b (5%)

10.4b36.2%Octave 3.8, jcobi/4
7.9b31.9%_divideComplex, real part
7.4b29.6%_divideComplex, imaginary part
6.9b11%Octave 3.8, jcobi/2
3.3b75.4%Octave 3.8, jcobi/1

localize8.2s (0.4%)

bsearch1.6s (0.1%)

end1.0ms (0.0%)