Details

simplify22.8m (42.5%)

rewrite16.3m (30.4%)

Algorithm
151×rewrite-expression-head
Calls

442 calls:

39.1s
(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- 0 z))) (/ -0.13857109526572012 (+ 6.0 (- 0 z)))) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- 0 z))) (/ 12.507343278686905 (+ (- 0 z) 5.0))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))))
31.5s
(* (/ (+ (+ (+ (+ (+ 1.0 (* 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 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
20.6s
(* (* (+ 8.0 (- 0 z)) (+ 6.0 (- 0 z))) (* (* (+ 7.0 (- 0 z)) (+ (- 0 z) 5.0)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1.0 z)) (/ 676.5203681218851 (- 1.0 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (+ (* (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))) (- (* (/ -1259.1392167224028 (+ (- 0 z) 2.0)) (/ -1259.1392167224028 (+ (- 0 z) 2.0))) (* (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))))))
18.9s
(* (+ (* 1.5056327351493116e-07 (+ 6.0 (- 0 z))) (* (+ 8.0 (- 0 z)) -0.13857109526572012)) (* (* (+ 7.0 (- 0 z)) (+ (- 0 z) 5.0)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1.0 z)) (/ 676.5203681218851 (- 1.0 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (+ (* (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))) (- (* (/ -1259.1392167224028 (+ (- 0 z) 2.0)) (/ -1259.1392167224028 (+ (- 0 z) 2.0))) (* (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))))))
17.8s
(/ (+ (+ (+ (+ (+ 1.0 (* 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 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
Rules
710900×frac-times
405363×flip-+ flip3-+
328613×frac-add
307173×associate-*r/
240791×associate-*l/
159496×times-frac
136102×frac-sub
90943×add-sqr-sqrt
74700×*-un-lft-identity
71013×sqrt-prod
53035×add-cube-cbrt
18529×difference-of-squares
12960×sub-div
9354×distribute-lft-out--
8239×associate-/r/
6629×flip3-- flip--
4765×div-inv
3250×add-exp-log
2693×pow1
2402×add-cbrt-cube
1598×distribute-lft-out
1562×associate-*r*
1335×prod-exp
1209×associate-/l*
977×prod-diff
937×associate-*l*
889×cbrt-unprod
854×div-exp
806×add-log-exp
703×pow-prod-down
614×pow-prod-up
593×associate-/r*
524×cbrt-prod
478×cbrt-undiv
443×log1p-expm1-u
442×expm1-log1p-u
441×insert-posit16
300×unswap-sqr
279×sqrt-div
273×pow-plus
251×pow-exp
242×unpow-prod-down
209×sum-log
187×cube-prod
175×log-pow
167×*-commutative
163×fma-def
161×1-exp
159×rec-exp
156×fma-neg
146×pow-sqr
139×swap-sqr
135×distribute-rgt-in distribute-lft-in
123×exp-sum
112×pow-to-exp
111×pow2
99×sqrt-pow1
97×log-prod
93×frac-2neg clear-num
88×pow1/2
84×associate-/l/
83×sqr-pow
55×sub-neg
54×fma-udef
47×cbrt-div
44×diff-log
42×pow1/3
38×unpow3 cube-mult
35×cube-unmult
34×pow-flip
33×associate-+l+ distribute-rgt-out
31×+-commutative
28×distribute-rgt1-in pow3
25×rem-sqrt-square
24×div-sub
19×exp-prod
18×pow-unpow
15×distribute-lft-neg-in distribute-rgt-neg-in
14×associate-+r+ sqrt-unprod
13×hypot-udef
12×rem-cube-cbrt inv-pow
11×hypot-def un-div-inv
9×pow-pow
6×associate--l+ pow-div associate-+l-
5×rem-exp-log distribute-neg-in
4×sin-sum neg-log cos-sum associate--r+ neg-mul-1 rem-cbrt-cube rem-log-exp
3×log1p-expm1 cube-div log1p-udef
2×expm1-log1p expm1-udef distribute-lft1-in distribute-rgt-neg-out rem-square-sqrt count-2
1×unpow-prod-up distribute-lft-neg-out exp-diff associate--l- associate-+r- distribute-rgt-out-- neg-sub0 pow-sub difference-cubes remove-posit16 exp-neg associate--r- log-div

prune9.3m (17.3%)

sample2.3m (4.3%)

Algorithm
98×intervals
Results
48.1s438968×body80valid
27.1s27584×body1280valid
13.5s20851×body640valid
7.4s69018×body80nan
6.0s8067×body10240exit
3.9s10670×body320valid
3.0s9213×body160valid
1.9s49536×pre80true
854.0ms1464×body2560valid
357.0ms632×body5120valid
145.0ms83×body1280nan
86.0ms71×body640nan
27.0ms28×body320nan
6.0ms11×body160nan

series2.2m (4.1%)

Calls

441 calls:

5.0s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
5.0s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
3.4s
(+ (* (/ (* (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.421413741) (/ (/ 1.0 (* (cbrt (fma 0.3275911 (fabs x) 1.0)) (cbrt (fma 0.3275911 (fabs x) 1.0)))) (cbrt (fma 0.3275911 (fabs x) 1.0))) -0.284496736) 0.254829592)) (exp (* (fabs x) (fabs x)))) (/ (* (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.421413741) (/ (/ 1.0 (* (cbrt (fma 0.3275911 (fabs x) 1.0)) (cbrt (fma 0.3275911 (fabs x) 1.0)))) (cbrt (fma 0.3275911 (fabs x) 1.0))) -0.284496736) 0.254829592)) (exp (* (fabs x) (fabs x))))) (* 1.0 (/ (* (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.421413741) (/ (/ 1.0 (* (cbrt (fma 0.3275911 (fabs x) 1.0)) (cbrt (fma 0.3275911 (fabs x) 1.0)))) (cbrt (fma 0.3275911 (fabs x) 1.0))) -0.284496736) 0.254829592)) (exp (* (fabs x) (fabs x))))))
2.8s
(- (pow 1.0 3) (pow (/ (* (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.421413741) (/ (/ 1.0 (* (cbrt (fma 0.3275911 (fabs x) 1.0)) (cbrt (fma 0.3275911 (fabs x) 1.0)))) (cbrt (fma 0.3275911 (fabs x) 1.0))) -0.284496736) 0.254829592)) (exp (* (fabs x) (fabs x)))) 3))
2.7s
(- (pow 1.0 3) (* (sqrt (pow (/ (* (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.421413741) (/ (/ 1.0 (* (cbrt (fma 0.3275911 (fabs x) 1.0)) (cbrt (fma 0.3275911 (fabs x) 1.0)))) (cbrt (fma 0.3275911 (fabs x) 1.0))) -0.284496736) 0.254829592)) (exp (* (fabs x) (fabs x)))) 3)) (sqrt (pow (/ (* (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.421413741) (/ (/ 1.0 (* (cbrt (fma 0.3275911 (fabs x) 1.0)) (cbrt (fma 0.3275911 (fabs x) 1.0)))) (cbrt (fma 0.3275911 (fabs x) 1.0))) -0.284496736) 0.254829592)) (exp (* (fabs x) (fabs x)))) 3))))

regimes28.9s (0.9%)

Accuracy

Total 32.9b remaining (24.1%)

Threshold costs 5.7b (4.2%)

10.7b27.9%_divideComplex, real part
7.8b36.4%_divideComplex, imaginary part
3.5b72%Octave 3.8, jcobi/1
2.9b22.4%Octave 3.8, jcobi/4
1.2b0%Jmat.Real.lambertw, newton loop step

localize16.4s (0.5%)

bsearch1000.0ms (0.0%)

end1.0ms (0.0%)