Details

simplify17.4m (36.1%)

prune10.4m (21.5%)

sample9.6m (19.9%)

Algorithm
94×intervals
Results
6.5m100099×body10240exit
1.2m400273×body80valid
37.1s26434×body1280valid
20.6s20165×body640valid
12.0s70231×body80nan
7.7s10889×body320valid
4.7s1613×body1280nan
4.0s1339×body640nan
2.3s49536×pre80true
2.0s5367×body160valid
1.7s1476×body2560valid
1.6s671×body320nan
653.0ms590×body5120valid
289.0ms321×body160nan

rewrite8.7m (18.0%)

Algorithm
147×rewrite-expression-head
Calls

451 calls:

3.6m
(/ (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- (- 6 z) 1))) (+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))) (exp (+ (- 7 z) 0.5)))
1.0m
(* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))))))
57.9s
(/ (+ (pow (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) 3) (pow (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))))) 3)) (+ (* (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5)))) (- (* (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))))) (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))))) (* (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))))))))
23.3s
(+ (pow (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) 3) (pow (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))))) 3))
21.1s
(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp (+ 0.5 (+ z 6))))
Rules
67107×frac-add
58471×frac-sub
49411×frac-times
36843×*-un-lft-identity
34734×flip3-- flip--
31095×associate-*l/
28214×times-frac
16933×associate-*r/
15194×add-sqr-sqrt
14471×flip-+ flip3-+
14277×distribute-lft-out
11981×add-cube-cbrt
8948×associate-/r/
6423×sqrt-prod
3912×prod-diff
3775×pow1
3575×add-exp-log
3250×associate-*r*
2901×associate-+l+
2467×add-cbrt-cube
1520×prod-exp
1462×associate-*l*
1311×distribute-rgt-in distribute-lft-in
1284×pow-prod-up
1249×distribute-lft-out--
1053×unpow-prod-down
939×cbrt-unprod
898×div-exp
859×associate-/l*
830×div-inv
696×difference-of-squares
680×pow-plus
639×add-log-exp
612×pow-prod-down
519×cbrt-undiv
509×associate-/r*
480×sub-div
456×expm1-log1p-u
452×log1p-expm1-u
451×insert-posit16
433×unswap-sqr
336×pow-div
324×sqr-pow
298×log-pow
290×associate-/l/
277×pow-sqr
266×cbrt-prod
229×pow2
199×sqrt-div
184×exp-sum
178×sqrt-pow1
157×cube-prod
155×fma-def
152×fma-neg
142×1-exp *-commutative
139×pow-exp
127×log-prod
106×pow-flip
104×rec-exp
96×inv-pow
90×frac-2neg clear-num
84×swap-sqr
77×pow1/2
76×pow-to-exp
69×pow1/3 associate--r+ sub-neg
66×fma-udef
64×sum-log
55×cube-unmult
50×cube-div
42×pow3
41×diff-log
37×cbrt-div
34×associate--l+
33×+-commutative
19×div-sub rem-sqrt-square
17×exp-prod
15×distribute-rgt-out
14×distribute-rgt1-in hypot-udef
12×sin-sum associate-+r+ pow-unpow
11×rem-log-exp
10×hypot-def log-div
distribute-lft-neg-in distribute-rgt-neg-in
associate-+l-
exp-to-pow
exp-diff log1p-expm1 distribute-frac-neg sqrt-unprod sum-cubes pow-pow log1p-udef
expm1-udef difference-cubes
cube-neg unpow-prod-up distribute-neg-in un-div-inv unsub-neg
expm1-log1p distribute-lft-neg-out unpow3 neg-mul-1 cube-mult
associate-+r- distribute-rgt-neg-out rem-square-sqrt associate--r- pow-sub
rem-cube-cbrt distribute-rgt-out-- neg-sub0 rem-exp-log cos-sum rem-cbrt-cube

series1.9m (3.9%)

Calls

451 calls:

9.8s
(/ (+ (pow (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) 3) (pow (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))))) 3)) (+ (* (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5)))) (- (* (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))))) (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))))) (* (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))))))))
6.9s
(+ (pow (- (+ (+ (/ 0.284496736 (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (/ (/ (/ 1.453152027 (exp (* (fabs x) (fabs x)))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1)))) (- 1 (/ (/ 0.254829592 (fma (fabs x) 0.3275911 1)) (exp (* (fabs x) (fabs x)))))) (/ (/ 1.061405429 (exp (* (fabs x) (fabs x)))) (pow (fma (fabs x) 0.3275911 1) 5))) 3) (pow (/ (- 1.421413741) (* (fma (fabs x) 0.3275911 1) (* (exp (* (fabs x) (fabs x))) (* (fma (fabs x) 0.3275911 1) (fma (fabs x) 0.3275911 1))))) 3))
4.2s
(+ (pow (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 3) (pow 1.0 3))
3.2s
(* (/ (/ (* 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))))
3.1s
(* (/ (/ (* 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))))))

regimes8.5s (0.3%)

Accuracy

Total 35.9b remaining (31%)

Threshold costs 4.6b (4%)

8.9b16.1%_divideComplex, real part
7.6b33.2%_divideComplex, imaginary part
6.3b26.4%Octave 3.8, jcobi/2
3.3b74%Octave 3.8, jcobi/1
2.3b20.9%Octave 3.8, jcobi/4

localize7.8s (0.3%)

bsearch1.4s (0.0%)

end1.0ms (0.0%)