Details

simplify50.5m

Calls

18433 calls:

Slowest
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)))))
2.2s
(* (/ (* (/ (* (* 1 1) 1) (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))) (/ (* (* (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (/ 1 (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))))
2.1s
(* (/ (* (/ (* (* 1 1) 1) (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))) (/ (* (* (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (/ 1 (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))))
2.0s
(+ (* (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ 12.507343278686905 (+ z 4))) (/ -176.6150291621406 (+ 3 z))) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1)))))) (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ 12.507343278686905 (+ z 4))) (/ -176.6150291621406 (+ 3 z))) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))))) (- (* (/ -0.13857109526572012 (- z -5)) (/ -0.13857109526572012 (- z -5))) (* (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ 12.507343278686905 (+ z 4))) (/ -176.6150291621406 (+ 3 z))) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1)))))) (/ -0.13857109526572012 (- z -5)))))
1.7s
(* (* (* (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x)))) (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x))))) (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x))))) (/ (* (/ (* (* 1 1) 1) (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))))

sample9.3m

Algorithm
88×intervals
Results
6.5m100812×body10240exit
1.0m384784×body80valid
38.7s26020×body1280valid
20.9s20640×body640valid
11.1s69415×body80nan
6.8s10736×body320valid
5.5s1544×body1280nan
3.0s1335×body640nan
2.2s41536×pre80true
2.1s5706×body160valid
1.5s669×body320nan
1.2s1389×body2560valid
792.0ms352×body160nan
533.0ms590×body5120valid

prune5.1m

rewrite2.5m

Algorithm
153×rewrite-expression-head
Calls

463 calls:

Slowest
1.3m
(* (/ 1 (exp (+ (- (- 1 z) -6) 0.5))) (+ (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (+ (+ (+ (/ -1259.1392167224028 (+ (- 1 z) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (/ -176.6150291621406 (- 5 (+ z 1))))) (+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))))
31.4s
(* (* (pow (+ (+ z 0.5) 6) (+ 0.5 (+ z -1))) (/ (sqrt (* PI 2)) (exp (+ (+ z 0.5) 6)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ 12.507343278686905 (+ z 4))) (/ -176.6150291621406 (+ 3 z))) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1)))))) (/ -0.13857109526572012 (- z -5))))
5.7s
(+ (+ (/ 676.5203681218851 (- 1 z)) (+ (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))) 0.9999999999998099)) (+ (+ (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z))) (+ (/ 9.984369578019572e-06 (- 7 z)) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (+ (- 6 z) -1))))))
3.7s
(- (log (+ (+ (/ 676.5203681218851 (- 1 z)) (+ (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))) 0.9999999999998099)) (+ (+ (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z))) (+ (/ 9.984369578019572e-06 (- 7 z)) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (+ (- 6 z) -1))))))) (+ (- 7 z) 0.5))
2.7s
(+ (+ (+ (/ -1259.1392167224028 (+ (- 1 z) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (/ -176.6150291621406 (- 5 (+ z 1))))
Rules
15485×*-un-lft-identity
11543×times-frac
7561×add-sqr-sqrt
6106×add-cube-cbrt
5458×distribute-lft-out
3420×pow1
2764×add-exp-log
2014×frac-add
1952×add-cbrt-cube
1463×prod-diff
1293×sqrt-prod
1196×pow-prod-up
1110×associate-*r*
1032×flip-+ flip3-+
1010×prod-exp
942×associate-*l*
839×div-exp
798×add-log-exp
753×associate-/l*
598×pow-plus
595×unpow-prod-down
593×cbrt-unprod
582×log-pow
531×div-inv
519×pow-prod-down
509×associate-/r* associate-*r/
485×frac-times
467×expm1-log1p-u
463×log1p-expm1-u insert-posit16
461×cube-prod
406×associate-/r/
392×cbrt-undiv
334×difference-of-squares
331×associate-*l/
326×unswap-sqr
255×distribute-lft-out--
250×pow-sqr
245×swap-sqr
225×flip3-- flip--
223×distribute-rgt-in distribute-lft-in
218×sqrt-div
209×sqrt-pow1
204×sqr-pow
200×fma-def
195×sum-log fma-neg
194×pow2
157×*-commutative
142×pow1/2
139×exp-prod
131×1-exp
130×exp-sum
127×log-prod rec-exp
125×cbrt-prod
115×pow1/3
106×pow-exp
99×cube-mult
98×unpow3
97×frac-2neg clear-num
91×log-div
84×fma-udef
73×associate--r+
71×associate--l-
68×associate-/l/
65×sub-neg
62×cube-unmult
56×associate--l+
50×pow-to-exp
46×cbrt-div
38×frac-sub diff-log
37×+-commutative
33×pow-flip associate-+l+
32×pow-div
27×pow-unpow
25×inv-pow
24×rem-cube-cbrt
22×distribute-rgt-out
18×distribute-rgt1-in rem-sqrt-square
17×sqrt-unprod
16×div-sub
14×pow3
12×sin-sum pow-pow
11×hypot-def
8×rem-log-exp hypot-udef associate-+l-
7×rem-square-sqrt
6×associate-+r+ exp-to-pow cube-div
5×unpow-prod-up exp-diff un-div-inv rem-cbrt-cube pow-sub
4×log1p-expm1 associate--r- log1p-udef
3×distribute-lft1-in difference-cubes rem-exp-log
2×cos-sum
1×expm1-log1p expm1-udef distribute-rgt-out--

series1.3m

Calls

459 calls:

Slowest
1.6s
(- (log (/ (fma (fma (/ 676.5203681218851 (- 1 z)) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* (+ (+ (/ 771.3234287776531 (- 3 z)) (/ -1259.1392167224028 (- 2 z))) 0.9999999999998099) (* (+ (+ (/ 771.3234287776531 (- 3 z)) (/ -1259.1392167224028 (- 2 z))) 0.9999999999998099) (+ (+ (/ 771.3234287776531 (- 3 z)) (/ -1259.1392167224028 (- 2 z))) 0.9999999999998099)))) (* (- (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z))) (* (- 7 z) (fma (/ 12.507343278686905 (- 5 z)) (- (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z)))))) (* (fma (fma (fma (/ 12.507343278686905 (- 5 z)) (- (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z)))) 9.984369578019572e-06 (* (- 7 z) (fma (/ 12.507343278686905 (- 5 z)) (* (/ 12.507343278686905 (- 5 z)) (/ 12.507343278686905 (- 5 z))) (* (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z))) (/ -0.13857109526572012 (- 6 z)))))) (- (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z))) (* (+ (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z))) (* (- (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z))) (* (- 7 z) (fma (/ 12.507343278686905 (- 5 z)) (- (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z)))))))) (fma (+ (+ (/ 771.3234287776531 (- 3 z)) (/ -1259.1392167224028 (- 2 z))) 0.9999999999998099) (+ (+ (/ 771.3234287776531 (- 3 z)) (/ -1259.1392167224028 (- 2 z))) (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z)))) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))))) (* (* (fma (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)) (- (* (+ (/ 771.3234287776531 (- 3 z)) (+ (/ -1259.1392167224028 (- 2 z)) 0.9999999999998099)) (+ (/ 771.3234287776531 (- 3 z)) (+ (/ -1259.1392167224028 (- 2 z)) 0.9999999999998099))) (* (+ (/ 771.3234287776531 (- 3 z)) (+ (/ -1259.1392167224028 (- 2 z)) 0.9999999999998099)) (/ 676.5203681218851 (- 1 z))))) (- (/ -176.6150291621406 (- 4 z)) (/ 1.5056327351493116e-07 (- 8 z)))) (* (fma (/ 12.507343278686905 (- 5 z)) (- (/ 12.507343278686905 (- 5 z)) (/ -0.13857109526572012 (- 6 z))) (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z)))) (- 7 z))))) (+ (- 7 z) 0.5))
1.1s
(+ (* (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x)))) (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x))))) (* 1 (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x))))))
1.1s
(* (* (/ 1 (cbrt 6)) (/ 1 (cbrt 6))) (/ (pow (* -2 (log u1)) 0.5) (cbrt 6)))
1.1s
(* (sqrt (/ 1 PI)) (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
1.1s
(/ 1 (/ 6 (pow (* -2 (log u1)) 0.5)))

localize7.6s

regimes6.9s

Accuracy

Total 29.3b remaining (26.6%)

6.9b33.7%_divideComplex, real part
6.8b32.1%_divideComplex, imaginary part
5.7b14.2%Octave 3.8, jcobi/2
3.0b76.9%Octave 3.8, jcobi/1
1.4b48.2%Octave 3.8, jcobi/4

bsearch1.8s

end1.0ms