Details

simplify49.7m

Calls

17857 calls:

Slowest
2.4s
(/ (* (* (* (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))))))
1.8s
(/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ 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)))))
1.8s
(/ (* (* (* (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)))))

sample10.1m

Algorithm
89×intervals
Results
6.8m103330×body10240exit
1.2m394817×body80valid
39.0s26142×body1280valid
19.9s20952×body640valid
11.4s3138×body1280nan
11.1s69415×body80nan
7.9s10679×body320valid
7.1s2651×body640nan
3.2s1320×body320nan
2.5s5468×body160valid
2.2s41536×pre80true
1.2s1406×body2560valid
839.0ms630×body160nan
662.0ms630×body5120valid

prune4.7m

rewrite2.8m

Algorithm
142×rewrite-expression-head
Calls

451 calls:

Slowest
37.2s
(* (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5)))))
29.6s
(* (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5)))) (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))))
16.2s
(* (/ (+ (+ (+ (+ (+ 1 (* (* x x) 0.1049934947)) (* 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)
16.0s
(* (/ (+ (+ (+ (+ (+ 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)
9.1s
(/ (+ (+ (+ (+ (+ 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)))))
Rules
14355×*-un-lft-identity
9186×times-frac
6428×add-sqr-sqrt
5171×add-cube-cbrt
4352×distribute-lft-out
3018×pow1
2884×add-exp-log
1846×sqrt-prod
1836×add-cbrt-cube
1653×prod-diff
1183×prod-exp
1140×pow-prod-up
977×distribute-lft-out--
880×associate-*l*
834×div-exp
718×associate-*r*
676×add-log-exp
647×associate-*l/
622×sqrt-pow1
621×unpow-prod-down
613×associate-/l*
571×cbrt-unprod
567×frac-times
561×frac-add
527×flip-+ flip3-+
522×pow-prod-down
509×cube-prod
494×pow-plus
474×associate-/r*
451×expm1-log1p-u log1p-expm1-u insert-posit16
440×div-inv
427×distribute-rgt-in distribute-lft-in
365×cbrt-div
353×cbrt-prod
351×cbrt-undiv
343×pow1/2
327×associate-/r/
323×difference-of-squares
311×associate-*r/
310×pow-sqr
308×pow-exp
288×unswap-sqr
275×flip3-- flip--
236×swap-sqr
228×fma-def
193×1-exp rec-exp
188×sqr-pow
183×fma-neg
167×pow2
142×*-commutative
138×exp-sum
133×pow-to-exp
125×log-pow
99×cube-mult
98×unpow3
94×associate-/l/
93×sum-log log-prod frac-2neg clear-num
90×pow1/3
88×sqrt-div
85×associate-+l-
82×pow-sub
79×exp-neg
75×distribute-rgt-out
69×sub-neg
65×fma-udef
54×exp-diff
53×neg-sub0
41×exp-prod
40×diff-log
39×cube-unmult
34×un-div-inv
32×distribute-rgt1-in pow-div
29×pow-flip +-commutative
27×pow-unpow
25×inv-pow
24×rem-cube-cbrt frac-sub rem-sqrt-square
19×sqrt-unprod
18×associate-+l+ div-sub
17×hypot-udef
12×pow-pow
11×sin-sum associate--l+
10×pow3 hypot-def
sum-cubes
rem-square-sqrt
rem-exp-log cube-div
associate-+r+ rem-log-exp exp-to-pow
unpow-prod-up sqrt-undiv associate--r+
log-div
distribute-lft1-in difference-cubes rem-cbrt-cube associate--r-
expm1-log1p expm1-udef associate--l- cos-sum sin-mult

series1.2m

Calls

447 calls:

Slowest
1.3s
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
1.1s
(/ 1 (* (pow -2 1.0) (pow (log u1) 1.0)))
1.1s
(/ 1 (* (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5) 6))
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
(* (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5) 6)

regimes8.0s

Accuracy

Total 27.9b remaining (24.5%)

10.7b25%_divideComplex, real part
5.6b10.1%Octave 3.8, jcobi/2
3.2b0%_divideComplex, imaginary part
2.3b20.4%Octave 3.8, jcobi/4
0.7b62.3%Jmat.Real.lambertw, newton loop step

localize7.2s

bsearch1.2s

end2.0ms