Details

simplify8.0m (32.9%)

rewrite7.8m (32.3%)

Algorithm
152×rewrite-expression-head
Calls

442 calls:

58.5s
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
51.8s
(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
45.8s
(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
42.7s
(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
41.9s
(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
Rules
2800345×frac-times
1104589×cbrt-div
1078974×associate-*r/
788286×associate-*l/
746717×flip3-- flip--
373441×associate-/l/
13823×*-un-lft-identity
12850×times-frac
9865×add-sqr-sqrt
6766×add-cube-cbrt
4846×sqrt-prod
3326×distribute-lft-out
3018×add-exp-log
2782×frac-add
2475×add-cbrt-cube
1669×prod-diff
1642×associate-*l*
1376×cbrt-prod
1259×pow1
1175×flip-+ flip3-+
1166×associate-*r*
1109×prod-exp
918×cbrt-unprod
904×add-log-exp
795×div-exp
779×unpow-prod-down
678×associate-/r*
676×difference-of-squares
609×associate-/l*
597×cbrt-undiv
536×distribute-lft-out-- cube-prod
489×unswap-sqr
474×associate-/r/
448×log1p-expm1-u
442×expm1-log1p-u
418×div-inv
343×swap-sqr
327×pow-prod-down
296×sum-log
285×distribute-rgt-neg-in
245×sqr-pow
237×exp-sum
205×distribute-rgt-in distribute-lft-in
199×fma-def
191×exp-diff
163×fma-neg
124×*-commutative
123×log-pow
103×frac-2neg clear-num
90×fma-udef unpow3 cube-mult
77×pow-prod-up log-prod
73×pow-unpow rec-exp pow-exp 1-exp
71×associate--r+
67×sub-neg
66×sqrt-div
61×associate--l+
56×exp-prod
55×pow1/3
54×pow-to-exp
52×sqrt-pow1
42×pow1/2 diff-log
32×frac-sub
30×+-commutative
29×pow-sqr
28×distribute-lft-neg-in
27×pow-plus
24×pow-pow
19×pow2
18×associate-+l+
16×pow-flip
15×div-sub
14×inv-pow
13×associate-+l-
12×rem-sqrt-square
11×rem-cube-cbrt
log-div
cube-div associate-+r+ neg-mul-1
un-div-inv expm1-udef
distribute-neg-in expm1-log1p rem-log-exp
hypot-def associate--l-
sin-sum sub-div pow-sub cos-sum
sqrt-undiv log1p-udef log1p-expm1 unpow-prod-up hypot-udef associate--r- distribute-rgt-out-- distribute-rgt-neg-out unpow2
rem-exp-log pow3 distribute-lft-neg-out associate-+r- neg-sub0 neg-log sum-cubes distribute-neg-frac
difference-cubes sqrt-pow2 distribute-rgt-out

prune5.3m (21.7%)

sample2.0m (8.1%)

Algorithm
99×intervals
Results
47.9s15615×body10240exit
20.9s468966×body80valid
13.9s30619×body1280valid
6.3s22638×body640valid
2.6s3031×body1280nan
2.5s71226×body80nan
2.1s11975×body320valid
1.5s2469×body640nan
1.3s10186×body160valid
556.0ms1283×body320nan
503.0ms41536×pre80true
365.0ms1509×body2560valid
190.0ms649×body160nan
140.0ms576×body5120valid

series1.0m (4.3%)

Calls

442 calls:

891.0ms
(* (/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))) (/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)))
858.0ms
(* (* (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0))
838.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
725.0ms
(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
718.0ms
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

regimes4.8s (0.3%)

Accuracy

Total 30.8b remaining (30.3%)

Threshold costs 6.0b (5.9%)

10.4b27.5%_divideComplex, real part
7.9b31.9%_divideComplex, imaginary part
2.9b77.4%Octave 3.8, jcobi/1
2.0b0%Jmat.Real.lambertw, newton loop step
1.6b35.5%Octave 3.8, jcobi/3

localize2.7s (0.2%)

bsearch702.0ms (0.0%)

end1.0ms (0.0%)