Details

rewrite12.1m (48.2%)

Algorithm
155×rewrite-expression-head
Calls

462 calls:

3.3m
(* (/ (* (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))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))
2.4m
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))
1.9m
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (- z 1.0) 7.0))) (* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))
32.9s
(+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ (- z) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))
24.7s
(* (/ (+ (+ (+ (+ (+ 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)
Rules
25069×times-frac
18928×*-un-lft-identity
14868×add-sqr-sqrt
12408×add-cube-cbrt
6398×sqrt-prod
4048×frac-add
3563×associate-*r*
3066×distribute-lft-out
2698×add-exp-log
2311×prod-diff
2036×add-cbrt-cube
1918×flip-+ flip3-+
1477×frac-times
1445×pow1
1230×cbrt-prod
1171×associate-*r/
1037×associate-/l*
971×distribute-rgt-in distribute-lft-in
963×prod-exp
774×add-log-exp
723×div-exp
709×div-inv
705×associate-*l*
677×difference-of-squares
658×cbrt-unprod
641×associate-/r/
519×associate-/r*
462×log1p-expm1-u expm1-log1p-u
451×cbrt-undiv
439×frac-sub
394×unpow-prod-down
372×distribute-lft-out--
369×associate-*l/
351×pow-prod-down
321×flip3-- flip--
288×unswap-sqr
203×cube-prod
202×log-pow
191×fma-neg
172×pow-exp
168×sum-log
167×exp-sum
145×sqr-pow
144×fma-def
120×distribute-rgt-neg-in
117×*-commutative
113×swap-sqr
109×clear-num frac-2neg
101×pow1/3
100×exp-prod
95×pow-prod-up pow-to-exp
87×sqrt-pow1
86×associate-/l/
82×1-exp
81×rec-exp
78×sub-neg
77×log-prod
75×sqrt-div
74×fma-udef
73×associate--r+
67×pow-sqr
61×pow-unpow
60×associate--l+
52×unpow3 cube-mult
49×pow-plus
48×diff-log
44×pow1/2
38×pow2
33×cbrt-div
27×pow-pow associate-+r+
26×rem-sqrt-square
24×+-commutative
15×distribute-lft-neg-in div-sub
14×log-div
13×cube-div rem-cube-cbrt associate-+l-
12×exp-diff
11×associate-+l+
10×unpow-prod-up distribute-rgt-neg-out rem-log-exp
9×un-div-inv inv-pow pow-flip
8×difference-cubes sin-sum
7×sqrt-unprod
5×distribute-lft-neg-out neg-mul-1 rem-cbrt-cube associate--l-
4×expm1-udef distribute-neg-in sub-div expm1-log1p cos-sum
3×unpow2 pow-sub sum-cubes
2×rem-exp-log log1p-udef exp-neg log1p-expm1 hypot-udef neg-sub0 hypot-def associate--r- distribute-neg-frac
1×sqrt-undiv distribute-rgt-out distribute-rgt-out-- cube-neg

simplify5.3m (21.2%)

sample3.4m (13.6%)

Algorithm
99×intervals
Results
1.0m11861×body10240exit
57.2s463720×body80valid
24.8s26847×body1280valid
12.0s21154×body640valid
6.2s68831×body80nan
4.1s1622×body1280nan
3.6s10550×body320valid
2.5s9636×body160valid
2.4s1297×body640nan
2.1s49536×pre80true
871.0ms1506×body2560valid
798.0ms631×body320nan
371.0ms618×body5120valid
198.0ms341×body160nan

prune2.5m (10.0%)

series1.5m (6.0%)

Calls

460 calls:

1.9s
(pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5)
1.7s
(* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)
1.3s
(/ (/ (* (* 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))
1.2s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.1s
(* (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))) (* (cbrt (* 0.5 (cos re))) (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))))

regimes8.5s (0.6%)

Accuracy

Total 25.8b remaining (20.2%)

Threshold costs 6.6b (5.2%)

7.5b33%_divideComplex, real part
5.3b40.4%_divideComplex, imaginary part
3.0b76.8%Octave 3.8, jcobi/1
2.2b37.6%Octave 3.8, jcobi/4
1.1b68.4%Octave 3.8, jcobi/3

localize5.4s (0.4%)

bsearch955.0ms (0.1%)

end1.0ms (0.0%)