Details

rewrite10.9m (30.8%)

Algorithm
154×rewrite-expression-head
Calls

448 calls:

23.6s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ (sqrt 1.875) (/ (pow (fabs x) 7) (sqrt 1.875))) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
4.0s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
3.0s
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
3.0s
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
2.8s
(* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)
Rules
47207×frac-times
31187×associate-*r/
18345×associate-*l/
15184×exp-neg
13358×flip-+ flip3-+
13060×frac-add
13022×exp-diff
13015×neg-sub0
6955×*-un-lft-identity
6726×times-frac
6358×add-sqr-sqrt
4748×add-cube-cbrt
4528×pow1
2989×add-exp-log
2306×add-cbrt-cube
2175×un-div-inv
1662×sqrt-prod
1587×pow-prod-up
1349×prod-diff
1302×prod-exp
1290×associate-*r*
989×associate-*l*
961×pow-prod-down
896×cbrt-unprod
847×distribute-lft-out
766×pow-plus
698×div-exp
640×add-log-exp
596×unpow-prod-down
535×associate-/l*
466×associate-/r*
455×difference-of-squares
448×log1p-expm1-u
446×expm1-log1p-u
445×pow-sqr
421×cube-prod
391×cbrt-undiv
369×div-inv
327×distribute-lft-out--
302×pow2
294×associate-/r/
292×cbrt-prod
289×unswap-sqr
263×pow-exp
197×distribute-rgt-in distribute-lft-in
196×cbrt-div
186×sqr-pow
178×swap-sqr
163×fma-neg
161×fma-def
157×exp-sum
152×*-commutative
147×flip3-- flip--
146×1-exp
138×rec-exp
132×log-pow
118×pow-to-exp
106×pow1/3
99×unpow3 cube-mult
98×sqrt-div
94×associate-/l/
92×frac-2neg clear-num
90×cube-div
79×sum-log
71×cube-unmult
64×fma-udef
60×sqrt-pow1 sub-neg
53×log-prod
48×pow1/2
47×associate--l+
34×diff-log
30×+-commutative
24×pow-unpow div-sub
23×associate-+l+
22×frac-sub distribute-rgt-out
21×pow-pow
20×pow-flip rem-cube-cbrt
19×unpow-prod-up
18×distribute-rgt1-in
17×pow3 rem-sqrt-square
16×exp-prod
13×pow-sub
12×sub0-neg cos-sum
10×inv-pow associate-+l- distribute-rgt-out--
9×hypot-def
8×associate-+r+
6×distribute-lft-neg-in associate-+r- distribute-rgt-neg-in unsub-neg
5×associate--r+ rem-exp-log
4×sin-sum neg-log
3×rem-cbrt-cube log1p-udef
2×expm1-log1p expm1-udef log1p-expm1 sqrt-unprod sub-div difference-cubes hypot-udef rem-square-sqrt
1×neg-mul-1 rem-log-exp distribute-neg-in associate--r-

simplify9.7m (27.2%)

prune5.8m (16.3%)

series5.2m (14.8%)

Calls

442 calls:

4.5s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
4.2s
(+ (* (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))) (* 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))
3.5s
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
3.0s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
2.9s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

sample3.6m (10.0%)

Algorithm
98×intervals
Results
1.3m11978×body10240exit
54.3s450253×body80valid
25.0s27048×body1280valid
13.8s21157×body640valid
6.9s70443×body80nan
5.1s1557×body1280nan
4.9s10846×body320valid
2.7s1342×body640nan
1.5s49536×pre80true
1.3s693×body320nan
1.2s5664×body160valid
886.0ms1395×body2560valid
683.0ms616×body5120valid
275.0ms327×body160nan

regimes11.6s (0.5%)

Accuracy

Total 23.5b remaining (17.3%)

Threshold costs 5.0b (3.7%)

7.2b34.1%_divideComplex, imaginary part
3.3b-14.4%_divideComplex, real part
3.1b75.1%Octave 3.8, jcobi/1
2.3b36.3%Octave 3.8, jcobi/4
1.5b40.8%Octave 3.8, jcobi/3

localize8.1s (0.4%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)