Details

simplify14.1m (39.6%)

rewrite10.8m (30.2%)

Algorithm
161×rewrite-expression-head
Calls

478 calls:

15.3s
(* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1))
2.4s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
2.4s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
1.3s
(* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1))
1.3s
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
Rules
10727×times-frac
9188×*-un-lft-identity
8331×add-sqr-sqrt
6334×add-cube-cbrt
3505×add-exp-log
3423×pow1
2287×add-cbrt-cube
1930×sqrt-prod
1650×prod-exp
1551×associate-*r*
1360×pow-prod-up
1238×distribute-lft-out
1174×associate-*l*
867×prod-diff
791×cbrt-unprod
745×cbrt-prod
671×add-log-exp
662×associate-/l*
649×div-exp
626×pow-plus
520×div-inv
502×pow-prod-down
487×cbrt-undiv
477×log1p-expm1-u difference-of-squares expm1-log1p-u
451×associate-*l/
430×associate-/r*
368×unswap-sqr
352×distribute-lft-out--
344×frac-times
280×cbrt-div
267×log-prod
266×flip-+ flip3-+
262×associate-*r/
255×distribute-rgt-in flip3-- distribute-lft-in flip--
247×pow-sqr
241×swap-sqr
224×log-pow
213×fma-def
207×pow2
205×pow-exp
193×associate-/r/
176×exp-sum
165×*-commutative
142×sqrt-pow1
127×unpow-prod-down
124×fma-neg
115×pow1/3
106×pow-to-exp
93×clear-num frac-2neg
86×pow1/2
84×sqrt-div
75×associate-/l/
67×sum-log
66×1-exp rec-exp sub-neg
62×fma-udef
52×cube-unmult frac-add
43×diff-log
40×unpow-prod-up
33×+-commutative exp-prod
30×sqr-pow
25×pow-flip
23×associate--r+
22×pow3 frac-sub
21×distribute-rgt-out
20×pow-unpow associate-+l+ distribute-rgt1-in
18×div-sub
17×un-div-inv
16×rem-sqrt-square rem-log-exp
15×distribute-rgt-neg-in distribute-lft-neg-in
14×hypot-udef
12×inv-pow
11×associate-+l-
9×exp-diff
8×sqrt-unprod pow-sub associate-+r+
7×rem-exp-log cos-sum log-div
6×hypot-def
5×pow-pow distribute-neg-in associate--l+
4×pow-div sub0-neg sin-sum neg-log neg-mul-1
3×rem-square-sqrt associate--r- distribute-rgt-neg-out rem-cbrt-cube
2×log1p-udef associate-+r- log1p-expm1 expm1-log1p unsub-neg expm1-udef
1×e-exp-1 count-2 exp-neg neg-sub0 log-rec associate--l-

sample5.1m (14.3%)

Algorithm
99×intervals
Results
1.7m12067×body10240exit
1.4m484080×body80valid
37.3s26965×body1280valid
18.1s21055×body640valid
10.5s69961×body80nan
6.3s1545×body1280nan
5.4s10601×body320valid
4.3s9404×body160valid
3.5s1379×body640nan
2.6s49536×pre80true
1.3s1516×body2560valid
1.3s622×body5120valid
1.1s671×body320nan
561.0ms318×body160nan

prune3.3m (9.1%)

series1.8m (5.1%)

Calls

476 calls:

1.7s
(- (* 1.0 1.0) (* (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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)))))))
1.6s
(- 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))))))
1.5s
(* (* (cbrt (* 0.5 (cos re))) (cbrt (- (* (* (* im im) im) -1/3) (fma (pow im 5) 1/60 (+ im im))))) (cbrt (* (* 0.5 (cos re)) (- (* (* (* im im) im) -1/3) (fma (pow im 5) 1/60 (+ im im))))))
1.5s
(- (* 1.0 1.0) (* (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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)))))))
1.5s
(- (* 1.0 1.0) (* (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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)))))))

regimes19.8s (0.9%)

Accuracy

Total 41.2b remaining (35.9%)

Threshold costs 6.3b (5.5%)

10.7b27%_divideComplex, real part
9.5b41%Octave 3.8, jcobi/4
7.1b35.8%_divideComplex, imaginary part
5.4b57.2%Octave 3.8, jcobi/1
1.2b52.6%Octave 3.8, jcobi/3

localize12.9s (0.6%)

bsearch1.8s (0.1%)

end1.0ms (0.0%)