Details

rewrite14.2m (53.3%)

Algorithm
161×rewrite-expression-head
Calls

494 calls:

5.0m
(* (+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))) (sqrt (* PI 2.0)))
4.1m
(* (+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))) (sqrt (* PI 2.0)))
1.1m
(* (* (/ (* (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))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))
56.8s
(* (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (- 1.0 7.0))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))
26.0s
(* (/ (+ (+ (+ (+ (+ 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
27298×times-frac
18424×*-un-lft-identity
16910×add-sqr-sqrt
11155×add-cube-cbrt
6824×sqrt-prod
3762×frac-add
3002×add-exp-log
2728×distribute-lft-out
2657×associate-*l*
2561×associate-*r*
2070×add-cbrt-cube
1909×difference-of-squares
1859×distribute-rgt-neg-in
1848×distribute-lft-neg-in
1791×flip-+ flip3-+
1594×pow1
1128×div-inv
1062×frac-times
1061×distribute-lft-out--
971×prod-exp
883×div-exp
869×cbrt-prod
816×associate-/r*
787×add-log-exp
762×associate-/l*
717×associate-/r/
712×associate-*r/
655×associate-*l/
639×cbrt-unprod
532×cbrt-undiv
454×exp-diff
449×unswap-sqr
417×unpow-prod-down neg-mul-1
380×sqrt-div
343×pow-prod-down
272×log-pow
256×pow-unpow
240×sqrt-pow1
239×associate-+l-
231×pow-sub
212×cbrt-div
187×flip3-- flip--
171×cube-prod
148×pow1/2
131×associate-/l/
130×sqr-pow *-commutative
124×log-prod
121×swap-sqr
109×sum-log
98×pow1/3
97×pow-exp
94×clear-num frac-2neg
91×1-exp
89×pow-prod-up
88×rec-exp
77×rem-sqrt-square
67×sub-neg
63×exp-prod
62×pow-to-exp
61×diff-log
59×distribute-rgt-in distribute-lft-in
57×pow-sqr
55×+-commutative
47×exp-sum
40×associate--l+
37×pow-pow
33×pow-plus
30×distribute-neg-frac
28×pow2
19×unpow3 cube-mult rem-log-exp
17×log-div
15×pow-flip associate-+r+ div-sub
14×cube-div un-div-inv unpow-prod-up
11×rem-exp-log frac-sub
10×difference-cubes
9×associate-+l+
8×rem-cube-cbrt inv-pow
7×neg-sub0 sum-cubes
6×sin-sum associate--r+
4×sqrt-undiv unpow1/3 rem-cbrt-cube unpow2
3×sqrt-unprod rem-square-sqrt associate--r-
2×distribute-rgt-out neg-log
1×cos-sum sqrt-pow2 associate-+r- distribute-rgt-out-- distribute-frac-neg exp-to-pow associate--l-

simplify5.2m (19.4%)

sample3.1m (11.5%)

Algorithm
100×intervals
Results
53.3s458907×body80valid
31.9s30213×body1280valid
31.7s13251×body10240exit
16.5s23676×body640valid
6.5s68944×body80nan
5.7s11805×body320valid
3.3s10229×body160valid
3.2s2091×body1280nan
2.2s1743×body640nan
2.0s49536×pre80true
1.0s1506×body2560valid
873.0ms882×body320nan
392.0ms618×body5120valid
197.0ms444×body160nan

prune2.4m (8.9%)

series1.5m (5.7%)

Calls

494 calls:

3.1s
(* (/ (/ (* 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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
3.1s
(* (/ (/ (* 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))))
1.5s
(- 1.0 (/ (* 1.0 (/ (log (* (exp 0.254829592) (exp (* (/ 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 (* (* (/ (sqrt 1.0) (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (/ (sqrt 1.0) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429)))))))))) (exp (* (fabs x) (fabs x))))) (+ 1.0 (* 0.3275911 (fabs x)))))
1.5s
(* (/ (sqrt (/ 1 (sqrt 2.0))) (+ (sqrt 2.0) (sqrt (/ (sqrt 1.0) i)))) (/ (sqrt (/ (/ 1 (sqrt 2.0)) 2.0)) (- (sqrt 2.0) (sqrt (/ (sqrt 1.0) i)))))
1.3s
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)

regimes9.0s (0.6%)

Accuracy

Total 88.2b remaining (32.1%)

Threshold costs 3.8b (1.4%)

10.6b56.3%math.log/2 on complex, real part
10.0b58.8%math.log10 on complex, real part
10.0b58.9%math.log/1 on complex, real part
9.7b58.9%math.abs on complex
9.0b58.9%math.sqrt on complex, real part

localize5.4s (0.3%)

bsearch2.8s (0.2%)

end1.0ms (0.0%)