Details

rewrite11.8m (48.8%)

Algorithm
165×rewrite-expression-head
Calls

490 calls:

4.9m
(* (+ (+ (/ 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)))
2.6m
(* (sqrt PI) (+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 771.3234287776531 (- 3.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (/ -176.6150291621406 (+ (- z) 4.0)))))
1.4m
(* (/ (* (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))) (+ (+ (+ (/ 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))))))
1.3m
(/ (* (sqrt PI) (- (* (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0)))) (* (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 771.3234287776531 (- 3.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 771.3234287776531 (- 3.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (/ -176.6150291621406 (+ (- z) 4.0)))))) (- (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 771.3234287776531 (- 3.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (/ -176.6150291621406 (+ (- z) 4.0)))))
14.7s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
Rules
20781×frac-add
15839×times-frac
12432×*-un-lft-identity
10751×add-sqr-sqrt
7524×add-cube-cbrt
7098×flip-+ flip3-+
5509×frac-times
5247×associate-*r/
3612×add-exp-log
3512×associate-/l/
3412×frac-sub
2908×sqrt-prod
2692×add-cbrt-cube
2170×distribute-lft-out
2127×pow1
1597×associate-*l*
1546×prod-exp
1365×associate-*l/
1036×cbrt-unprod
1005×associate-/l*
991×associate-*r*
989×difference-of-squares
812×div-exp
784×sqrt-div
761×associate-/r/
719×add-log-exp
585×associate-/r*
562×cbrt-undiv
555×div-inv
508×pow-prod-down
503×unpow-prod-down
451×distribute-lft-out--
422×log-pow
362×unswap-sqr
343×cbrt-prod
330×swap-sqr
307×flip3-- flip--
302×sqrt-pow1
252×pow-prod-up
244×distribute-rgt-neg-in
228×cbrt-div
201×pow-exp
189×pow1/2
188×pow-plus
164×*-commutative
158×pow1/3
154×sqr-pow
111×pow-to-exp
109×distribute-lft-neg-in
98×distribute-rgt-in pow-sqr distribute-lft-in
96×clear-num frac-2neg
85×sub-neg
79×sum-log
75×rem-sqrt-square
72×exp-prod
70×log-prod
58×cube-prod
57×pow2
50×diff-log
48×1-exp
47×div-sub
43×exp-sum
37×+-commutative
36×rec-exp
33×log-div
30×unpow2
28×neg-mul-1
21×pow-unpow
16×pow-pow unpow-prod-up associate--l+
14×unpow3 pow3 cube-mult
12×associate-+l-
11×associate-+r+ neg-sub0
10×exp-diff associate-+l+
8×associate--r+
7×sqrt-unprod
6×exp-neg pow-flip inv-pow
5×un-div-inv rem-exp-log sqrt-undiv rem-log-exp
4×cube-div sin-sum pow-sub rem-square-sqrt
3×rem-cube-cbrt associate-+r-
2×difference-cubes associate--r- associate--l-
1×cos-sum sqrt-pow2 distribute-frac-neg distribute-rgt-out neg-log rem-cbrt-cube

simplify5.2m (21.5%)

sample2.8m (11.5%)

Algorithm
99×intervals
Results
47.6s437592×body80valid
32.7s30483×body1280valid
18.5s23434×body640valid
16.1s11842×body10240exit
7.2s70642×body80nan
6.2s11584×body320valid
3.6s10052×body160valid
3.3s1584×body1280nan
2.1s49536×pre80true
1.8s1477×body2560valid
1.4s1331×body640nan
1.0s636×body320nan
386.0ms634×body5120valid
130.0ms333×body160nan

prune2.6m (10.7%)

series1.5m (6.1%)

Calls

490 calls:

4.9s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3))
1.5s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.4s
(- (pow (sqrt 1.0) 3) (sqrt (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3)))
1.3s
(sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))
1.2s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (* (fabs x) (fabs x))))))

regimes11.0s (0.8%)

Accuracy

Total 105.2b remaining (39.1%)

Threshold costs 3.8b (1.4%)

13.3b53.7%math.sqrt on complex, real part
10.6b56.4%math.log/2 on complex, real part
10.3b58.3%math.log10 on complex, real part
10.1b37.7%powComplex, imaginary part
10.0b59.1%math.log/1 on complex, real part

bsearch5.6s (0.4%)

localize5.3s (0.4%)

end1.0ms (0.0%)