Details

rewrite9.2m (38.0%)

Algorithm
166×rewrite-expression-head
Calls

529 calls:

2.3m
(* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI)))
2.0m
(* (* (+ (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) 0.9999999999998099) (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (- (+ z 4.0) 1.0)))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ 1.5056327351493116e-07 (+ 8.0 (- z 1.0))))) (pow (+ (+ 7.0 (- z 1.0)) 0.5) (- z (- 1.0 0.5)))) (/ (sqrt (* PI 2.0)) (exp (+ (+ 7.0 (- z 1.0)) 0.5))))
1.6m
(* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI)))
1.5m
(* (+ (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) 0.9999999999998099) (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (- (+ z 4.0) 1.0)))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ 1.5056327351493116e-07 (+ 8.0 (- z 1.0))))) (pow (+ (+ 7.0 (- z 1.0)) 0.5) (- z (- 1.0 0.5))))
23.8s
(* (+ (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))) (/ 12.507343278686905 (+ 5.0 (- z))))) (sqrt (* 2.0 PI)))
Rules
54478×times-frac
38630×*-un-lft-identity
24149×add-sqr-sqrt
21055×add-cube-cbrt
9048×distribute-lft-out
8213×sqrt-prod
5079×add-exp-log
4913×frac-add
4325×frac-times
4065×associate-*l/
3193×flip-+ flip3-+
2788×div-exp
2750×flip3-- flip--
2572×associate-*r*
2238×add-cbrt-cube
2143×div-inv
2063×associate-*l*
1920×swap-sqr
1638×associate-/r/
1636×associate-*r/
1569×pow1
1485×associate-/l*
1199×prod-exp
845×add-log-exp
825×unpow-prod-down
679×associate-/r*
627×cbrt-undiv
563×unswap-sqr
555×cbrt-unprod
548×1-exp
503×cbrt-prod
495×distribute-lft-out--
380×pow-prod-down
376×cube-prod
365×difference-of-squares
345×rec-exp
313×cbrt-div
296×sqrt-div
292×sqrt-pow1
253×pow-sub
212×log-pow
183×log-prod
174×pow-exp
150×associate-/l/
147×sqr-pow
138×*-commutative
135×pow-unpow
130×sum-log
124×pow1/2
113×distribute-rgt-neg-in
112×pow1/3
108×distribute-lft-neg-in
102×pow-to-exp
99×frac-2neg clear-num
96×distribute-rgt-in distribute-lft-in
76×sub-neg
68×pow-prod-up exp-prod
63×exp-sum +-commutative
60×rem-sqrt-square
53×diff-log
49×pow-pow
48×cube-div
44×pow-sqr
42×unpow3 cube-mult
37×frac-sub
30×exp-diff
27×neg-mul-1
26×rem-cube-cbrt
24×pow-plus
23×associate-+r+
22×div-sub
19×associate--l+ rem-log-exp
17×associate-+l+ pow2
15×log-div
13×unpow-prod-up
11×associate-+r- associate--r+
sin-sum rem-exp-log
rem-cbrt-cube
pow-flip difference-cubes inv-pow associate-+l-
neg-sub0 un-div-inv
sqrt-unprod rem-square-sqrt
pow3 sum-cubes unpow2 distribute-rgt-out-- unsub-neg
associate--l- sqrt-undiv pow-neg distribute-frac-neg sub-div exp-to-pow cos-sum associate--r- distribute-rgt-out

prune4.9m (20.5%)

simplify4.0m (16.6%)

sample3.4m (14.3%)

Algorithm
100×intervals
Results
1.0m16169×body10240exit
50.6s459773×body80valid
32.3s31044×body1280valid
15.3s23726×body640valid
6.8s69248×body80nan
6.2s11802×body320valid
5.3s3116×body1280nan
3.0s2701×body640nan
2.7s10206×body160valid
1.7s49536×pre80true
1.4s1222×body320nan
1.3s1531×body2560valid
342.0ms597×body5120valid
311.0ms698×body160nan

series2.0m (8.4%)

Calls

529 calls:

25.5s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 0.254829592) (* (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))))) (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))))))) (- 0.254829592 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0))))))))) (exp (- (* (fabs x) (fabs x))))))
3.5s
(/ (* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i))
3.0s
(* (/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (* (/ (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))) (+ (+ i alpha) beta)) (+ alpha (+ beta (* i 2.0))))) (/ (/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (+ alpha (+ beta (* i 2.0)))) (/ (+ (+ beta (* i 2.0)) (- alpha (sqrt 1.0))) i)))
1.8s
(- 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 1.0) (* (* (pow (fabs x) 2) 0.3275911) 0.3275911))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
1.8s
(exp (log (- 1.0 (* (exp (- (pow (fabs x) 2))) (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 0.254829592 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0))))))))))))

regimes16.7s (1.2%)

Accuracy

Total 126.3b remaining (49.4%)

Threshold costs 4.8b (1.9%)

23.9b35%math.sqrt on complex, real part
17.5b44.1%math.log10 on complex, real part
17.0b46.7%math.log/2 on complex, real part
9.9b59.4%math.log/1 on complex, real part
9.6b59.5%math.abs on complex

localize11.1s (0.8%)

bsearch3.8s (0.3%)

end1.0ms (0.0%)