Details

simplify7.3m (32.6%)

rewrite6.1m (27.4%)

Algorithm
154×rewrite-expression-head
Calls

474 calls:

1.1m
(* (/ (* (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))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
48.1s
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (- z 1.0) 7.0))) (* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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))))))))
44.4s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
42.2s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
42.1s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
Rules
21344×times-frac
14998×*-un-lft-identity
12032×add-sqr-sqrt
9886×add-cube-cbrt
8942×frac-add
4904×sqrt-prod
3263×flip-+ flip3-+
2966×frac-times
2511×distribute-lft-out
2477×add-exp-log
2439×associate-*r/
2038×associate-*l*
1856×add-cbrt-cube
1456×pow1
1384×associate-*r*
929×associate-/r/
897×prod-exp
883×unpow-prod-down
857×cbrt-prod
753×associate-*l/
735×div-inv
715×add-log-exp div-exp
656×associate-/l*
635×associate-/r*
528×cbrt-unprod
509×cbrt-div
425×cbrt-undiv
421×unswap-sqr
398×difference-of-squares
359×distribute-lft-out--
343×log-pow
331×swap-sqr
295×pow-prod-down
290×cube-prod
223×sqrt-div
193×sqr-pow
189×associate-/l/ sqrt-pow1
160×exp-sum
159×flip3-- flip--
147×pow1/2
145×unpow-prod-up
144×sub-neg
138×*-commutative
137×pow-exp
127×pow1/3
105×pow-to-exp
91×frac-2neg sum-log clear-num
88×distribute-rgt-in distribute-lft-in
57×pow-unpow rem-sqrt-square
56×cube-div
55×+-commutative
53×log-prod
44×1-exp
43×pow-prod-up
42×diff-log
36×rec-exp
35×pow-sqr pow-pow
24×associate-+r+ pow-plus
23×unpow3 cube-mult div-sub
20×pow2
18×associate-+l- associate--r+
16×exp-diff rem-cube-cbrt
11×exp-prod
10×log-div
un-div-inv pow-sub
associate--r- sum-cubes rem-cbrt-cube
distribute-rgt-neg-in inv-pow pow-flip associate--l+ unpow2
associate-+l+ sqrt-undiv associate-+r- sin-sum
cos-sum
sqrt-unprod pow3 rem-square-sqrt neg-sub0
difference-cubes sqrt-pow2 rem-exp-log unpow1/3 associate--l- unsub-neg distribute-rgt-out rem-log-exp

sample4.0m (17.9%)

Algorithm
99×intervals
Results
1.4m15908×body10240exit
52.5s435680×body80valid
32.1s30526×body1280valid
16.2s23536×body640valid
7.1s69906×body80nan
6.3s3002×body1280nan
5.8s2648×body640nan
5.0s12105×body320valid
3.3s9946×body160valid
1.4s49536×pre80true
1.1s1329×body320nan
794.0ms1451×body2560valid
766.0ms595×body160nan
477.0ms589×body5120valid

prune2.7m (12.3%)

series1.9m (8.4%)

Calls

474 calls:

4.6s
(- (pow 1.0 3) (pow (/ 1.0 (/ (+ (* 0.3275911 (fabs x)) 1.0) (/ (+ 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 (pow (fabs x) 2))))) 3))
4.6s
(- (pow 1.0 3) (/ (* (* 1.0 1.0) 1.0) (/ (* (* (+ (* 0.3275911 (fabs x)) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)) (+ (* 0.3275911 (fabs x)) 1.0)) (/ (* (* (+ 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)))))))) (+ 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))))))))) (+ 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 (pow (fabs x) 2)) (exp (pow (fabs x) 2))) (exp (pow (fabs x) 2)))))))
4.5s
(- (pow 1.0 3) (/ (* (* 1.0 1.0) 1.0) (/ (* (* (+ (* 0.3275911 (fabs x)) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)) (+ (* 0.3275911 (fabs x)) 1.0)) (/ (* (cbrt (pow (* (+ 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)))))))) (+ 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))))))))) 3)) (+ 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 (pow (fabs x) 2)) (exp (pow (fabs x) 2))) (exp (pow (fabs x) 2)))))))
3.4s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) 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))))
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))))

regimes10.8s (0.8%)

Accuracy

Total 123.1b remaining (43.4%)

Threshold costs 5.8b (2%)

17.5b28.2%math.log10 on complex, real part
17.3b28.5%math.log/1 on complex, real part
13.8b37.9%math.sqrt on complex, imaginary part, im greater than 0 branch
12.7b39%math.sqrt on complex, real part
10.8b55.9%math.log/2 on complex, real part

localize4.3s (0.3%)

bsearch3.7s (0.3%)

end1.0ms (0.0%)