Details

rewrite14.5m (44.2%)

Algorithm
159×rewrite-expression-head
Calls

489 calls:

5.8m
(* (+ (+ (/ 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)))
1.9m
(* (/ (* (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
(* (/ (* (* (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (cbrt (* (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))))))
16.1s
(/ (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (+ (+ (+ (/ 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)))))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
10.1s
(+ (+ (+ (/ -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))))
Rules
34671×times-frac
23428×*-un-lft-identity
18938×add-sqr-sqrt
14005×add-cube-cbrt
6574×sqrt-prod
4751×distribute-lft-out
2995×frac-add
2423×add-exp-log
2283×associate-*r*
1911×add-cbrt-cube
1907×flip-+ flip3-+
1793×pow1
1675×difference-of-squares
1406×associate-*l*
1327×associate-/r/
1269×div-inv
954×associate-*r/
952×associate-/r*
854×associate-/l*
776×unpow-prod-down
739×add-log-exp
687×prod-exp
635×div-exp
613×log-pow
576×frac-times
568×distribute-lft-out--
540×cbrt-prod
512×cbrt-unprod
451×unswap-sqr
439×cbrt-undiv
434×associate-/l/
360×associate-*l/
311×pow-prod-down
309×cube-prod
287×sqr-pow
223×sqrt-div
191×flip-- flip3--
168×sqrt-pow1
148×*-commutative
131×pow-exp
128×swap-sqr
121×associate-+l-
116×log-prod
113×pow-sub
103×frac-2neg clear-num
93×pow1/2
90×sum-log
83×distribute-rgt-in distribute-lft-in
82×cbrt-div
80×sub-neg distribute-rgt-neg-in
79×pow-to-exp
78×exp-prod
76×distribute-lft-neg-in
75×frac-sub
72×pow1/3
66×pow-unpow
64×rem-sqrt-square
53×1-exp
52×+-commutative
49×diff-log
47×pow-prod-up
43×exp-sum
41×rec-exp
38×unpow3 cube-mult
35×pow-sqr
32×pow-pow
24×rem-cube-cbrt pow-plus
23×cube-div
20×div-sub
18×neg-mul-1
17×pow2 unpow2
16×associate--l+ log-div
13×exp-diff
12×associate-+r+
10×inv-pow pow-flip
9×associate-+l+
8×sin-sum rem-log-exp
6×associate--r+
4×sum-cubes rem-cbrt-cube
3×sqrt-undiv associate--r-
2×difference-cubes sqrt-unprod pow3 distribute-rgt-out-- unpow-prod-up
1×cos-sum un-div-inv rem-exp-log cube-unmult rem-square-sqrt distribute-rgt-out

simplify6.8m (20.8%)

series3.8m (11.5%)

Calls

488 calls:

38.5s
(- (pow 1.0 3) (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (/ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 1.421413741 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 1.0 (* 0.3275911 (fabs x)))) 3))
37.2s
(- (pow 1.0 3) (* (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (/ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 1.421413741 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 1.0 (* 0.3275911 (fabs x)))) 3)) (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (/ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 1.421413741 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 1.0 (* 0.3275911 (fabs x)))) 3))))
8.7s
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))
6.9s
(* (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (/ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 1.421413741 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 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 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 1.0 (* 0.3275911 (fabs x)))) 1.0))
6.5s
(* (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (/ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 1.421413741 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 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 1.421413741) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))) (- 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)))) (+ 1.0 (* 0.3275911 (fabs x)))) 1.0))

sample3.7m (11.3%)

Algorithm
99×intervals
Results
1.3m488977×body80valid
37.6s30713×body1280valid
20.2s12141×body10240exit
20.0s23518×body640valid
9.6s69263×body80nan
7.4s12203×body320valid
3.9s9916×body160valid
3.0s1642×body1280nan
2.6s1330×body640nan
2.0s49536×pre80true
1.1s1410×body2560valid
934.0ms672×body320nan
479.0ms615×body5120valid
165.0ms320×body160nan

prune3.4m (10.4%)

regimes20.6s (1.0%)

Accuracy

Total 92.7b remaining (34.9%)

Threshold costs 3.7b (1.4%)

13.1b55.9%math.sqrt on complex, real part
10.8b56.9%math.log10 on complex, real part
10.6b57.5%math.log/1 on complex, real part
10.4b58%math.log/2 on complex, real part
9.9b58.9%math.abs on complex

localize8.7s (0.4%)

bsearch4.8s (0.2%)

end1.0ms (0.0%)