Details

sample10.0m (31.5%)

Algorithm

90×

intervals

Results

6.8m	103454×	body	10240	exit
1.2m	401945×	body	80	valid
34.3s	26217×	body	1280	valid
18.1s	20383×	body	640	valid
11.8s	70635×	body	80	nan
9.3s	3006×	body	1280	nan
7.4s	2565×	body	640	nan
6.9s	10366×	body	320	valid
5.2s	9639×	body	160	valid
3.1s	1225×	body	320	nan
2.4s	49536×	pre	80	true
1.6s	1444×	body	2560	valid
620.0ms	662×	body	160	nan
550.0ms	590×	body	5120	valid

prune8.6m (27.0%)

simplify6.7m (20.9%)

rewrite4.6m (14.3%)

Algorithm

141×	rewrite-expression-head

Calls

428 calls:

Slowest

31.9s	(/ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (/ 12.507343278686905 (- z (- 1 5))) (/ 9.984369578019572e-06 (+ 7 (- z 1))))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))) (+ (/ 771.3234287776531 (+ 3 (- z 1))) (+ (/ -1259.1392167224028 (+ 2 (- z 1))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1) 4)))))) (exp (+ (+ 7 (- z 1)) 0.5)))
31.3s	(/ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (/ 12.507343278686905 (- z (- 1 5))) (/ 9.984369578019572e-06 (+ 7 (- z 1))))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))) (+ (/ 771.3234287776531 (+ 3 (- z 1))) (+ (/ -1259.1392167224028 (+ 2 (- z 1))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1) 4)))))) (exp (+ (+ 7 (- z 1)) 0.5)))
28.4s	(* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (/ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (/ 12.507343278686905 (- z (- 1 5))) (/ 9.984369578019572e-06 (+ 7 (- z 1))))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))) (+ (/ 771.3234287776531 (+ 3 (- z 1))) (+ (/ -1259.1392167224028 (+ 2 (- z 1))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1) 4)))))) (exp (+ (+ 7 (- z 1)) 0.5))))
27.9s	(* (* (pow (+ (+ 7 (- z 1)) 0.5) z) (sqrt (* PI 2))) (/ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (/ 12.507343278686905 (- z (- 1 5))) (/ 9.984369578019572e-06 (+ 7 (- z 1))))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))) (+ (/ 771.3234287776531 (+ 3 (- z 1))) (+ (/ -1259.1392167224028 (+ 2 (- z 1))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1) 4)))))) (exp (+ (+ 7 (- z 1)) 0.5))))
16.9s	(/ (/ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (/ 9.984369578019572e-06 (+ 7 (- z 1))) (/ 12.507343278686905 (+ (- z 1) 5)))) (+ (/ 1.5056327351493116e-07 (+ (- z 1) 8)) (+ (+ (/ 771.3234287776531 (+ 3 (- z 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (+ (/ -176.6150291621406 (+ 4 (- z 1))) (+ (/ 676.5203681218851 z) 0.9999999999998099))))) (exp (+ 7 (- z 1)))) (exp 0.5))

Rules

22690×	`*-un-lft-identity`
19916×	`times-frac`
10463×	`add-sqr-sqrt`
9472×	`add-cube-cbrt`
8945×	`distribute-lft-out`
4614×	`sqrt-prod`
3236×	`add-exp-log`
2888×	`pow1`
2343×	`frac-add`
1888×	`add-cbrt-cube`
1598×	`associate-*l/`
1533×	`associate-/l*`
1373×	`flip-+` `flip3-+`
1362×	`frac-times`
1305×	`prod-diff`
1302×	`prod-exp`
1130×	`frac-sub`
1107×	`associate-r`
1054×	`pow-prod-up`
922×	`div-exp`
858×	`associate-l`
715×	`associate-/r/`
632×	`cbrt-unprod`
631×	`exp-sum`
609×	`add-log-exp`
598×	`associate-*r/`
561×	`flip3--` `flip--`
481×	`associate-/r*`
479×	`pow-prod-down`
475×	`div-inv`
468×	`pow-plus`
428×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
366×	`associate-/l/`
358×	`cbrt-undiv`
338×	`sqrt-div`
326×	`unpow-prod-down`
287×	`fma-def`
278×	`distribute-lft-out--`
265×	`cbrt-prod`
263×	`distribute-rgt-in` `distribute-lft-in`
257×	`pow-exp`
240×	`pow-sqr`
230×	`unswap-sqr`
221×	`difference-of-squares`
206×	`pow2`
189×	`log-pow`
173×	`sqrt-pow1`
167×	`sqr-pow`
154×	`fma-neg`
147×	`pow-to-exp`
138×	`*-commutative`
100×	`cbrt-div`
91×	`frac-2neg` `clear-num` `swap-sqr`
83×	`pow1/2`
81×	`sub-neg`
73×	`1-exp`
69×	`associate--r+`
65×	`rec-exp`
62×	`sum-log`
60×	`fma-udef`
56×	`log-prod` `pow1/3`
43×	`unpow-prod-up` `cube-prod`
39×	`associate--l+` `pow-unpow`
37×	`diff-log`
35×	`+-commutative`
34×	`associate-+l+`
29×	`pow3`
26×	`cube-unmult`
22×	`exp-diff` `cube-mult`
21×	`unpow3`
19×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`rem-sqrt-square`
17×	`hypot-udef`
16×	`associate-+r-` `pow-sub`
14×	`distribute-rgt1-in` `un-div-inv` `distribute-rgt-out`
13×	`pow-flip` `div-sub`
11×	`associate-+l-`
10×	`sin-sum` `pow-pow` `hypot-def`
9×	`exp-prod` `log-div`
8×	`inv-pow`
7×	`neg-sub0` `associate-+r+` `neg-mul-1` `pow-neg`
6×	`distribute-neg-in`
5×	`sqrt-undiv` `sub0-neg` `sqrt-unprod` `rem-square-sqrt` `rem-log-exp`
3×	`distribute-rgt-neg-out` `rem-cbrt-cube`
2×	`distribute-lft-neg-out` `exp-to-pow` `rem-exp-log` `unsub-neg` `associate--r-` `sin-mult`
1×	`associate--l-` `difference-cubes` `cos-sum` `exp-neg`

series1.6m (4.9%)

Calls

428 calls:

Slowest

3.3s	(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (/ (cbrt (* (* (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (- (* 0.254829592 0.254829592) (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (- (* 0.254829592 0.254829592) (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))))) (cbrt (* (- 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (- 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))))))) (exp (- (* (fabs x) (fabs x))))))
3.3s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
3.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
3.2s	(- (pow 1 3) (pow (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (/ (cbrt (* (* (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (- (* 0.254829592 0.254829592) (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (- (* 0.254829592 0.254829592) (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))))) (cbrt (* (- 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (- 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
1.5s	(cbrt (* (* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (pow (* -2 (log u1)) 0.5) 6)) (/ (pow (* -2 (log u1)) 0.5) 6)))

regimes12.2s (0.6%)

Accuracy

Total 29.1b remaining (22.8%)

Threshold costs 5.6b (4.4%)

10.1b	27.5%	_divideComplex, imaginary part
6.7b	35.3%	_divideComplex, real part
2.8b	79.4%	Octave 3.8, jcobi/1
1.5b	43.7%	Octave 3.8, jcobi/4
1.3b	0%	Jmat.Real.lambertw, newton loop step

Details

sample10.0m (31.5%)

prune8.6m (27.0%)

simplify6.7m (20.9%)

rewrite4.6m (14.3%)

series1.6m (4.9%)

regimes12.2s (0.6%)

localize9.8s (0.5%)

bsearch1.8s (0.1%)

end1.0ms (0.0%)