Details

prune11.8m

simplify8.9m

sample8.0m

Algorithm

89×

intervals

Results

4.8m	75204×	body	10240	exit
1.2m	389803×	body	80	valid
33.2s	26185×	body	1280	valid
17.9s	20489×	body	640	valid
11.4s	3038×	body	1280	nan
10.9s	70101×	body	80	nan
6.6s	10653×	body	320	valid
6.2s	2550×	body	640	nan
5.2s	9420×	body	160	valid
2.3s	1285×	body	320	nan
1.9s	41536×	pre	80	true
1.2s	1396×	body	2560	valid
652.0ms	636×	body	5120	valid
643.0ms	649×	body	160	nan

rewrite3.8m

Algorithm

153×	rewrite-expression-head

Calls

476 calls:

Slowest

46.1s	(* (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) 1) (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
32.3s	(* (/ (sqrt (* PI 2)) (* (/ (exp 0.5) (pow (sqrt (+ 0.5 (+ z 6))) (+ (- z 1) 0.5))) (/ (exp (+ z 6)) (pow (sqrt (+ 0.5 (+ z 6))) (+ (- z 1) 0.5))))) (+ (/ -0.13857109526572012 (+ z 5)) (+ (+ (+ (+ (/ 12.507343278686905 (+ z 4)) (/ 9.984369578019572e-06 (+ z 6))) (/ 1.5056327351493116e-07 (+ z 7))) (/ 771.3234287776531 (+ 2 z))) (+ (/ -1259.1392167224028 (+ 1 z)) (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099))))))
27.0s	(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)
19.0s	(* (+ (/ -0.13857109526572012 (+ z 5)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 12.507343278686905 (+ 4 z))) (+ (/ 1.5056327351493116e-07 (+ z 7)) (/ 771.3234287776531 (+ 2 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (+ 3 z)) 0.9999999999998099)) (/ -1259.1392167224028 (+ 1 z))))) (/ 1 (/ (/ (exp (+ (+ 0.5 z) 6)) (pow (sqrt (+ (+ 0.5 z) 6)) (+ 0.5 (- z 1)))) (pow (sqrt (+ (+ 0.5 z) 6)) (+ 0.5 (- z 1))))))
8.0s	(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))

Rules

227789×	`*-un-lft-identity`
196520×	`times-frac`
103740×	`distribute-lft-out`
93818×	`sqrt-prod`
71102×	`add-sqr-sqrt`
58185×	`add-cube-cbrt`
28978×	`associate-r`
9912×	`add-exp-log`
5054×	`prod-exp`
4660×	`pow1`
3873×	`unpow-prod-down`
3640×	`div-exp`
3179×	`associate-/r/`
2713×	`add-cbrt-cube`
2550×	`associate-l`
2349×	`pow-prod-up`
2310×	`flip-+` `flip3-+`
2231×	`associate-/l*`
1836×	`div-inv`
1573×	`unswap-sqr`
1450×	`difference-of-squares`
1345×	`sqrt-div`
1165×	`pow-plus`
1141×	`frac-add`
1018×	`cbrt-unprod`
981×	`pow-exp`
790×	`distribute-lft-out--`
752×	`exp-sum`
727×	`add-log-exp`
653×	`associate-*l/`
633×	`pow-prod-down`
617×	`associate-/r*`
609×	`cbrt-undiv`
572×	`frac-times`
557×	`sqr-pow`
519×	`pow-to-exp`
478×	`associate-*r/`
476×	`insert-posit16`
467×	`unpow-prod-up`
389×	`cbrt-div`
386×	`1-exp`
366×	`cbrt-prod`
337×	`pow-sqr`
288×	`pow2`
239×	`sqrt-pow1`
234×	`flip3--` `flip--`
207×	`swap-sqr`
154×	`*-commutative` `pow1/2`
153×	`associate-/l/`
135×	`log-pow`
118×	`pow1/3`
90×	`cube-unmult`
89×	`sum-log`
85×	`frac-2neg` `clear-num`
70×	`log-prod`
69×	`distribute-rgt-in` `distribute-lft-in`
65×	`pow-sub`
64×	`sub-neg` `rem-sqrt-square`
59×	`+-commutative`
58×	`associate-+r-`
52×	`rec-exp`
50×	`cube-prod`
49×	`diff-log`
46×	`frac-sub`
35×	`pow3` `log-div`
22×	`div-sub`
16×	`associate--l+`
15×	`associate-+l+` `pow-unpow` `exp-prod`
14×	`pow-flip` `associate-+l-`
10×	`associate--r+`
9×	`rem-cube-cbrt` `sqrt-unprod` `inv-pow`
8×	`pow-div` `rem-log-exp` `distribute-rgt-out`
7×	`difference-cubes` `pow-pow`
6×	`sin-sum` `associate--r-` `distribute-rgt1-in`
5×	`associate-+r+` `rem-square-sqrt`
4×	`sum-cubes` `cube-mult`
3×	`unpow3` `cube-div`
2×	`associate--l-` `un-div-inv`
1×	`exp-diff` `distribute-lft1-in` `distribute-rgt-out--` `cos-sum`

series2.6m

Calls

476 calls:

Slowest

31.4s	(- (pow 1 3) (* (sqrt (pow (/ (+ (/ (- (* (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (* -0.284496736 -0.284496736)) (* (+ 1 (* (fabs x) 0.3275911)) (- (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))) 3)) (sqrt (pow (/ (+ (/ (- (* (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (* -0.284496736 -0.284496736)) (* (+ 1 (* (fabs x) 0.3275911)) (- (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))) 3))))
30.8s	(- (pow 1 3) (pow (/ (+ (/ (- (* (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (* -0.284496736 -0.284496736)) (* (+ 1 (* (fabs x) 0.3275911)) (- (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))) 3))
4.1s	(pow (/ (+ (/ (- (* (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (* -0.284496736 -0.284496736)) (* (+ 1 (* (fabs x) 0.3275911)) (- (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))) 3)
4.1s	(- 1 (/ (+ (/ (- (* (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (* -0.284496736 -0.284496736)) (* (+ 1 (* (fabs x) 0.3275911)) (- (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))))
4.0s	(pow (/ (+ (/ (- (* (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (* -0.284496736 -0.284496736)) (* (+ 1 (* (fabs x) 0.3275911)) (- (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))) 3)

regimes14.4s

Accuracy

Total 97.2b remaining (40.7%)

Threshold costs 3.9b (1.6%)

11.9b	41.8%	math.sqrt on complex, imaginary part, im greater than 0 branch
10.7b	54.5%	math.log10 on complex, real part
10.5b	54.9%	math.log/1 on complex, real part
10.2b	53.3%	math.abs on complex
10.2b	52.3%	math.log/2 on complex, real part

Details

prune11.8m

simplify8.9m

sample8.0m

rewrite3.8m

series2.6m

regimes14.4s

bsearch9.4s

localize8.7s

end1.0ms