Date:	Tuesday, February 25th, 2020
Commit:	61e80a61 on faster-rr
Hostname:	warfa with Racket 7.5
Seed:	2020056
Parameters:	256 points for 4 iterations
Flags:	`setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback` `+o rules:numerics`

Details

sample1.9m (40.8%)

Algorithm

99×

intervals

Results

48.3s	15781×	body	10240	exit
17.5s	438509×	body	80	valid
14.0s	30719×	body	1280	valid
6.6s	23690×	body	640	valid
2.7s	3221×	body	1280	nan
2.5s	70235×	body	80	nan
2.2s	11834×	body	320	valid
1.6s	2548×	body	640	nan
1.2s	10091×	body	160	valid
654.0ms	49536×	pre	80	true
547.0ms	1221×	body	320	nan
328.0ms	1394×	body	2560	valid
192.0ms	648×	body	160	nan
146.0ms	593×	body	5120	valid

series1.2m (25.3%)

Calls

456 calls:

1.9s	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
1.5s	(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (- (* (fabs x) (fabs x))))))
1.4s	(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (- (* (fabs x) (fabs x))))))
1.3s	(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (- (* (fabs x) (fabs x))))))
1.3s	(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (- (* (fabs x) (fabs x))))))

prune1.0m (23.0%)

simplify14.7s (5.4%)

Algorithm

252×	egg-herbie

rewrite5.8s (2.1%)

Algorithm

154×	rewrite-expression-head

Calls

456 calls:

201.0ms	(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
199.0ms	(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
167.0ms	(/ (* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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)))
164.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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)))
156.0ms	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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))))

Rules

6949×	`*-un-lft-identity`
6389×	`times-frac`
5780×	`add-sqr-sqrt`
4752×	`add-cube-cbrt`
2558×	`add-exp-log`
1952×	`add-cbrt-cube`
1529×	`pow1` `prod-diff`
1278×	`sqrt-prod`
1036×	`prod-exp`
984×	`distribute-lft-out`
884×	`associate-r`
748×	`frac-add`
714×	`associate-l`
697×	`cbrt-unprod`
678×	`add-log-exp`
604×	`associate-/l*`
525×	`div-exp`
521×	`pow-prod-down`
460×	`log1p-expm1-u`
457×	`expm1-log1p-u`
432×	`flip-+` `flip3-+`
412×	`associate-*r/`
388×	`associate-/r*`
372×	`associate-/r/`
340×	`div-inv`
323×	`cbrt-undiv`
271×	`cbrt-prod`
243×	`difference-of-squares`
238×	`unpow-prod-down`
237×	`distribute-lft-out--`
228×	`fma-def`
227×	`unswap-sqr`
226×	`fma-neg`
224×	`distribute-rgt-in` `distribute-lft-in`
212×	`log-pow`
204×	`frac-times`
185×	`exp-sum`
182×	`sqrt-div`
145×	`associate-/l/`
136×	`associate--l+`
125×	`associate-*l/`
124×	`*-commutative`
120×	`flip3--` `flip--`
115×	`sqr-pow`
114×	`associate-+l-`
109×	`1-exp`
104×	`pow-sub`
103×	`cube-prod`
94×	`clear-num` `frac-2neg`
92×	`pow-exp`
88×	`sub-neg`
83×	`log-prod`
77×	`sqrt-pow1`
74×	`diff-log`
71×	`associate--r+`
68×	`cbrt-div`
67×	`pow1/3`
66×	`pow-to-exp`
64×	`swap-sqr`
62×	`exp-prod`
61×	`fma-udef`
58×	`rec-exp`
52×	`pow1/2` `pow-unpow`
47×	`sum-log`
34×	`+-commutative`
33×	`pow-prod-up`
32×	`unpow3` `cube-mult`
27×	`distribute-rgt-neg-in` `distribute-lft-neg-in`
24×	`div-sub`
23×	`rem-sqrt-square` `pow-sqr` `pow-plus` `neg-mul-1`
18×	`pow-pow` `associate-+l+` `associate-+r+`
17×	`hypot-udef`
14×	`pow2` `associate--l-`
13×	`pow-flip`
12×	`hypot-def`
10×	`inv-pow`
9×	`exp-diff` `rem-cube-cbrt`
8×	`rem-exp-log`
6×	`log1p-udef` `sqrt-unprod` `log1p-expm1` `rem-log-exp` `unpow2`
5×	`rem-cbrt-cube` `distribute-rgt-neg-out`
4×	`sqrt-undiv` `un-div-inv` `sin-sum` `distribute-neg-in` `unpow-prod-up` `expm1-log1p` `frac-sub` `expm1-udef`
2×	`sqrt-pow2` `pow3` `rem-square-sqrt` `neg-sub0` `neg-log` `log-div`
1×	`unsub-neg` `cos-sum` `associate--r-`

regimes5.7s (2.1%)

Accuracy

Total 41.5b remaining (31.9%)

Threshold costs 6.9b (5.3%)

9.0b	31.9%	_divideComplex, imaginary part
7.4b	33.4%	_divideComplex, real part
5.9b	9.9%	Octave 3.8, jcobi/2
4.1b	26.8%	math.sqrt on complex, imaginary part, im greater than 0 branch
3.9b	38.1%	math.sqrt on complex, real part

Details

sample1.9m (40.8%)

series1.2m (25.3%)

prune1.0m (23.0%)

simplify14.7s (5.4%)

rewrite5.8s (2.1%)

regimes5.7s (2.1%)

localize2.5s (0.9%)

bsearch1.1s (0.4%)

end1.0ms (0.0%)