Date:	Wednesday, February 26th, 2020
Commit:	a943e6d1 on master
Hostname:	warfa with Racket 7.5
Seed:	2020057
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

prune2.6m (33.1%)

series1.9m (24.6%)

Calls

455 calls:

20.6s	(fma 1.0 (* 1.0 1.0) (- (* (/ (pow (exp (- (* (fabs x) (fabs x)))) 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))))))))) (/ (pow (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 0.254829592 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))))))) (* (/ 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)))))))) (- 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)))))))))))))
20.3s	(- (pow 1.0 3) (/ (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 0.254829592 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))))))) (* (/ 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))))) 3) (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)))))))) 3)))
4.4s	(fma (- (/ (pow (exp (- (* (fabs x) (fabs x)))) 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)))))))))) (/ (pow (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 0.254829592 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))))))) (* (/ 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)))))))) (- 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)))))))))) (* (/ (pow (exp (- (* (fabs x) (fabs x)))) 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))))))))) (/ (pow (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 0.254829592 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))))))) (* (/ 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)))))))) (- 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))))))))))))
3.4s	(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 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))))) 3))
2.2s	(* (/ (/ (sqrt i) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1)) 1) (/ (/ (sqrt i) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))))

sample1.9m (24.2%)

Algorithm

100×

intervals

Results

46.9s	15826×	body	10240	exit
21.6s	495010×	body	80	valid
13.9s	30438×	body	1280	valid
6.4s	23246×	body	640	valid
2.8s	3072×	body	1280	nan
2.4s	70135×	body	80	nan
2.1s	11954×	body	320	valid
1.6s	2517×	body	640	nan
1.2s	10236×	body	160	valid
652.0ms	49536×	pre	80	true
597.0ms	1258×	body	320	nan
392.0ms	1532×	body	2560	valid
209.0ms	694×	body	160	nan
125.0ms	540×	body	5120	valid

rewrite43.2s (9.2%)

Algorithm

155×	rewrite-expression-head

Calls

455 calls:

31.4s	(* (/ (/ (sqrt i) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1)) 1) (/ (/ (sqrt i) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))))
270.0ms	(/ (/ (sqrt i) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
158.0ms	(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ z 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (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))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ z 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))))
151.0ms	(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ z 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))

Rules

118395×	`times-frac`
72726×	`*-un-lft-identity`
57609×	`add-sqr-sqrt`
43465×	`add-cube-cbrt`
15303×	`sqrt-prod`
13620×	`distribute-lft-out`
10441×	`associate-r`
6365×	`difference-of-squares`
5826×	`cbrt-prod`
3613×	`div-inv`
3300×	`prod-diff`
3146×	`add-exp-log`
2968×	`associate-/r/`
2910×	`distribute-lft-out--`
2288×	`add-cbrt-cube`
1552×	`pow1`
1378×	`flip-+` `flip3-+`
1344×	`unpow-prod-down`
1229×	`associate-l`
1162×	`cube-prod`
1079×	`div-exp`
1009×	`prod-exp`
856×	`associate-/l*`
748×	`frac-add`
701×	`cbrt-unprod`
698×	`associate-/r*`
693×	`add-log-exp`
589×	`sqr-pow`
583×	`cbrt-undiv`
489×	`pow-prod-down`
460×	`unpow3` `cube-mult` `unswap-sqr`
457×	`expm1-log1p-u`
455×	`log1p-expm1-u`
412×	`frac-times`
406×	`associate-*r/`
371×	`distribute-rgt-in` `distribute-lft-in`
289×	`fma-neg`
248×	`associate-*l/`
231×	`log-pow`
194×	`exp-sum`
182×	`1-exp`
172×	`associate--l+`
157×	`flip3--` `flip--`
148×	`fma-def`
144×	`associate-/l/` `log-prod`
131×	`*-commutative`
105×	`cbrt-div`
100×	`associate-+l-`
98×	`sub-neg`
96×	`clear-num` `frac-2neg`
92×	`pow-sub`
89×	`diff-log`
88×	`exp-prod`
86×	`pow-exp`
85×	`swap-sqr`
84×	`pow1/3`
77×	`associate--r+`
75×	`sqrt-div` `rec-exp`
66×	`sqrt-pow1`
65×	`pow-to-exp`
64×	`pow-unpow`
63×	`exp-diff`
62×	`distribute-rgt-neg-in` `fma-udef`
60×	`distribute-lft-neg-in` `exp-neg`
46×	`pow1/2` `cube-div`
44×	`neg-sub0`
39×	`sum-log`
36×	`pow-prod-up`
34×	`pow-sqr`
32×	`neg-mul-1`
26×	`pow-pow` `+-commutative`
22×	`rem-sqrt-square`
20×	`un-div-inv`
19×	`pow-plus`
18×	`rem-exp-log`
17×	`div-sub` `associate--l-`
16×	`pow-flip` `pow2`
14×	`unpow-prod-up`
13×	`rem-cube-cbrt` `inv-pow`
12×	`hypot-def` `rem-log-exp` `log-div`
11×	`associate-+l+`
10×	`neg-log`
8×	`frac-sub`
6×	`unpow2` `associate-+r+`
4×	`sin-sum`
3×	`difference-cubes`
2×	`log1p-udef` `log1p-expm1` `distribute-neg-in` `expm1-log1p` `distribute-rgt-neg-out` `expm1-udef` `exp-to-pow`
1×	`sqrt-pow2` `sqrt-unprod` `hypot-udef` `rem-square-sqrt` `distribute-rgt-out` `cos-sum` `associate--r-` `distribute-rgt-out--` `rem-cbrt-cube`

simplify33.0s (7.0%)

Algorithm

255×	egg-herbie

regimes5.5s (1.2%)

Accuracy

Total 51.6b remaining (46.8%)

Threshold costs 7.0b (6.3%)

8.9b	46.7%	Octave 3.8, jcobi/4
8.5b	33.3%	_divideComplex, imaginary part
7.7b	30.4%	_divideComplex, real part
6.4b	-6.7%	math.sqrt on complex, imaginary part, im greater than 0 branch
5.6b	11.1%	Octave 3.8, jcobi/2

Details

prune2.6m (33.1%)

series1.9m (24.6%)

sample1.9m (24.2%)

rewrite43.2s (9.2%)

simplify33.0s (7.0%)

regimes5.5s (1.2%)

localize2.6s (0.5%)

bsearch877.0ms (0.2%)

end1.0ms (0.0%)