Date:	Thursday, June 4th, 2020
Commit:	630fd560 on ival-find-range
Hostname:	warfa with Racket 7.5
Seed:	2020156
Parameters:	256 points for 4 iterations
Flags:	`setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback` default

Details

sample4.0m (52.9%)

Algorithm

99×

intervals

Results

2.3m	19120×	body	5120	exit
23.3s	434300×	body	80	valid
16.8s	30249×	body	1280	valid
13.0s	8446×	body	1280	nan
8.5s	23490×	body	640	valid
8.0s	6959×	body	640	nan
3.1s	41308×	body	80	nan
3.1s	12223×	body	320	valid
2.9s	3486×	body	320	nan
2.1s	13428×	body	80	overflowed
1.9s	9997×	body	160	valid
951.0ms	49536×	pre	80	true
933.0ms	1766×	body	160	nan
499.0ms	1539×	body	2560	valid
217.0ms	613×	body	5120	valid

prune2.5m (33.4%)

Filtered: 13464 candidates to 22769 candidates (-69.1%)

series20.3s (4.5%)

Calls

484 calls:

7.5s	(- (pow 1.0 3) (/ (pow (* 1.0 (- (* 0.254829592 0.254829592) (* (* (/ 1 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ 1.0 (sqrt (+ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ 1.0 (sqrt (+ 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) (pow (* (* (+ 1.0 (* 0.3275911 (fabs x))) (- 0.254829592 (* (/ 1 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ 1.0 (sqrt (+ 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)))
797.0ms	(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ 1.0 (sqrt (+ 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 (neg (* (fabs x) (fabs x))))) 3))
477.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
452.0ms	(* (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ 1.0 (sqrt (+ 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 (neg (* (fabs x) (fabs x))))) (+ (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ 1.0 (sqrt (+ 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 (neg (* (fabs x) (fabs x))))) 1.0))
390.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))

simplify17.7s (3.9%)

Algorithm

258×	egg-herbie

regimes11.7s (2.6%)

Accuracy

Total 92.3b remaining (34.8%)

Threshold costs 3.9b (1.5%)

15.7b	53.9%	math.sqrt on complex, imaginary part, im greater than 0 branch
11.5b	53.2%	math.sqrt on complex, real part
8.9b	60.4%	math.log/2 on complex, real part
8.1b	63.8%	math.log10 on complex, real part
7.9b	64.7%	math.log/1 on complex, real part

rewrite8.2s (1.8%)

Algorithm

160×	rewrite-expression-head

Calls

484 calls:

243.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
203.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
151.0ms	(/ (* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -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)))
146.0ms	(/ (* (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)) (/ -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)))))
144.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -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)))

Rules

20371×	`times-frac`
15401×	`*-un-lft-identity`
11476×	`add-sqr-sqrt`
9244×	`add-cube-cbrt`
5974×	`cbrt-prod`
4304×	`sqrt-prod`
3847×	`add-exp-log`
2950×	`distribute-lft-out`
2591×	`add-cbrt-cube`
2459×	`pow1`
2338×	`associate-r`
1699×	`prod-exp`
1384×	`associate-/r/`
1255×	`flip-+` `flip3-+`
1154×	`associate-l`
1009×	`cbrt-unprod`
926×	`frac-times`
901×	`div-exp`
894×	`associate-*r/`
863×	`associate-/r*`
802×	`add-log-exp`
754×	`frac-add`
737×	`div-inv`
710×	`pow-prod-down`
606×	`difference-of-squares`
605×	`sqrt-div`
599×	`associate-/l*`
510×	`cbrt-undiv`
503×	`cbrt-div`
485×	`log-pow`
415×	`unswap-sqr`
390×	`distribute-lft-out--`
372×	`associate-*l/`
296×	`unpow-prod-down`
247×	`flip--` `flip3--`
241×	`swap-sqr`
190×	`sqrt-pow1`
165×	`associate-/l/`
164×	`*-commutative`
158×	`sqr-pow`
149×	`1-exp`
148×	`rec-exp`
143×	`pow-prod-up`
127×	`cube-prod`
119×	`distribute-rgt-in` `distribute-lft-in`
110×	`pow1/2`
103×	`diff-log` `associate-+l-`
100×	`log-prod` `clear-num` `frac-2neg`
94×	`sub-neg`
93×	`pow-sqr`
89×	`pow-exp` `pow-sub`
81×	`pow-plus`
76×	`sum-log`
71×	`pow-to-exp`
70×	`pow1/3`
48×	`pow2` `exp-sum`
47×	`rem-sqrt-square`
45×	`associate--l+`
42×	`+-commutative`
36×	`pow-unpow`
32×	`cube-mult` `exp-diff` `unpow3`
28×	`cube-div` `exp-neg`
25×	`pow-pow`
24×	`neg-sub0`
23×	`unpow2`
22×	`exp-prod`
19×	`div-sub`
18×	`associate-+r+`
15×	`associate--l-` `associate-+l+` `un-div-inv` `associate--r+`
13×	`pow-flip` `rem-cube-cbrt`
11×	`inv-pow`
10×	`log-div`
9×	`rem-exp-log`
6×	`pow3`
5×	`rem-log-exp`
4×	`unpow-prod-up` `frac-sub` `sin-sum` `rem-cbrt-cube`
3×	`rem-square-sqrt` `sqrt-unprod`
1×	`difference-cubes` `cos-sum` `sqrt-undiv` `associate-+r-` `sqrt-pow2` `associate--r-`

Details

sample4.0m (52.9%)

prune2.5m (33.4%)

series20.3s (4.5%)

simplify17.7s (3.9%)

regimes11.7s (2.6%)

rewrite8.2s (1.8%)

localize2.5s (0.6%)

bsearch1.2s (0.3%)

end1.0ms (0.0%)

Profiling