Date:	Tuesday, March 3rd, 2020
Commit:	ee6b458f on refactor-and-minor
Hostname:	warfa with Racket 7.5
Seed:	2020063
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

series3.9m (44.2%)

Calls

520 calls:

2.4m	(- (pow (pow 1.0 3) 3) (pow (* (sqrt (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)) (sqrt (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))) 3))
3.3s	(- (pow 1.0 3) (* (sqrt (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)) (sqrt (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))))
3.3s	(- (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))
2.3s	(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
2.0s	(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))

prune2.2m (24.7%)

Filtered: 40550 candidates to 20418 candidates (50.4%)

sample1.9m (21.8%)

Algorithm

100×

intervals

Results

47.8s	16209×	body	10240	exit
19.6s	460784×	body	80	valid
14.7s	30843×	body	1280	valid
6.9s	23564×	body	640	valid
3.0s	3108×	body	1280	nan
2.6s	67977×	body	80	nan
2.3s	12037×	body	320	valid
1.8s	2617×	body	640	nan
1.2s	10164×	body	160	valid
669.0ms	49536×	pre	80	true
643.0ms	1273×	body	320	nan
366.0ms	1503×	body	2560	valid
215.0ms	646×	body	160	nan
143.0ms	619×	body	5120	valid

simplify28.2s (5.3%)

Algorithm

264×	egg-herbie

rewrite11.2s (2.1%)

Algorithm

164×	rewrite-expression-head

Calls

520 calls:

597.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
175.0ms	(- (+ (/ (/ x (+ (pow wj 3) (pow 1 3))) (/ (exp wj) (+ (* wj wj) (- 1 (* wj 1))))) wj) (/ 1 (/ (+ wj 1) wj)))
153.0ms	(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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))))
150.0ms	(* (* (* (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 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))))
149.0ms	(* (* (* (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))))

Rules

105891×	`times-frac`
72445×	`*-un-lft-identity`
40300×	`sqrt-prod`
39385×	`add-sqr-sqrt`
38055×	`add-cube-cbrt`
19066×	`distribute-lft-out`
5590×	`associate-/r/`
3073×	`flip-+` `flip3-+`
3024×	`div-inv`
2890×	`add-exp-log`
2017×	`prod-diff`
1899×	`add-cbrt-cube`
1455×	`pow1`
1122×	`prod-exp`
1102×	`frac-add`
1029×	`associate-/r*`
1025×	`associate-l`
745×	`add-log-exp`
733×	`div-exp`
699×	`associate-r`
606×	`associate-/l*`
591×	`unpow-prod-down`
523×	`log1p-expm1-u`
520×	`expm1-log1p-u`
512×	`cbrt-unprod`
499×	`associate-*r/`
426×	`frac-times`
410×	`cbrt-prod`
407×	`cube-prod`
396×	`cbrt-undiv`
365×	`difference-of-squares`
320×	`pow-prod-down`
291×	`associate-*l/`
288×	`log-pow`
286×	`distribute-lft-out--`
268×	`fma-neg`
238×	`unswap-sqr`
205×	`sqr-pow`
202×	`sqrt-div`
191×	`log-prod`
189×	`pow-exp`
183×	`associate--l+`
180×	`1-exp`
168×	`distribute-rgt-in` `distribute-lft-in`
152×	`flip3--` `flip--`
148×	`exp-sum`
147×	`pow-to-exp`
145×	`exp-neg`
141×	`associate-/l/`
140×	`fma-def`
136×	`*-commutative`
119×	`associate-+l-` `pow1/3`
114×	`exp-diff`
113×	`cube-div`
110×	`pow-sub`
107×	`neg-sub0`
105×	`cbrt-div`
103×	`unpow3` `cube-mult`
102×	`frac-2neg` `rec-exp` `clear-num`
99×	`swap-sqr`
96×	`sqrt-pow1`
91×	`pow-unpow`
88×	`sub-neg`
87×	`diff-log`
79×	`pow1/2`
71×	`associate--r+`
67×	`exp-prod`
60×	`pow-pow`
55×	`fma-udef`
51×	`associate-+l+`
49×	`pow-prod-up`
41×	`un-div-inv` `pow-sqr`
39×	`sum-log`
38×	`rem-sqrt-square`
36×	`rem-cube-cbrt`
31×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
28×	`pow-plus` `pow2`
27×	`+-commutative` `rem-log-exp`
24×	`neg-mul-1` `associate-+r+`
21×	`pow-flip`
19×	`hypot-udef` `div-sub`
18×	`associate--l-`
17×	`inv-pow` `hypot-def`
13×	`unpow-prod-up` `log-div`
11×	`rem-exp-log`
10×	`sqrt-unprod` `distribute-rgt-out`
8×	`frac-sub` `unpow2`
7×	`distribute-rgt-neg-out`
6×	`neg-log`
5×	`distribute-lft1-in` `expm1-log1p` `expm1-udef`
4×	`sin-sum` `unpow1/2`
3×	`log1p-udef` `log1p-expm1` `unsub-neg`
2×	`sqrt-undiv` `difference-cubes` `distribute-lft-neg-out` `rem-square-sqrt`
1×	`associate-+r-` `sqrt-pow2` `pow3` `distribute-neg-in` `log-rec` `cos-sum` `associate--r-` `distribute-rgt-out--` `rem-cbrt-cube`

regimes5.3s (1.0%)

Accuracy

Total 44.5b remaining (33.7%)

Threshold costs 5.9b (4.5%)

6.9b	-5.7%	Octave 3.8, jcobi/2
6.9b	41%	_divideComplex, real part
6.8b	-5.9%	math.sqrt on complex, imaginary part, im greater than 0 branch
4.8b	22.2%	math.sqrt on complex, real part
3.9b	52.8%	_divideComplex, imaginary part

Details

series3.9m (44.2%)

prune2.2m (24.7%)

sample1.9m (21.8%)

simplify28.2s (5.3%)

rewrite11.2s (2.1%)

regimes5.3s (1.0%)

localize2.8s (0.5%)

bsearch1.3s (0.2%)

end1.0ms (0.0%)