Metrics for Toniolo and Linder, Equation (7)

analyze433.0ms (1.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
0%	0%	99.9%	0.1%	0%	0%	0%	7
0%	0%	74.9%	0.1%	0%	25%	0%	8
4.2%	3.1%	71.8%	0.1%	0%	25%	0%	9
6.3%	4.7%	70.2%	0.1%	0%	25%	0%	10
11.3%	7%	55.4%	0.1%	0%	37.4%	0%	11
16.9%	10.5%	51.9%	0.1%	0%	37.4%	0%	12

Compiler

Compiled 31 to 19 computations (38.7% saved)

sample29.1s (97.8%)

Results

1.6s	5336×	0	valid
543.0ms	5327×	0	valid-sollya
802.0ms	2714×	0	invalid
437.0ms	2690×	0	invalid-sollya
1.5s	2168×	1	valid
303.0ms	2162×	1	valid-sollya
653.0ms	1242×	1	invalid
207.0ms	1230×	1	invalid-sollya
678.0ms	752×	2	valid
127.0ms	749×	2	valid-sollya
330.0ms	524×	2	invalid
92.0ms	518×	2	invalid-sollya
6.0ms	33×	0	exit-sollya
8.0ms	18×	1	exit-sollya
1.0ms	9×	2	exit-sollya

Sollya Eval

Pt	Rival-out	Sollya-interval	Sollya-point	status	Sollya status	Rival iter	sollya-time	check
(-5.20669923130458e-18 -3.1825546419214414e+245 4.206144815561353e+219)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.188363	#f
(4.008083269259686e-59 -6.1882534956467445e+81 3.509808003917725e+56)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.10817700000000001	#f
(-1.0394753454354162e+89 -1.905290025257624e+253 -1.2236941274959625e-168)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.239913	#f
(1.5623859105571175e-6 1.2277243471246236e-136 1.7197528873374646e-295)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.17973899999999998	#f
(-7.8704154884342e+157 -4.9142994044003626e+54 -5.177928581031458e-262)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.22908	#f
(-9.797396438606611e+110 3.738584828233843e+206 -1.122473662197442e-106)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.195718	#f
(-4.375894757978086e-26 8.41753763944704e-181 3.4529771162453505e-9)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.204902	#f
(1.5346315106109066e-68 -1.6374417615815958e+258 4.1263199502886675e-6)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.23952	#f
(-6.744285968654362e-23 -2.2621324638980172e-291 2.5963262328913317e-153)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.108637	#f
(-6.166800148664245e+304 -6.324420296113991e+246 1.0652362532353923e+75)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.21161	#f
(1.5656094178027918e-10 2.3613333389789643e+266 4.927832464561768e+202)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.165208	#f
(-1.8026850118316348e+194 3.026999474280908e+287 -1.8458337240724695e-263)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.11602	#f
(1.2089013755699376e-68 6.50107732488993e-111 -4.2898822958057435e-165)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.166501	#f
(-1.0823415260532426e+20 -6.012088667355016e-68 -8.790792478677492e+115)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.156544	#f
(-2.635934305284033e+263 4.56397884249293e+59 -1.2353678296916734e-188)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.10998	#f
(-3.5527390293322105e+205 1.1865046637875508e+284 -2.5759686428724677e-251)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.109979	#f
(7.20032092291941e-14 -17686623892081248.0 5.107281291206248e-295)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.085859	#f
(-4.1181043728458856e+175 9.093754089943286e+288 -8.360590588609859e-253)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.194628	#f
(4.12809062317013e+148 7.554295902863506e-96 5.871949401901202e-29)	1.0	(1.0 1.0)	+nan.0	valid	exit	0	0.359912	#f
(-6.581123442270188e+294 -4.8565699652075225e+30 -8.297752458247283e-219)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.180613	#f
(8.621196456776336e+295 -8144250812.7463045 -0.0002229611215599984)	-1.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.167646	#f
(-271529775244694720.0 7.12367629715004e+30 2.885255216610757e-127)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.20733500000000002	#f
(-1.7053326871265159e+186 -3.41978658045777e+251 5.2763977890095934e+51)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.11368400000000001	#f
(2.1734125287927485e+26 -3.3424432439052105e+209 -1.3644417793019774e+125)	-6.018136732243952e-72	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.185802	#f
(-2.6310392972306747e-47 40010845813437555000.0 1.237317519464795e-66)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.164246	#f
(1.6039522265376775e-53 5.57275977615387e-19 -211.52513064510742)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.21516300000000002	#f
(3.5160569907900376e+196 4.785857385116308e+112 -7.523478318459332e-115)	-2.947724382800576e-129	(+nan.0 +nan.0)	+nan.0	valid	exit	2	0.113284	#f
(7.863591853604385e-17 6.049890618367802e+220 3.3556049162232076)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.10861699999999999	#f
(-2.52725652628011e-46 2.7800341318774824e+101 3.2863610520160264e-110)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.171981	#f
(-2.8313132118976256e+20 1.218816541292324e-37 -1.2894292196388365e-86)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.16855599999999998	#f
(2.26066024245683e+297 -1.607340265506143e-151 -5.564903742189911e-47)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.250511	#f
(-8887.594697959958 -6.1858504041899874e+258 -1.7177843899915374e+28)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.256659	#f
(6.729986594496843e+233 5.627822820290544e-240 -7.658842215410442e-156)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.26866999999999996	#f
(3.1969721253229174e+239 8.926974777044527e-126 1.4182037058328892e-231)	1.0	(+nan.0 +nan.0)	+nan.0	valid	exit	2	0.2109	#f
(3.4918092570486913e-72 5.660685873642967e+226 3.2425989936580864e+59)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.143338	#f
(-1.0202199470322472e+38 -1.9449566868042645e+206 4.3236126832777797e-26)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.198457	#f
(-2.0996041232579914e+117 1.5600712087107295e+208 -4.404062748972083e-135)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.10983	#f
(-4.3863154033015036e+46 1.1741622418812446e+168 3.5799010519077197e-25)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.19467299999999998	#f
(8.446422976517055e+100 -1.1168601338443147e-150 -1.9106881087817774e+211)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.257125	#f
(-5.2797929103040794e+182 5.215913759874858e+144 8.239160672631863e+70)	1.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.23394	#f
(-3.703630633799456e+62 -5.105188153079547e-163 -1.2679813257537424e+293)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.298373	#f
(-1.5786188844696267e+129 -2.956232768053208e+61 -1.9631628074133912e-206)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.2203	#f
(-0.17060821946388607 2.1017142596588437e-31 -4.7190142262468354e-45)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.205847	#f
(-2.2549655627952838e+219 7.536627434228443e+39 2.2345445181495272e+176)	1.0	(1.0 1.0)	+nan.0	valid	exit	0	0.23802900000000002	#f
(2.040172530325387e+170 -6.722572736002771e+180 -5.771786641735861e+149)	-1.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.184804	#f
(3.20095709618046e-51 -1.4899858725684314e-308 -5.0098605230057845e+119)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.182203	#f
(4.2166777914919116e-66 -4.805264327928281e-243 -1.9424790551931568e-187)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.230879	#f
(1.0312601013001792e+37 -5.779370258065544e+182 -9.177108179286714e-291)	-0.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.239186	#f
(-2.50400687100061e-22 9.67044157114189e+163 -5.020636068425949e+45)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.108557	#f
(1.891293021689152e+242 -1.086797553319367e+292 1.2135740074666118e-180)	0.0	(+nan.0 +nan.0)	+nan.0	valid	exit	2	0.112579	#f
(1.2997758589577525e-65 3.5489719431525477e-132 1.2616495447760978e+207)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.206106	#f
(-2.7728166421755756e-53 -2.854691666236447e-128 4.94521922173583e-212)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.101934	#f
(-8.612116222755236e+133 -1.6993358778864968e+170 3.229834497416504e-278)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.238538	#f
(-1.1930616414757294e+263 -1.5847177963707421e+43 -2.965433253984221e-206)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.108561	#f
(5.881740956715788e+102 6.047169512754462e-269 -2.483336730031976e+87)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.356952	#f
(7.057380108671389e+136 -1.3748926223312642e-243 8.804209581960065e-209)	1.0	(1.0 1.0)	+nan.0	valid	exit	0	0.161193	#f
(2.4065891283259784e+61 -1.5467107673129448e+239 -3.12942754938924e-196)	-0.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	5.0	#f
(-4.4804849911268243e+253 2.866094118524299e+156 1.1807289779250182e-44)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.117372	#f
(-2.382969365251064e-40 2.4551257395573674e+281 -2.3349090046324766e-207)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.10268	#f
(-5.454315508376397e+267 9.19692611652329e+155 -7.082208997542134e-275)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.225181	#f

Sollya timings

Total time spent in Sollya 1.7s

Bogosity

preprocess163.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

502×	`distribute-lft-in`
493×	`fma-neg`
435×	`distribute-rgt-in`
308×	`distribute-lft-neg-out`
308×	`div-sub`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1172
1	256	1160
2	740	1156
3	2566	1156
4	7816	1156

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 (neg.f64 l) (neg.f64 l)) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 (neg.f64 l) (neg.f64 l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 t)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 t) (neg.f64 t))))) (.f64 l l))))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l)))))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 (neg.f64 l) (neg.f64 l)) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 (neg.f64 l) (neg.f64 l))))))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 t)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 t) (neg.f64 t))))) (.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 l #s(literal 1 binary64)) (-.f64 l #s(literal 1 binary64))) (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 x x))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 t #s(literal 1 binary64)) (-.f64 t #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 t t) (.f64 #s(literal 2 binary64) (.f64 l l)))) (.f64 t t))))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)) (+.f64 (neg.f64 x) #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t))) (neg.f64 (.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))) (*.f64 l l))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) (neg.f64 (.f64 l l))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) (.f64 l (neg.f64 l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 (neg.f64 l) (neg.f64 l)) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 (neg.f64 l) (neg.f64 l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 t)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 t) (neg.f64 t))))) (.f64 l l))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(.f64 t (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (neg.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)) (+.f64 (neg.f64 x) #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 t)) (sqrt.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))) (*.f64 l l))))
(.f64 t (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) (neg.f64 (.f64 l l))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) (.f64 l (neg.f64 l))))))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 (neg.f64 l) (neg.f64 l)) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 (neg.f64 l) (neg.f64 l))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(.f64 t (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 t)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 t) (neg.f64 t))))) (.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 l #s(literal 1 binary64)) (-.f64 l #s(literal 1 binary64))) (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 #s(literal 1 binary64) l) (+.f64 l #s(literal -1 binary64))) (fma.f64 x x (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 x x)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) l) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 x x))) (+.f64 l #s(literal -1 binary64))) (*.f64 x x))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 (+.f64 #s(literal 1 binary64) l) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 x x)) (+.f64 l #s(literal -1 binary64))) (neg.f64 (.f64 x x))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 (+.f64 #s(literal 1 binary64) l) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 x x)) (+.f64 l #s(literal -1 binary64))) (.f64 x (neg.f64 x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 t #s(literal 1 binary64)) (-.f64 t #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (sqrt.f64 (fma.f64 (/.f64 (+.f64 t #s(literal 1 binary64)) (+.f64 t #s(literal -1 binary64))) (fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 x x))) (neg.f64 (.f64 l l)))))
(.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 (/.f64 (.f64 (+.f64 t #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 x x) (.f64 l l))) (+.f64 t #s(literal -1 binary64))) (*.f64 l l)))))
(.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (+.f64 t #s(literal 1 binary64)) (+.f64 t #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 x x) (.f64 l l)) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (sqrt.f64 (fma.f64 (+.f64 t #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) (.f64 l l)) (+.f64 t #s(literal -1 binary64))) (.f64 l (neg.f64 l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 t t) (.f64 #s(literal 2 binary64) (.f64 l l)))) (.f64 t t))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 t t (.f64 #s(literal 2 binary64) (.f64 l l))) (neg.f64 (.f64 t t)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (-.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 l l) (.f64 t t)) (+.f64 x #s(literal -1 binary64)))) (*.f64 t t))))
(.f64 l (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 l l) (.f64 t t)) (+.f64 x #s(literal -1 binary64)))) (*.f64 t t)))))

Symmetry

(abs l)

(negabs t)

Compiler

Compiled 30 to 18 computations (40% saved)

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	37.8%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))

Status

Accuracy

Program

37.8%

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Compiler

Compiled 60 to 36 computations (40% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`unsub-neg`
8×	`neg-mul-1`
7×	`+-commutative`
6×	`*-commutative`
5×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	108
1	42	108
2	52	108
3	61	108
4	74	108
5	91	108

Stop Event

1×

saturated

Calls

Call 1

Inputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Outputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

soundness1.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 30 to 19 computations (36.7% saved)

preprocess53.0ms (0.2%)

Remove

(negabs t)

(abs l)

Compiler

Compiled 360 to 226 computations (37.2% saved)

Toniolo and Linder, Equation (7)

analyze433.0ms (1.5%)

sample29.1s (97.8%)

preprocess163.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

soundness1.0ms (0%)

preprocess53.0ms (0.2%)

end0.0ms (0%)

Profiling