Metrics for Toniolo and Linder, Equation (7)

analyze356.0ms (1.7%)

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)

sample20.6s (97.5%)

Results

1.2s	5302×	0	valid
532.0ms	5293×	0	valid-sollya
543.0ms	2678×	0	invalid
433.0ms	2650×	0	invalid-sollya
855.0ms	2216×	1	valid
308.0ms	2210×	1	valid-sollya
393.0ms	1151×	1	invalid
191.0ms	1144×	1	invalid-sollya
455.0ms	738×	2	valid
126.0ms	737×	2	valid-sollya
433.0ms	489×	2	invalid
87.0ms	483×	2	invalid-sollya
12.0ms	37×	0	exit-sollya
2.0ms	13×	1	exit-sollya
1.0ms	7×	2	exit-sollya

Sollya Eval

Pt	Rival-out	Sollya-interval	Sollya-point	status	Sollya status	Rival iter	sollya-time	check
(-3.380965955160656e-70 2.740713478217599e-177 3.878275472006805e-289)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.121964	#f
(-1.1323463103372095e+114 -4.740078011017948e+20 6.046232910794732e+197)	1.0	(1.0 1.0)	+nan.0	valid	exit	0	0.319963	#f
(-4.0923905988356405e+300 1.6836945438807768e+298 7.796021930045784e-105)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.24232	#f
(-2.674247013258289e+241 2.9375658849902445e+81 1.1249888140231323e-169)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.20540399999999998	#f
(1.741638253036901e+140 7.006007562514305e+56 -8.155230141136778e+208)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.338928	#f
(1.3765786126633647e+243 -8.528769857557208e+257 -1.492004456269634e-259)	-0.0	(+nan.0 +nan.0)	+nan.0	valid	exit	2	0.251047	#f
(7.796172495336584e-9 -4.150651599890974e-287 1.8407223045500223e-30)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.099258	#f
(3.9379953030621183e-72 -1.8586301679903056e+183 -9.419193866861593e+38)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.224283	#f
(-1.2826877862880822e+45 -9.322805891216606e-58 8.21397191097912e+130)	1.0	(1.0 1.0)	+nan.0	valid	exit	0	0.27097200000000005	#f
(-1.4144126537958653e-11 5.888802714737221e-124 4.2066529537192616e-159)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.205099	#f
(4.59160114932089e+259 5.092565201023266e-53 -4.875935499634594e-52)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.31373399999999996	#f
(-6.048384023383111e-27 -1.1073527278714566e+201 -3.6863380092352964e-264)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.125856	#f
(0.005277807747124217 3.1021763378069536e-208 -7.712264471070785e-63)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.19514900000000002	#f
(2.1044094922014965e-30 8.650219309556901e+191 1.7035355064470535e-273)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.106613	#f
(-8.476517362039332e-8 5.654937697105062e-221 6.775167224484469e-99)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.20539700000000002	#f
(3.3064223127894026e+70 -2.7649368440586046e+167 -1.0807361514034748e+52)	-7.107446920191535e-81	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.205384	#f
(-4.557229391831899e+231 5.1631605055692385e-65 -8.145636225032511e-265)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.11140599999999999	#f
(3.9364438515425713e-13 -2.4057795092110466e+249 -6.742479018448641e+202)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.156525	#f
(-28917596.818750303 7.253183053038345e-202 -5.936376900141327e-293)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.172641	#f
(5.423449306346955e+68 5.222187509530124e+255 -4.156309894762708e+148)	-1.8535028237129173e-73	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.11225700000000001	#f
(2.35479023928434e+281 -8.460382709443017e-194 -2.515267595667316e+117)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.335631	#f
(-1.5275448785516204e+175 -1.6193351764554357e-6 -2.4336667507938627e-200)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.167614	#f
(-1.126990187338535e-39 1.4771928576695826e-230 3.2899758736931567e-223)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.098934	#f
(2.704845946010758e-28 7.226309690347294e+296 -2.266609897155442e-290)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.178691	#f
(-4.68372089690421e+196 -8.129418970914112e+235 -1.5340869687437722e+168)	-1.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.11536500000000001	#f
(-1.3055378172316917e+236 -5.281712594150469e-79 -5.3766577757257504e-304)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.10331900000000001	#f
(-54964440.174985476 3.20080625775373e+206 4.27434662683169e-262)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.16683900000000002	#f
(-3.8111548081849557e+171 -1.2342886069137601e+97 2.983607310373483e-289)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.111651	#f
(-1.799928372674053e+182 -1.9280220213762566e-96 -2.3906018804608732e-91)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.31964899999999996	#f
(-2.9028788095430703e+209 -1.1401993087796605e-42 -6.058885562531988e-301)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.201227	#f
(-227113382029.72726 2.2946434640537403e-173 1.5798784707706038e+193)	1.0000000000044031	(1.0000000000044031 1.0000000000044031)	+nan.0	valid	exit	0	0.157076	#f
(-9.836556845115967e+210 5.3757774109306355e+91 6.218574083023141e-118)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.12914299999999998	#f
(-2.706452074969248e+116 -8.126343437413273e+103 3.1041822806354657e-25)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.11212899999999999	#f
(-6.640496124586235e-40 -4.010406494174309e-247 1.1568477411752131e-291)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.114845	#f
(-4.0176143723060147e-53 -5.513861865598235e+143 -1.945805458183028e+134)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.219025	#f
(2.8120657203686722e+138 -1.996548753651265e-183 3.945217361708495e-292)	3.3136279831359592e-40	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.174733	#f
(4.827487763474579e-41 -7.056106125783316e-123 -1.5818148156952353e+109)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.106155	#f
(-6.287946197183152e+121 -8.236701180461546e+300 6.219503088197789e+190)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.115804	#f
(-7.265330987525702e-65 -2.292851215608743e-226 -3.323985169298461e-259)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.10346999999999999	#f
(1.1585356549231961e+167 1.9273116813455524e+169 6.7129457007796225e+115)	1.0	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.23619900000000002	#f
(-1.758378931368378e+244 -7.957920685136166e+228 -2.662182057896322e-274)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	2	0.242421	#f
(2.4978418004595155e-20 2.318522671740723e+25 -145659648447988.8)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.202397	#f
(-8.06959578477835e-12 4.154037698676917e-110 -1.2294992156465788e+301)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.11071299999999999	#f
(0.00026007058157266193 2.671693063971789e+69 6.394692271889172e-225)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.17715999999999998	#f
(3.734875695285639e-65 3.8466187033072256e+55 3.527729000742922e-286)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.137502	#f
(-4.128318303658776e-52 2.0497342058605495e+28 -8.183694178922533e-243)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.09568600000000001	#f
(-3.269265908859669e+103 7170538.482742458 1.4951641845436812e-179)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.174548	#f
(2.123280591385353e+188 1.1735633873286293e+264 3.711624970823966e-6)	4.608517392628623e-176	(+nan.0 +nan.0)	+nan.0	valid	exit	1	0.126003	#f
(1.8073947716273048e-13 -4.992544151935004e+182 -2.4259450537572694e+146)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.16502899999999998	#f
(6.376458395066962e-6 1.1090522809155191e-95 -1.441890080603766e+155)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	5.0	#f
(-1.3285334920185942e-29 4.6471375931607685e+118 1.0762685905980334e-204)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.188419	#f
(2.5909229266449332e-42 -4.7967407998968e-102 9.025790873022948e+157)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.160616	#f
(2.258780145502088e+292 -1.2770308122781662e-161 1.6946413661050625e+83)	1.0	(1.0 1.0)	+nan.0	valid	exit	0	0.156011	#f
(1.0414125807113765e-61 -3.7675767016770866e-6 -5.436173441762925e-28)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.195827	#f
(-5.569699729930199e+238 4.879103249583639e+110 -4.846366941974053e+156)	-1.0	(-1.0 -1.0)	+nan.0	valid	exit	0	0.157865	#f
(3.7285763691921885e-22 -6.764928703884485e-129 3.729264103921825e-309)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.178216	#f
(-2.0661942790227789e+93 7.255785678864888e-142 3.1474641494709618e-257)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	1	0.144957	#f

Sollya timings

Total time spent in Sollya 1.7s

Bogosity

preprocess140.0ms (0.7%)

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
	36.2%	(/.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

36.2%

(/.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)

simplify4.0ms (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))))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 30 to 19 computations (36.7% saved)

preprocess29.0ms (0.1%)

Remove

(negabs t)

(abs l)

Compiler

Compiled 360 to 226 computations (37.2% saved)

Toniolo and Linder, Equation (7)

analyze356.0ms (1.7%)

sample20.6s (97.5%)

preprocess140.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

soundness0.0ms (0%)

preprocess29.0ms (0.1%)

end0.0ms (0%)

Profiling