Metrics for Toniolo and Linder, Equation (7)

analyze632.0ms (14.6%)

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)

Precisions

Click to see histograms. Total time spent on operations: 215.0ms

ival-mult: 93.0ms (43.3% of total)

ival-sqrt: 43.0ms (20% of total)

ival-sub: 26.0ms (12.1% of total)

ival-add: 25.0ms (11.6% of total)

ival-div: 24.0ms (11.2% of total)

const: 4.0ms (1.9% of total)

sample3.2s (73.4%)

Results

1.0s	6032×	256	valid
435.0ms	1164×	1024	valid
389.0ms	3182×	256	invalid
290.0ms	849×	1024	invalid
236.0ms	993×	512	valid
130.0ms	525×	512	invalid
30.0ms	67×	2048	valid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-mult: 689.0ms (35.6% of total)

ival-div: 464.0ms (24% of total)

ival-sqrt: 326.0ms (16.8% of total)

ival-sub: 214.0ms (11.1% of total)

ival-add: 213.0ms (11% of total)

const: 29.0ms (1.5% of total)

Bogosity

preprocess131.0ms (3%)

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)

explain362.0ms (8.3%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
118	-	1	(1.3203063872863291e+259 2.2122817933671033e-247 1.6571987275848755e-159)	`(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)))`
91	-	2	(87.22149369999794 5.3234034282243835e+78 9.351080761507237e-25)	`(-.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))`
0	-	0	-	`x`
0	-	0	-	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`
0	-	0	-	`l`
0	-	0	-	`(-.f64 x #s(literal 1 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 t t)`
0	-	0	-	`(/.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))))`
0	-	0	-	`(sqrt.f64 #s(literal 2 binary64))`
0	-	0	-	`(*.f64 l l)`
0	-	0	-	`(+.f64 x #s(literal 1 binary64))`
0	-	0	-	`(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 t t))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`t`
0	-	0	-	`(.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))))`
0	-	0	-	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`

Results

156.0ms	66×	512	valid
75.0ms	390×	256	valid
55.0ms	54×	1024	valid
1.0ms	2×	2048	valid

Compiler

Compiled 300 to 56 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 219.0ms

ival-div: 140.0ms (64% of total)

ival-mult: 31.0ms (14.2% of total)

ival-sqrt: 23.0ms (10.5% of total)

ival-add: 16.0ms (7.3% of total)

ival-sub: 7.0ms (3.2% of total)

const: 1.0ms (0.5% of total)

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
	35.5%	(/.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

35.5%

(/.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 (0.1%)

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)

preprocess27.0ms (0.6%)

Remove

(negabs t)

(abs l)

Compiler

Compiled 360 to 226 computations (37.2% saved)

Toniolo and Linder, Equation (7)

analyze632.0ms (14.6%)

sample3.2s (73.4%)

preprocess131.0ms (3%)

explain362.0ms (8.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

soundness0.0ms (0%)

preprocess27.0ms (0.6%)

end0.0ms (0%)

Profiling