Metrics for Toniolo and Linder, Equation (3a)

analyze131.0ms (2.7%)

Memory

-18.1MiB live, 50.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
50%	49.9%	49.9%	0.2%	0%	0%	0%	3
50%	49.9%	49.9%	0.2%	0%	0%	0%	4
50%	49.9%	49.9%	0.2%	0%	0%	0%	5
50%	49.9%	49.9%	0.2%	0%	0%	0%	6
75%	74.9%	25%	0.2%	0%	0%	0%	7
75%	74.9%	25%	0.2%	0%	0%	0%	8
75%	74.9%	25%	0.2%	0%	0%	0%	9
75%	74.9%	25%	0.2%	0%	0%	0%	10
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	11
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	12

Compiler

Compiled 65 to 47 computations (27.7% saved)

sample4.6s (94.6%)

Memory

6.8MiB live, 1 382.6MiB allocated

Samples

1.3s	8 256×	valid-baseline
1.2s	8 256×	valid-rival
852.0ms	8 256×	valid-sollya

Bogosity

preprocess89.0ms (1.8%)

Memory

-5.1MiB live, 26.0MiB allocated

Algorithm

1×	egg-herbie

Rules

560×	`associate-r`
549×	`associate-l`
491×	`distribute-lft-neg-out`
424×	`distribute-rgt-neg-out`
381×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	142	1552
1	356	1376
2	968	1376
3	4270	1376

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 l)) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) (neg.f64 Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 l)) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) (neg.f64 Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64)))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) Om) l) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) kx) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 l) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) ky) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) kx) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 Om) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) ky) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))))

Outputs
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 l)) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) (neg.f64 Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 l)) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 l) Om)) #s(literal 2 binary64))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) (neg.f64 Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 l) Om)) #s(literal 2 binary64))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 l) Om)) #s(literal 2 binary64))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64)))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 l) Om)) #s(literal 2 binary64))))))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) Om) l) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 Om l)) #s(literal 2 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 Om l)) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) kx) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 l) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 kx Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 kx Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 kx (/.f64 #s(literal 2 binary64) Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) ky) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) ky) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 ky (/.f64 #s(literal 2 binary64) Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 ky Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 l) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) kx) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 Om) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) kx) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l kx)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) ky) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l ky)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l ky)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 l (/.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 Om) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 l Om)) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))

Symmetry

(abs l)

(abs Om)

(abs kx)

(abs ky)

(sort kx ky)

Compiler

Compiled 33 to 22 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 4 to 4 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Status

Accuracy

Program

98.8%

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify2.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
3×	`*-commutative`
3×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	95
1	42	95

Stop Event

1×

saturated

Calls

Call 1

Inputs

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Outputs

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

soundness0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 31 to 22 computations (29% saved)

preprocess42.0ms (0.9%)

Memory

4.0MiB live, 37.7MiB allocated

Remove

(sort kx ky)

(abs ky)

(abs kx)

(abs Om)

(abs l)

Compiler

Compiled 748 to 528 computations (29.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze131.0ms (2.7%)

sample4.6s (94.6%)

preprocess89.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify2.0ms (0%)

soundness0.0ms (0%)

preprocess42.0ms (0.9%)

end0.0ms (0%)

Profiling