Metrics for Toniolo and Linder, Equation (3a)

analyze168.0ms (1%)

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 34 to 30 computations (11.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

Operation ival-sin, time spent: 38.0ms, 32.0% of total-time

Operation ival-pow, time spent: 21.0ms, 17.0% of total-time

Operation ival-sqrt, time spent: 20.0ms, 17.0% of total-time

Operation ival-mult, time spent: 14.0ms, 12.0% of total-time

Operation ival-div, time spent: 14.0ms, 12.0% of total-time

Operation ival-add, time spent: 11.0ms, 9.0% of total-time

Operation const, time spent: 3.0ms, 2.0% of total-time

sample3.7s (23.3%)

Results

3.5s	8254×	0	valid
0.0ms	1×	0	valid
2.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.0s

Operation ival-sin, time spent: 672.0ms, 34.0% of total-time

Operation ival-add, time spent: 416.0ms, 21.0% of total-time

Operation ival-div, time spent: 220.0ms, 11.0% of total-time

Operation ival-sqrt, time spent: 218.0ms, 11.0% of total-time

Operation ival-pow, time spent: 212.0ms, 11.0% of total-time

Operation ival-mult, time spent: 191.0ms, 10.0% of total-time

Operation const, time spent: 61.0ms, 3.0% of total-time

Bogosity

preprocess8.3s (51.4%)

Algorithm

1×	egg-herbie

Rules

952×	`distribute-lft-neg-out`
926×	`associate-*r/`
860×	`associate-r`
850×	`associate-l`
838×	`associate-*l/`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`l`
-	-	`(*.f64 2 l)`
-	-	`(.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))`
-	-	`(+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))`
-	-	`(sin.f64 kx)`
-	-	`(pow.f64 (sin.f64 kx) 2)`
-	-	`(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))`
-	-	`(/.f64 (*.f64 2 l) Om)`
-	-	`(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))`
-	-	`(pow.f64 (sin.f64 ky) 2)`
-	-	`(pow.f64 (/.f64 (*.f64 2 l) Om) 2)`
-	-	`(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))`
-	-	`kx`
-	-	`ky`
-	-	`(+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))`
-	-	`(sin.f64 ky)`
-	-	`(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))`
-	-	`(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))`
-	-	`(/.f64 1 2)`
-	-	`Om`
-	-	`2`
-	-	`1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	142	1552
1	384	1376
2	1031	1376
3	5324	1376

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 (neg.f64 l)) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) (neg.f64 Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 (neg.f64 ky)) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 (neg.f64 l)) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 2 (/.f64 Om (neg.f64 l))) 2)))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (*.f64 l -2) Om) 2) 1))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) (neg.f64 Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 2 (/.f64 Om (neg.f64 l))) 2)))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (*.f64 l -2) Om) 2) 1))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) 2) (pow.f64 (sin.f64 ky) 2))))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 2 (/.f64 Om (neg.f64 l))) 2)))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (*.f64 l -2) Om) 2) 1))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))))))
(neg.f64 (sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 (neg.f64 ky)) 2))))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 2 (/.f64 Om (neg.f64 l))) 2)))))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (*.f64 l -2) Om) 2) 1))))))
(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (*.f64 2 Om) l) 2))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (*.f64 (/.f64 2 l) Om) 2) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (*.f64 Om (/.f64 2 l)) 2) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 kx) Om) 2) (+.f64 (pow.f64 (sin.f64 l) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om kx)) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 l) 2)))))))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 2 (/.f64 Om kx)) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 l) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 kx (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 l) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 ky) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 l) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om ky)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 l) 2)))))))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) ky) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 l) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 ky Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 l) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) kx) 2) (+.f64 (pow.f64 (sin.f64 Om) 2) (pow.f64 (sin.f64 ky) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 kx l)) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 Om) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 kx) l) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 Om) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) kx) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 Om) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) ky) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 Om) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) ky) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 Om) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 ky) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 Om) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 l (/.f64 2 ky)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 Om) 2)) 1)))))
(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 l Om) 2) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Symmetry

(abs l)

(abs Om)

(abs kx)

(abs ky)

(sort kx ky)

Compiler

Compiled 451 to 325 computations (27.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.4s

Operation ival-sin, time spent: 2.2s, 40.0% of total-time

Operation ival-add, time spent: 911.0ms, 17.0% of total-time

Operation ival-pow, time spent: 740.0ms, 14.0% of total-time

Operation ival-mult, time spent: 717.0ms, 13.0% of total-time

Operation ival-div, time spent: 446.0ms, 8.0% of total-time

Operation ival-sqrt, time spent: 280.0ms, 5.0% of total-time

Operation const, time spent: 129.0ms, 2.0% of total-time

eval2.0ms (0%)

Compiler: Compiled 79 to 63 computations (20.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))

Compiler

Compiled 31 to 27 computations (12.9% saved)

localize3.7s (22.8%)

Compiler: Compiled 203 to 132 computations (35% saved)
Precisions: Click to see histograms. Total time spent on operations: 2.4s
Operation ival-sin, time spent: 1.1s, 44.0% of total-time
Operation ival-add, time spent: 447.0ms, 19.0% of total-time
Operation ival-pow, time spent: 352.0ms, 15.0% of total-time
Operation ival-div, time spent: 223.0ms, 9.0% of total-time
Operation ival-sqrt, time spent: 132.0ms, 5.0% of total-time
Operation ival-mult, time spent: 128.0ms, 5.0% of total-time
Operation const, time spent: 63.0ms, 3.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 4 to 4 computations (0% saved)

prune3.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	0	0
Total	1	1

Accuracy

99.2%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))

Compiler

Compiled 91 to 77 computations (15.4% saved)

regimes57.0ms (0.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))

Calls

19 calls:

6.0ms	(sin.f64 ky)
5.0ms	Om
4.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
3.0ms	(pow.f64 (sin.f64 ky) 2)

Results

Accuracy	Segments	Branch
99.2%	1	`l`
99.2%	1	`Om`
99.2%	1	`kx`
99.2%	1	`ky`
99.2%	1	`(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))`
99.2%	1	`(.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))`
99.2%	1	`(+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))`
99.2%	1	`(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))`
99.2%	1	`(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))`
99.2%	1	`(+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))`
99.2%	1	`(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))`
99.2%	1	`(pow.f64 (/.f64 (*.f64 2 l) Om) 2)`
99.2%	1	`(/.f64 (*.f64 2 l) Om)`
99.2%	1	`(*.f64 2 l)`
99.2%	1	`(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))`
99.2%	1	`(pow.f64 (sin.f64 kx) 2)`
99.2%	1	`(sin.f64 kx)`
99.2%	1	`(pow.f64 (sin.f64 ky) 2)`
99.2%	1	`(sin.f64 ky)`

Compiler

Compiled 275 to 232 computations (15.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	95
1	40	95

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 2 (/.f64 Om l)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 1/2)))

Outputs

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

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

Compiler

Compiled 31 to 27 computations (12.9% saved)

soundness107.0ms (0.7%)

Rules

952×	`distribute-lft-neg-out`
926×	`associate-*r/`
860×	`associate-r`
850×	`associate-l`
838×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	142	1552
1	384	1376
2	1031	1376
3	5324	1376

Stop Event

1×	node limit

end0.0ms (0%)

preprocess68.0ms (0.4%)

Remove

(sort kx ky)

(abs ky)

(abs kx)

(abs Om)

(abs l)

Compiler

Compiled 748 to 652 computations (12.8% saved)

analyze168.0ms (1%)

sample3.7s (23.3%)

preprocess8.3s (51.4%)

eval2.0ms (0%)

prune1.0ms (0%)

localize3.7s (22.8%)

eval0.0ms (0%)

prune3.0ms (0%)

regimes57.0ms (0.4%)

simplify3.0ms (0%)

soundness107.0ms (0.7%)

end0.0ms (0%)

preprocess68.0ms (0.4%)

Profiling