Metrics for Toniolo and Linder, Equation (3b), real

analyze222.0ms (9.1%)

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
25%	25%	74.9%	0.1%	0%	0%	0%	5
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	6
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	7
53.1%	53%	46.8%	0.1%	0%	0%	0%	8
60.9%	60.8%	39%	0.1%	0%	0%	0%	9
60.9%	60.8%	39%	0.1%	0%	0%	0%	10
64.8%	64.7%	35.1%	0.1%	0%	0%	0%	11
68.4%	68.3%	31.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 20 to 14 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-sin: 36.0ms (28.7% of total)

ival-pow: 36.0ms (28.7% of total)

ival-mult: 23.0ms (18.3% of total)

ival-sqrt: 14.0ms (11.1% of total)

ival-add: 9.0ms (7.2% of total)

ival-div: 5.0ms (4% of total)

const: 2.0ms (1.6% of total)

sample1.8s (73.9%)

Results

1.5s

8256×

256

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sin: 665.0ms (59% of total)

ival-pow: 201.0ms (17.8% of total)

ival-div: 64.0ms (5.7% of total)

ival-mult: 63.0ms (5.6% of total)

ival-sqrt: 62.0ms (5.5% of total)

ival-add: 61.0ms (5.4% of total)

const: 11.0ms (1% of total)

Bogosity

preprocess184.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-define`
307×	`fma-neg`
195×	`unsub-neg`
181×	`times-frac`
170×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	717
1	111	529
2	240	529
3	420	529
4	940	529
5	2219	529
6	3233	529
7	3758	529
8	4126	529
9	4217	529
10	4256	529
11	4256	529

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 (neg.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 (neg.f64 th)))
(*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (neg.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)))
(*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 th)))
(neg.f64 (*.f64 (/.f64 (sin.f64 (neg.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 (neg.f64 ky)) #s(literal 2 binary64))))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(neg.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 (neg.f64 th))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 th) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 kx))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 th) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 th))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 th)))

Symmetry

(abs kx)

(negabs ky)

(negabs th)

explain188.0ms (7.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
18	0	-	2	(5.0119416686454945e-174 5.216607872214278e-159 5.878614312733771e-147)	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	0	-	0	-	`kx`
0	0	-	0	-	`ky`
0	0	-	0	-	`(sin.f64 ky)`
0	0	-	0	-	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
0	0	-	0	-	`th`
0	56	(3.24743661708475e-140 1.6435067760412601e+292 4.703455556137049e-245)	0	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	0	-	0	-	`(sin.f64 th)`
0	0	-	0	-	`(sin.f64 kx)`
0	0	-	0	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	56	(7.785852684796318e-24 2.9824582254147075e-50 8.84378732549076e-252)	0	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`

Results

109.0ms

512×

256

valid

Compiler

Compiled 159 to 41 computations (74.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-sin: 42.0ms (54.4% of total)

ival-pow: 15.0ms (19.4% of total)

ival-mult: 10.0ms (13% of total)

ival-div: 4.0ms (5.2% of total)

ival-sqrt: 4.0ms (5.2% of total)

ival-add: 3.0ms (3.9% of total)

const: 1.0ms (1.3% of total)

eval0.0ms (0%)

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

prune6.0ms (0.2%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.1%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative`
1×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	63
1	22	63

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 19 to 13 computations (31.6% saved)

preprocess34.0ms (1.4%)

Remove

(negabs th)

(negabs ky)

(abs kx)

Compiler

Compiled 304 to 208 computations (31.6% saved)

Toniolo and Linder, Equation (3b), real

analyze222.0ms (9.1%)

sample1.8s (73.9%)

preprocess184.0ms (7.5%)

explain188.0ms (7.7%)

eval0.0ms (0%)

prune6.0ms (0.2%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

preprocess34.0ms (1.4%)

end0.0ms (0%)

Profiling