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

analyze432.0ms (5.7%)

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
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 15 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 348.0ms

Operation ival-pow, time spent: 234.0ms, 67.0% of total-time

Operation ival-sin, time spent: 56.0ms, 16.0% of total-time

Operation ival-mult, time spent: 20.0ms, 6.0% of total-time

Operation ival-sqrt, time spent: 20.0ms, 6.0% of total-time

Operation ival-add, time spent: 9.0ms, 3.0% of total-time

Operation ival-div, time spent: 6.0ms, 2.0% of total-time

Operation const, time spent: 3.0ms, 1.0% of total-time

sample2.5s (32.8%)

Results

2.4s	8249×	0	valid
1.0ms	3×	1	valid
4.0ms	2×	3	valid
0.0ms	1×	0	valid
1.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

Operation ival-sin, time spent: 905.0ms, 57.0% of total-time

Operation ival-pow, time spent: 275.0ms, 17.0% of total-time

Operation ival-add, time spent: 140.0ms, 9.0% of total-time

Operation ival-sqrt, time spent: 115.0ms, 7.0% of total-time

Operation ival-mult, time spent: 70.0ms, 4.0% of total-time

Operation ival-div, time spent: 64.0ms, 4.0% of total-time

Operation const, time spent: 29.0ms, 2.0% of total-time

Bogosity

preprocess3.0s (39.2%)

Algorithm

1×	egg-herbie

Rules

1262×	`fma-def`
834×	`unswap-sqr`
814×	`associate-/r/`
798×	`distribute-lft-neg-in`
694×	`div-sub`

FPErrors

Click to see full error table

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	717
1	123	529
2	298	529
3	657	529
4	2780	529
5	7692	529

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(abs kx)

(negabs ky)

(negabs th)

Compiler

Compiled 159 to 90 computations (43.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.5s

Operation ival-sin, time spent: 1.6s, 65.0% of total-time

Operation ival-pow, time spent: 443.0ms, 17.0% of total-time

Operation ival-add, time spent: 224.0ms, 9.0% of total-time

Operation ival-sqrt, time spent: 130.0ms, 5.0% of total-time

Operation ival-div, time spent: 49.0ms, 2.0% of total-time

Operation const, time spent: 31.0ms, 1.0% of total-time

Operation ival-mult, time spent: 26.0ms, 1.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
▶	92.8%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Compiler

Compiled 33 to 23 computations (30.3% saved)

localize1.5s (19.5%)

Compiler: Compiled 103 to 41 computations (60.2% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.3s
Operation ival-sin, time spent: 795.0ms, 62.0% of total-time
Operation ival-pow, time spent: 217.0ms, 17.0% of total-time
Operation ival-add, time spent: 99.0ms, 8.0% of total-time
Operation ival-sqrt, time spent: 65.0ms, 5.0% of total-time
Operation ival-div, time spent: 44.0ms, 3.0% of total-time
Operation ival-mult, time spent: 25.0ms, 2.0% of total-time
Operation ival-hypot, time spent: 22.0ms, 2.0% of total-time
Operation const, time spent: 16.0ms, 1.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	0	0
Total	2	2

Accuracy

99.7%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	92.8%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Compiler

Compiled 63 to 40 computations (36.5% saved)

regimes30.0ms (0.4%)

Accuracy

Total -4.4b remaining (-2047%)

Threshold costs -4.4b (-2047%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Calls

9 calls:

5.0ms	th
3.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
3.0ms	(sin.f64 th)
3.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
99.7%	1	`kx`
99.7%	1	`ky`
99.7%	1	`th`
99.7%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))`
99.7%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))`
99.7%	1	`(sin.f64 ky)`
99.7%	1	`(pow.f64 (sin.f64 kx) 2)`
99.7%	1	`(sin.f64 kx)`
99.7%	1	`(sin.f64 th)`

Compiler

Compiled 69 to 53 computations (23.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	17	47

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Compiler

Compiled 14 to 9 computations (35.7% saved)

soundness152.0ms (2%)

Rules

1262×	`fma-def`
834×	`unswap-sqr`
814×	`associate-/r/`
798×	`distribute-lft-neg-in`
694×	`div-sub`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	717
1	123	529
2	298	529
3	657	529
4	2780	529
5	7692	529

Stop Event

1×	node limit

Compiler

Compiled 267 to 150 computations (43.8% saved)

end0.0ms (0%)

preprocess34.0ms (0.4%)

Remove

(negabs th)

(negabs ky)

(abs kx)

Compiler

Compiled 234 to 154 computations (34.2% saved)

analyze432.0ms (5.7%)

sample2.5s (32.8%)

preprocess3.0s (39.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize1.5s (19.5%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes30.0ms (0.4%)

simplify2.0ms (0%)

soundness152.0ms (2%)

end0.0ms (0%)

preprocess34.0ms (0.4%)

Profiling