Metrics for Falkner and Boettcher, Appendix B, 2

analyze5.0ms (0.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 21 to 15 computations (28.6% saved)

Precisions

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

ival-mult: 1.0ms (41.4% of total)

ival-sqrt: 1.0ms (41.4% of total)

ival-div: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

const: 0.0ms (0% of total)

sample1.1s (72.9%)

Results

828.0ms	8256×	256	valid
1.0ms	13×	256	invalid

Precisions

Click to see histograms. Total time spent on operations: 620.0ms

ival-mult: 269.0ms (43.4% of total)

ival-sqrt: 150.0ms (24.2% of total)

ival-sub: 98.0ms (15.8% of total)

ival-div: 83.0ms (13.4% of total)

const: 20.0ms (3.2% of total)

Bogosity

preprocess267.0ms (17.2%)

Algorithm

1×	egg-herbie

Rules

1731×	`fma-define`
509×	`distribute-lft-in`
502×	`fma-neg`
465×	`distribute-rgt-in`
435×	`unsub-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	280
1	81	276
2	199	260
3	637	256
4	1910	244
5	4131	244
6	5472	244
7	5803	244
8	5857	244
9	5917	244
10	6013	244
11	7603	244

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))
(neg.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))))

Outputs
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal -1/4 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal -1/4 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal -1/4 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(neg.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v))))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 v v))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) #s(literal 4 binary64)) (+.f64 (.f64 v v) #s(literal -1 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 v v #s(literal -1 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal 4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal 1/4 binary64))))

Symmetry

(abs v)

explain120.0ms (7.8%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 #s(literal 1 binary64) (*.f64 v v))`
-	-	`#s(literal 2 binary64)`
-	-	`v`
-	-	`(.f64 #s(literal 3 binary64) (.f64 v v))`
-	-	`#s(literal 4 binary64)`
-	-	`(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))`
-	-	`(sqrt.f64 #s(literal 2 binary64))`
-	-	`(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 3 binary64)`
-	-	`(*.f64 v v)`
-	-	`(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))`
-	-	`(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v)))))`
-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))`

Results

65.0ms

512×

256

valid

Compiler

Compiled 166 to 44 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 13.0ms (35.7% of total)

ival-sqrt: 10.0ms (27.4% of total)

ival-div: 6.0ms (16.5% of total)

ival-sub: 5.0ms (13.7% of total)

const: 1.0ms (2.7% of total)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Status

Accuracy

Program

100.0%

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Compiler

Compiled 40 to 28 computations (30% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative`
6×	`sub-neg`
6×	`+-commutative`
4×	`neg-sub0`
4×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	69
1	37	69
2	53	69
3	61	69
4	65	69

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Outputs

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess24.0ms (1.6%)

Remove: (abs v)
Compiler: Compiled 160 to 112 computations (30% saved)

Falkner and Boettcher, Appendix B, 2

analyze5.0ms (0.3%)

sample1.1s (72.9%)

preprocess267.0ms (17.2%)

explain120.0ms (7.8%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify3.0ms (0.2%)

soundness0.0ms (0%)

preprocess24.0ms (1.6%)

end0.0ms (0%)

Profiling