Metrics for Bouland and Aaronson, Equation (26)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 20 to 13 computations (35% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

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

sample877.0ms (77.8%)

Results

658.0ms

8256×

256

valid

Precisions

Click to see histograms. Total time spent on operations: 434.0ms

ival-mult: 180.0ms (41.4% of total)

ival-pow: 101.0ms (23.3% of total)

ival-add: 86.0ms (19.8% of total)

ival-sub: 51.0ms (11.7% of total)

const: 16.0ms (3.7% of total)

Bogosity

preprocess104.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

821×	`unsub-neg`
800×	`fma-neg`
601×	`sub-neg`
410×	`fma-define`
374×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	449
1	99	421
2	233	413
3	700	413
4	2734	413
5	7202	413

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 a a))) #s(literal 1 binary64))

Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 (.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 (.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 (.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 (.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 (.f64 b b) #s(literal 4 binary64) (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (fma.f64 b (.f64 b #s(literal 4 binary64)) (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64))))
(-.f64 (fma.f64 b (.f64 b #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 (.f64 b b) #s(literal 4 binary64) (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (fma.f64 b (.f64 b #s(literal 4 binary64)) (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64))))
(-.f64 (fma.f64 b (.f64 b #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 a a))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (-.f64 (.f64 (*.f64 a a) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 (.f64 a a) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) #s(literal 2 binary64)) (fma.f64 a (.f64 a #s(literal 4 binary64)) #s(literal -1 binary64)))

Symmetry

(abs a)

(abs b)

explain116.0ms (10.3%)

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
48	(1.0016935890433179e-63 5.006567923731775e-238)	-	`(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64))`
0	-	-	`b`
0	-	-	`(+.f64 (.f64 a a) (.f64 b b))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(.f64 #s(literal 4 binary64) (.f64 b b))`
0	-	-	`(*.f64 b b)`
0	-	-	`(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`a`
0	-	-	`(*.f64 a a)`

Results

54.0ms

512×

256

valid

Compiler

Compiled 153 to 38 computations (75.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 11.0ms (42.7% of total)

ival-pow: 6.0ms (23.3% of total)

ival-add: 5.0ms (19.4% of total)

ival-sub: 3.0ms (11.7% of total)

const: 1.0ms (3.9% of total)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))

Compiler

Compiled 38 to 24 computations (36.8% saved)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
3×	`1-exp`
2×	`unsub-neg`
2×	`sub-neg`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	28	67
2	32	67
3	35	67
4	38	67
5	41	67

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 b b))) #s(literal 1 binary64))

Outputs

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 (*.f64 b b) #s(literal 4 binary64))) #s(literal 1 binary64))

(+.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 (*.f64 b b) #s(literal 4 binary64))) #s(literal -1 binary64))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 19 to 12 computations (36.8% saved)

preprocess25.0ms (2.2%)

Remove

(abs b)

(abs a)

Compiler

Compiled 228 to 144 computations (36.8% saved)

Bouland and Aaronson, Equation (26)

analyze0.0ms (0%)

sample877.0ms (77.8%)

preprocess104.0ms (9.2%)

explain116.0ms (10.3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify3.0ms (0.3%)

soundness0.0ms (0%)

preprocess25.0ms (2.2%)

end0.0ms (0%)

Profiling