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

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation ival-pow, time spent: 0.0ms, 0.0% of total-time

sample1.5s (48.8%)

Results

860.0ms	5051×	infinite
565.0ms	3204×	valid
0.0ms	1×	infinite

Precisions

Click to see histograms. Total time spent on operations: 789.0ms

Operation ival-add, time spent: 298.0ms, 38.0% of total-time

Operation ival-mult, time spent: 213.0ms, 27.0% of total-time

Operation ival-sub, time spent: 135.0ms, 17.0% of total-time

Operation ival-pow, time spent: 111.0ms, 14.0% of total-time

Operation const, time spent: 31.0ms, 4.0% of total-time

Bogosity

preprocess590.0ms (18.7%)

Algorithm

1×	egg-herbie

Rules

1486×	`unsub-neg`
1342×	`fma-def`
1230×	`sub-neg`
610×	`associate-+l-`
496×	`distribute-lft-out`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`b`
-	-	`(+.f64 (.f64 a a) (.f64 b b))`
-	-	`(.f64 4 (.f64 b b))`
-	-	`(*.f64 b b)`
-	-	`(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)`
-	-	`(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)`
-	-	`(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))`
-	-	`4`
-	-	`2`
-	-	`a`
-	-	`1`
-	-	`(*.f64 a a)`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	449
1	108	421
2	251	413
3	773	413
4	3444	315
5	6954	315

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) 2) (.f64 4 (.f64 (neg.f64 b) (neg.f64 b)))) 1)
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) 2) (.f64 4 (.f64 (neg.f64 b) (neg.f64 b)))) 1))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (.f64 a a))) 1)

Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 b b) 4) 1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 (.f64 b b) 4 -1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 b (.f64 b 4) -1))
(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 b b) 4) 1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 (.f64 b b) 4 -1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 b (.f64 b 4) -1))
(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 b b) 4) 1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 (.f64 b b) 4 -1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 b (.f64 b 4) -1))
(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) 2) (.f64 4 (.f64 (neg.f64 b) (neg.f64 b)))) 1)
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 b b) 4) 1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 (.f64 b b) 4 -1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 b (.f64 b 4) -1))
(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 b b) 4) 1)))
(+.f64 (neg.f64 (fma.f64 (.f64 b b) 4 (pow.f64 (fma.f64 a a (.f64 b b)) 2))) 1)
(-.f64 1 (fma.f64 b (.f64 b 4) (pow.f64 (fma.f64 a a (.f64 b b)) 2)))
(-.f64 (fma.f64 b (.f64 b -4) 1) (pow.f64 (fma.f64 a a (.f64 b b)) 2))
(-.f64 (fma.f64 b (*.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 4))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) 2) (.f64 4 (.f64 (neg.f64 b) (neg.f64 b)))) 1))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 b b) 4) 1)))
(+.f64 (neg.f64 (fma.f64 (.f64 b b) 4 (pow.f64 (fma.f64 a a (.f64 b b)) 2))) 1)
(-.f64 1 (fma.f64 b (.f64 b 4) (pow.f64 (fma.f64 a a (.f64 b b)) 2)))
(-.f64 (fma.f64 b (.f64 b -4) 1) (pow.f64 (fma.f64 a a (.f64 b b)) 2))
(-.f64 (fma.f64 b (*.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 4))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (.f64 a a))) 1)
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (-.f64 (.f64 (*.f64 a a) 4) 1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 (.f64 a a) 4 -1))
(+.f64 (pow.f64 (fma.f64 a a (.f64 b b)) 2) (fma.f64 a (.f64 a 4) -1))
(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 a (*.f64 a 4) -1))
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 a (*.f64 a 4) -1))

Symmetry

(abs a)

(abs b)

Compiler

Compiled 153 to 62 computations (59.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 312.0ms

Operation ival-add, time spent: 106.0ms, 34.0% of total-time

Operation ival-mult, time spent: 81.0ms, 26.0% of total-time

Operation ival-pow, time spent: 73.0ms, 23.0% of total-time

Operation ival-sub, time spent: 35.0ms, 11.0% of total-time

Operation const, time spent: 17.0ms, 5.0% of total-time

eval6.0ms (0.2%)

Compiler: Compiled 75 to 39 computations (48% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))
▶	99.9%	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	100.0%	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Status

Accuracy

Program

▶

100.0%

(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))

▶

99.9%

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)

▶

100.0%

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 50 to 32 computations (36% saved)

localize808.0ms (25.7%)

Compiler: Compiled 137 to 61 computations (55.5% saved)
Precisions: Click to see histograms. Total time spent on operations: 580.0ms
Operation ival-mult, time spent: 152.0ms, 26.0% of total-time
Operation ival-pow, time spent: 145.0ms, 25.0% of total-time
Operation ival-fma, time spent: 104.0ms, 18.0% of total-time
Operation ival-add, time spent: 99.0ms, 17.0% of total-time
Operation const, time spent: 32.0ms, 6.0% of total-time
Operation ival-sub, time spent: 24.0ms, 4.0% of total-time
Operation ival-hypot, time spent: 24.0ms, 4.0% of total-time

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	0	0
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))
✓	99.9%	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	100.0%	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Status

Accuracy

Program

✓

100.0%

(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))

✓

99.9%

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)

✓

100.0%

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 96 to 59 computations (38.5% saved)

regimes18.0ms (0.6%)

Counts

3 → 1

Calls

Call 1

Inputs

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

(fma.f64 (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 3) (fma.f64 b (*.f64 b 4) -1))

Outputs
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Calls

6 calls:

4.0ms	b
3.0ms	a
3.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
3.0ms	(*.f64 a a)
3.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)`
100.0%	1	`(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 52 to 32 computations (38.5% saved)

regimes15.0ms (0.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Calls

6 calls:

4.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
3.0ms	b
3.0ms	a
2.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
2.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
99.9%	1	`a`
99.9%	1	`b`
99.9%	1	`(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)`
99.9%	1	`(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))`
99.9%	1	`(*.f64 a a)`
99.9%	1	`(*.f64 b b)`

Compiler

Compiled 52 to 32 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`*-commutative`
4×	`sub-neg`
3×	`1-exp`
2×	`*-rgt-identity`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	112
1	37	112
2	40	112
3	44	112

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Outputs

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)

(+.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) -1)

Compiler

Compiled 33 to 22 computations (33.3% saved)

soundness120.0ms (3.8%)

Rules

1486×	`unsub-neg`
1342×	`fma-def`
1230×	`sub-neg`
610×	`associate-+l-`
496×	`distribute-lft-out`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	449
1	108	421
2	251	413
3	773	413
4	3444	315
5	6954	315

Stop Event

1×	node limit

Compiler

Compiled 67 to 33 computations (50.7% saved)

end0.0ms (0%)

preprocess45.0ms (1.4%)

Remove

(abs b)

(abs a)

Compiler

Compiled 268 to 184 computations (31.3% saved)

analyze0.0ms (0%)

sample1.5s (48.8%)

preprocess590.0ms (18.7%)

eval6.0ms (0.2%)

prune2.0ms (0.1%)

localize808.0ms (25.7%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes18.0ms (0.6%)

regimes15.0ms (0.5%)

simplify4.0ms (0.1%)

soundness120.0ms (3.8%)

end0.0ms (0%)

preprocess45.0ms (1.4%)

Profiling