sqrt sqr

Time bar (total: 3.2s)

analyze2.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-div: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)

sample2.8s (85.4%)

Results
1.7s4179×2valid
610.0ms4077×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-div: 779.0ms (45.1% of total)
ival-sub: 323.0ms (18.7% of total)
ival-mult: 281.0ms (16.3% of total)
ival-sqrt: 175.0ms (10.1% of total)
backward-pass: 144.0ms (8.3% of total)
const: 25.0ms (1.4% of total)
Bogosity

preprocess52.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
85×fma-define
67×fma-neg
22×distribute-lft-neg-in
19×cancel-sign-sub-inv
19×sub-neg
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021128
16992
214192
325892
441292
553992
657492
758492
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (*.f64 (neg.f64 x) (neg.f64 x)))))
(neg.f64 (-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (*.f64 (neg.f64 x) (neg.f64 x))))))
Outputs
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (fabs.f64 x)))
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (fabs.f64 x)))
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (*.f64 (neg.f64 x) (neg.f64 x)))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(neg.f64 (-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (*.f64 (neg.f64 x) (neg.f64 x))))))
(neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 x))))
(-.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x))

explain254.0ms (7.9%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1400-2(-1.6441057378629712e-159)(sqrt.f64 (*.f64 x x))
00-0-x
00-0-(/.f64 x x)
00-0-(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x)))
00-0-(*.f64 x x)
00-0-(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
00-0-(/.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
Results
24.0ms190×256valid
89.0ms168×2048valid
85.0ms82×2048infinite
8.0ms72×256infinite
Compiler

Compiled 87 to 38 computations (56.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 98.0ms
ival-div: 47.0ms (48.1% of total)
ival-mult: 29.0ms (29.7% of total)
ival-sqrt: 11.0ms (11.3% of total)
ival-sub: 7.0ms (7.2% of total)
const: 4.0ms (4.1% of total)

eval0.0ms (0%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize23.0ms (0.7%)

Results
16.0ms256×256valid
Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-div: 2.0ms (34.5% of total)
ival-fabs: 2.0ms (34.5% of total)
ival-sub: 1.0ms (17.3% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Accuracy
100.0%
Counts
1 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes4.0ms (0.1%)

Accuracy

Total -35.3b remaining (-∞%)

Threshold costs -35.3b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Outputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
Calls

2 calls:

2.0ms
x
1.0ms
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Compiler

Compiled 15 to 9 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
4×sub-neg
4×+-commutative
3×1-exp
3×*-commutative
3×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
11723
22523
33123
43623
53823
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
Outputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))

soundness103.0ms (3.2%)

Rules
85×fma-define
67×fma-neg
22×distribute-lft-neg-in
19×cancel-sign-sub-inv
19×sub-neg
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021128
16992
214192
325892
441292
553992
657492
758492
Stop Event
1×done
1×saturated
Compiler

Compiled 233 to 82 computations (64.8% saved)

preprocess30.0ms (0.9%)

Compiler

Compiled 54 to 38 computations (29.6% saved)

end0.0ms (0%)

Profiling

Loading profile data...