sqrt sqr

Time bar (total: 2.1s)

analyze2.0ms (0.1%)

Memory
2.3MiB live, 2.3MiB allocated
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 10 computations (28.6% saved)

sample1.5s (72.8%)

Memory
41.3MiB live, 1 768.6MiB allocated
Samples
841.0ms4 105×2valid
411.0ms4 151×0valid
Precisions
Click to see histograms. Total time spent on operations: 999.0ms
ival-div: 436.0ms (43.6% of total)
ival-mult: 255.0ms (25.5% of total)
ival-sub: 105.0ms (10.5% of total)
adjust: 97.0ms (9.7% of total)
ival-sqrt: 92.0ms (9.2% of total)
ival-true: 6.0ms (0.6% of total)
exact: 5.0ms (0.5% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

preprocess41.0ms (1.9%)

Memory
-7.7MiB live, 72.5MiB allocated
Algorithm
1×egg-herbie
Rules
152×lower-fma.f64
152×lower-fma.f32
120×lower-*.f32
116×lower-*.f64
56×lower-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01021
13914
211112
322012
431312
536412
637512
737612
0812
0148
1286
2516
3796
41026
51346
61576
71836
82026
92096
102166
112316
123116
133316
143366
03366
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Outputs
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))

explain170.0ms (8%)

Memory
-28.0MiB live, 336.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1200-2(-1.5828149382012394e-160)(sqrt.f64 (*.f64 x x))
00-0-(/.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
00-0-(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x 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-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (*.f64 x x))oflow-rescue690
↳(*.f64 x x)overflow69
sqrt.f64(sqrt.f64 (*.f64 x x))uflow-rescue490
↳(*.f64 x x)underflow49
Confusion
Predicted +Predicted -
+1188
-0130
Precision
1.0
Recall
0.9365079365079365
Confusion?
Predicted +Predicted MaybePredicted -
+11808
-00130
Precision?
1.0
Recall?
0.9365079365079365
Freqs
test
numberfreq
0138
1118
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
54.0ms258×2valid
20.0ms254×0valid
Compiler

Compiled 100 to 36 computations (64% saved)

Precisions
Click to see histograms. Total time spent on operations: 50.0ms
ival-mult: 18.0ms (36% of total)
ival-div: 14.0ms (28% of total)
adjust: 6.0ms (12% of total)
ival-sqrt: 6.0ms (12% of total)
ival-sub: 5.0ms (10% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.5%
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

localize65.0ms (3.1%)

Memory
2.9MiB live, 79.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
✓accuracy100.0%
(*.f64 x x)
✓accuracy99.8%
(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x)))
✓accuracy56.5%
(sqrt.f64 (*.f64 x x))
Samples
31.0ms127×0valid
21.0ms129×2valid
Compiler

Compiled 37 to 10 computations (73% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
ival-mult: 28.0ms (65.9% of total)
ival-div: 6.0ms (14.1% of total)
adjust: 3.0ms (7.1% of total)
ival-sqrt: 3.0ms (7.1% of total)
ival-sub: 2.0ms (4.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series1.0ms (0.1%)

Memory
3.3MiB live, 3.3MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#<alt (sqrt.f64 (*.f64 x x))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x)))>
#<alt (*.f64 x x)>
#<alt (-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))>
Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt -1>
#<alt -1>
#<alt -1>
#<alt -1>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 2>
#<alt 2>
#<alt 2>
#<alt 2>
Calls

12 calls:

TimeVariablePointExpression
0.0ms
x
@0
(* x x)
0.0ms
x
@inf
(sqrt (* x x))
0.0ms
x
@inf
(* x x)
0.0ms
x
@0
(sqrt (* x x))
0.0ms
x
@-inf
(sqrt (* x x))

rewrite83.0ms (3.9%)

Memory
6.2MiB live, 84.2MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
206×lower-*.f32
204×lower-*.f64
108×lower-/.f32
106×lower-/.f64
84×lower-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0827
01419
1666
23736
07196
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
4 → 50
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x)))
(*.f64 x x)
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Outputs
x
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (log.f64 x))))
(fabs.f64 x)
(fabs.f64 (neg.f64 x))
(fabs.f64 (-.f64 x #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 x))
(sqrt.f64 (*.f64 x x))
(neg.f64 (neg.f64 x))
(/.f64 x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 x) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) x)) (/.f64 (sqrt.f64 x) x))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal -1 binary64) (neg.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 (neg.f64 x) #s(literal -1 binary64))
#s(literal 1 binary64)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(fabs.f64 (*.f64 x x))
(fabs.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))
#s(literal 0 binary64)

simplify5.0ms (0.2%)

Memory
9.5MiB live, 9.5MiB allocated
Algorithm
1×egg-herbie
Rules
12×lower-+.f64
12×lower-+.f32
6×lower-*.f64
6×lower-fma.f64
6×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0776
11176
21276
31376
41576
51776
62176
73076
83376
03376
Stop Event
1×iter limit
1×saturated
Counts
48 → 40
Calls
Call 1
Inputs
x
x
x
x
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
1
1
1
1
1
1
1
1
-1
-1
-1
-1
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
0
0
0
0
0
0
0
0
2
2
2
2
Outputs
x
x
x
x
x
x
x
x
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)
2
#s(literal 2 binary64)
2
#s(literal 2 binary64)
2
#s(literal 2 binary64)

eval9.0ms (0.4%)

Memory
20.0MiB live, 20.0MiB allocated
Compiler

Compiled 903 to 195 computations (78.4% saved)

prune25.0ms (1.2%)

Memory
-20.7MiB live, 15.9MiB allocated
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New88290
Fresh000
Picked101
Done000
Total89291
Accuracy
100.0%
Counts
91 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶51.2%
#s(literal 2 binary64)
▶51.9%
#s(literal 0 binary64)
Compiler

Compiled 4 to 4 computations (0% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

localize7.0ms (0.3%)

Memory
17.9MiB live, 17.9MiB allocated
Samples
4.0ms256×0valid
Compiler

Compiled 4 to 5 computations (-25% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Counts
0 → 0
Calls
Call 1
Inputs
Outputs

rewrite9.0ms (0.4%)

Memory
-25.1MiB live, 12.0MiB allocated
Algorithm
1×batch-egg-rewrite
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
000
000
Stop Event
1×saturated
1×saturated
1×saturated
Counts
0 → 0
Calls
Call 1
Inputs
Outputs

simplify2.0ms (0.1%)

Memory
5.7MiB live, 5.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
000
Stop Event
1×saturated
1×saturated
Counts
0 → 0
Calls
Call 1
Inputs
Outputs

eval0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Memory
4.5MiB live, 4.5MiB allocated
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked022
Done000
Total022
Accuracy
100.0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓51.2%
#s(literal 2 binary64)
✓51.9%
#s(literal 0 binary64)
Compiler

Compiled 19 to 14 computations (26.3% saved)

regimes4.0ms (0.2%)

Memory
10.4MiB live, 10.4MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 2 binary64)
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Outputs
#s(literal 2 binary64)
#s(literal 0 binary64)
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%2x
92.4%2(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Compiler

Compiled 15 to 9 computations (40% saved)

regimes3.0ms (0.1%)

Memory
7.7MiB live, 7.7MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
Outputs
#s(literal 0 binary64)
Calls

2 calls:

1.0ms
x
1.0ms
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Results
AccuracySegmentsBranch
51.9%1(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
51.9%1x
Compiler

Compiled 15 to 9 computations (40% saved)

bsearch34.0ms (1.6%)

Memory
-17.3MiB live, 65.9MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
32.0ms
-2.5826510152100602e-287
1.7108693859508186e-304
Samples
12.0ms80×2valid
10.0ms96×0valid
Compiler

Compiled 82 to 78 computations (4.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-div: 4.0ms (29.7% of total)
ival-mult: 4.0ms (29.7% of total)
adjust: 2.0ms (14.9% of total)
ival-sub: 2.0ms (14.9% of total)
ival-sqrt: 2.0ms (14.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

simplify5.0ms (0.3%)

Memory
14.0MiB live, 14.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x #s(literal -2024022533073/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(literal 2 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
Outputs
(if (<=.f64 x #s(literal -2024022533073/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(literal 2 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)

soundness60.0ms (2.8%)

Memory
-17.1MiB live, 57.1MiB allocated
Rules
206×lower-*.f32
204×lower-*.f64
108×lower-/.f32
106×lower-/.f64
84×lower-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0827
01419
1666
23736
07196
0776
11176
21276
31376
41576
51776
62176
73076
83376
03376
Stop Event
1×done
1×iter limit
1×saturated
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Compiler

Compiled 14 to 12 computations (14.3% saved)

preprocess50.0ms (2.4%)

Memory
-8.8MiB live, 83.2MiB allocated
Compiler

Compiled 56 to 38 computations (32.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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