sqrt sqr

Time bar (total: 2.3s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze2.0ms (0.1%)

Memory
2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Algorithm
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)

sample1.8s (79.8%)

Memory
69.0MiB live, 1 675.3MiB allocated; 1.0s collecting garbage
Samples
1.1s4 081×2valid
343.0ms4 175×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.2s
ival-mult: 489.0ms (42.2% of total)
ival-div: 314.0ms (27.1% of total)
adjust: 141.0ms (12.2% of total)
ival-sqrt: 124.0ms (10.7% of total)
ival-sub: 78.0ms (6.7% of total)
ival-true: 5.0ms (0.4% of total)
exact: 5.0ms (0.4% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

explain210.0ms (9.2%)

Memory
-39.0MiB live, 216.0MiB allocated; 26ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1300-3(1.9768574907513674e-156)(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))uflow-rescue660
(*.f64 x x)underflow66
sqrt.f64(sqrt.f64 (*.f64 x x))oflow-rescue610
(*.f64 x x)overflow61
Confusion
Predicted +Predicted -
+12717
-0112
Precision
1.0
Recall
0.8819444444444444
Confusion?
Predicted +Predicted MaybePredicted -
+127017
-00112
Precision?
1.0
Recall?
0.8819444444444444
Freqs
test
numberfreq
0129
1127
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
44.0ms244×2valid
40.0ms268×0valid
Compiler

Compiled 86 to 28 computations (67.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-div: 33.0ms (51.1% of total)
ival-mult: 11.0ms (17% of total)
adjust: 10.0ms (15.5% of total)
ival-sub: 5.0ms (7.7% of total)
ival-sqrt: 5.0ms (7.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess29.0ms (1.3%)

Memory
27.8MiB live, 27.8MiB allocated; 0ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01021
13814
28412
313112
420512
525512
627712
731512
833512
934312
1035512
1136112
0812
0148
1306
2586
31136
41806
52176
62436
72776
82936
93016
103136
113196
03196
Stop Event
iter limit
saturated
iter limit
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))
Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
47.5%
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

series3.0ms (0.1%)

Memory
4.3MiB live, 4.3MiB allocated; 0ms collecting garbage
Counts
8 → 8
Calls
Call 1
Inputs
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(/.f64 x x)
x
(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(sqrt.f64 (*.f64 x x))
(*.f64 x x)
Outputs
0
1
x
(/ 1 x)
(pow x 2)
2
-1
(* -1 x)
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))
1.0ms
x
@0
((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))
1.0ms
x
@inf
((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))

simplify8.0ms (0.4%)

Memory
-35.8MiB live, 8.8MiB allocated; 6ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11313
21613
33813
48913
512313
613213
013213
Stop Event
iter limit
saturated
Counts
8 → 7
Calls
Call 1
Inputs
0
1
x
(/ 1 x)
(pow x 2)
2
-1
(* -1 x)
Outputs
0
#s(literal 0 binary64)
1
#s(literal 1 binary64)
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(pow x 2)
(*.f64 x x)
2
#s(literal 2 binary64)
-1
#s(literal -1 binary64)
(* -1 x)
(neg.f64 x)

rewrite36.0ms (1.6%)

Memory
25.6MiB live, 70.2MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0835
01419
15912
036712
Stop Event
iter limit
iter limit
iter limit
unsound
iter limit
Counts
8 → 59
Calls
Call 1
Inputs
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
(/.f64 x x)
x
(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(sqrt.f64 (*.f64 x x))
(*.f64 x x)
Outputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))
(*.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (neg.f64 x))
(fabs.f64 x)
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal 1/2 binary64)))
x
#s(literal 1 binary64)
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))
(*.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (neg.f64 x))
(fabs.f64 x)
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal 1/2 binary64)))
x
(*.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x))
(*.f64 x x)
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval11.0ms (0.5%)

Memory
25.2MiB live, 25.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 786 to 384 computations (78.5% saved)

prune17.0ms (0.7%)

Memory
-35.7MiB live, 8.8MiB allocated; 4ms collecting garbage
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1132115
Fresh000
Picked101
Done000
Total1142116
Accuracy
100.0%
Counts
116 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.8%
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
49.3%
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
0
2
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)
0.0ms
x
@inf
((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)
0.0ms
x
@-inf
((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)

simplify3.0ms (0.1%)

Memory
4.7MiB live, 4.7MiB allocated; 0ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022
142
252
052
Stop Event
saturated
saturated
Counts
2 → 2
Calls
Call 1
Inputs
0
2
Outputs
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)

rewrite24.0ms (1%)

Memory
7.1MiB live, 7.1MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01230
01222
1588
03658
Stop Event
iter limit
iter limit
iter limit
unsound
saturated
Counts
4 → 4
Calls
Call 1
Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(literal 2 binary64)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 56 to 12 computations (78.6% saved)

prune1.0ms (0.1%)

Memory
1.1MiB live, 1.1MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New404
Fresh000
Picked022
Done000
Total426
Accuracy
100.0%
Counts
6 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.8%
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
49.3%
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
Compiler

Compiled 68 to 39 computations (42.6% saved)

regimes3.0ms (0.1%)

Memory
2.9MiB live, 2.9MiB allocated; 0ms collecting garbage
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #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
88.3%2(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
100.0%2x
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes2.0ms (0.1%)

Memory
2.5MiB live, 2.5MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #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
49.3%1(-.f64 (/.f64 x x) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 x x))))
49.3%1x
Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch24.0ms (1.1%)

Memory
12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
21.0ms
-8.293042940848845e-306
1.176333286359312e-306
Samples
12.0ms80×2valid
4.0ms64×0valid
Compiler

Compiled 267 to 210 computations (21.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-div: 3.0ms (25.2% of total)
adjust: 3.0ms (25.2% of total)
ival-mult: 3.0ms (25.2% of total)
ival-sqrt: 2.0ms (16.8% of total)
ival-sub: 1.0ms (8.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

simplify54.0ms (2.4%)

Memory
-35.0MiB live, 22.5MiB allocated; 7ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01534
13228
25928
312228
428528
565128
6101928
7109728
8121428
9121828
10121828
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64)) #s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64)))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
Outputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64)) #s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64)))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

derivations5.0ms (0.2%)

Memory
7.8MiB live, 7.8MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11313
21613
33813
48913
512313
613213
013213
Stop Event
done
iter limit
saturated
Compiler

Compiled 46 to 15 computations (67.4% saved)

preprocess25.0ms (1.1%)

Memory
5.4MiB live, 47.3MiB allocated; 9ms collecting garbage
Compiler

Compiled 128 to 56 computations (56.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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