sqrt E (should all be same)

Time bar (total: 947.0ms)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 10 to 6 computations (40% saved)

sample578.0ms (61.1%)

Memory
-9.2MiB live, 455.4MiB allocated; 86ms collecting garbage
Samples
379.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 210.0ms
ival-pow2: 110.0ms (52.5% of total)
ival-sqrt: 79.0ms (37.7% of total)
ival-add!: 20.0ms (9.5% of total)
adjust: 1.0ms (0.5% of total)
Bogosity

preprocess100.0ms (10.6%)

Memory
-13.6MiB live, 31.0MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01019
12919
28016
325916
4126616
5657216
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
54.1%
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Symmetry

(abs x)

Compiler

Compiled 14 to 10 computations (28.6% saved)

series4.0ms (0.4%)

Memory
5.1MiB live, 5.2MiB allocated; 0ms collecting garbage
Counts
5 → 5
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)
1.0ms
x
@0
((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)
1.0ms
x
@-inf
((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

rewrite133.0ms (14%)

Memory
-33.8MiB live, 52.4MiB allocated; 113ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01871
02256
15936
033436
179136
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
10 → 26
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
Outputs
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (fabs.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(sqrt.f64 (*.f64 (*.f64 (*.f64 x x) x) x))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
x
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(approx (pow x 2) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval2.0ms (0.2%)

Memory
2.8MiB live, 2.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 134 to 69 computations (48.5% saved)

prune2.0ms (0.2%)

Memory
2.0MiB live, 2.0MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New19423
Fresh000
Picked101
Done000
Total20424
Accuracy
99.6%
Counts
24 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
54.1%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
5.5%
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
99.4%
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
2.3%
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 34 to 30 computations (11.8% saved)

series4.0ms (0.4%)

Memory
3.6MiB live, 3.6MiB allocated; 0ms collecting garbage
Counts
13 → 6
Calls
Call 1
Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x x)
Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) x (sqrt 2) 2 (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms
x
@inf
((sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) x (sqrt 2) 2 (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms
x
@0
((sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) x (sqrt 2) 2 (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))

rewrite76.0ms (8.1%)

Memory
0.4MiB live, 50.4MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
031133
040103
19079
049879
1131779
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
19 → 67
Calls
Call 1
Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) x)
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 x (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
x
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))))
(fabs.f64 (sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(*.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x (*.f64 #s(literal -1 binary64) (neg.f64 x)))
(*.f64 x x)
(pow.f64 (fabs.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (*.f64 (*.f64 (*.f64 x x) x) x))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (neg x) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
#s(approx (neg x) (neg.f64 x))
#s(approx x x)
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(approx (* x x) (*.f64 x x))

eval5.0ms (0.5%)

Memory
10.9MiB live, 10.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 354 to 171 computations (51.7% saved)

prune3.0ms (0.4%)

Memory
6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New55055
Fresh000
Picked044
Done000
Total55459
Accuracy
99.6%
Counts
59 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
54.1%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
5.5%
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
99.4%
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
2.3%
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 66 to 50 computations (24.2% saved)

regimes14.0ms (1.4%)

Memory
-28.3MiB live, 16.8MiB allocated; 6ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Calls

4 calls:

8.0ms
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
2.0ms
x
2.0ms
(pow.f64 x #s(literal 2 binary64))
2.0ms
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.4%1(pow.f64 x #s(literal 2 binary64))
99.4%1(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
99.4%1(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
99.4%1x
Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes4.0ms (0.4%)

Memory
10.3MiB live, 10.3MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
Outputs
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
Calls

4 calls:

1.0ms
x
1.0ms
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms
(pow.f64 x #s(literal 2 binary64))
1.0ms
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
5.5%1(pow.f64 x #s(literal 2 binary64))
5.5%1(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
5.5%1(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
5.5%1x
Compiler

Compiled 17 to 13 computations (23.5% saved)

derivations3.0ms (0.4%)

Memory
5.1MiB live, 5.1MiB allocated; 0ms collecting garbage
Stop Event
done
Compiler

Compiled 15 to 11 computations (26.7% saved)

preprocess17.0ms (1.8%)

Memory
-11.0MiB live, 35.0MiB allocated; 4ms collecting garbage
Remove

(abs x)

Compiler

Compiled 58 to 48 computations (17.2% saved)

end0.0ms (0%)

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

Profiling

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