sqrt A (should all be same)

Time bar (total: 1.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 10 to 4 computations (60% saved)

sample590.0ms (41.1%)

Memory
-20.9MiB live, 692.4MiB allocated
Samples
429.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 170.0ms
ival-hypot: 161.0ms (94.8% of total)
ival-true: 6.0ms (3.5% of total)
ival-assert: 3.0ms (1.8% of total)
Bogosity

explain68.0ms (4.7%)

Memory
3.0MiB live, 123.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1300-5(-1.1473349322737174e-157)(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
00-0-(+.f64 (*.f64 x x) (*.f64 x x))
00-0-(*.f64 x x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))uflow-rescue690
↳(+.f64 (*.f64 x x) (*.f64 x x))underflow69
↳(*.f64 x x)underflow138
sqrt.f64(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))oflow-rescue560
↳(+.f64 (*.f64 x x) (*.f64 x x))overflow56
↳(*.f64 x x)overflow112
Confusion
Predicted +Predicted -
+1255
-0126
Precision
1.0
Recall
0.9615384615384616
Confusion?
Predicted +Predicted MaybePredicted -
+12505
-00126
Precision?
1.0
Recall?
0.9615384615384616
Freqs
test
numberfreq
0131
1125
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
25.0ms512×0valid
Compiler

Compiled 50 to 16 computations (68% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-hypot: 9.0ms (59.1% of total)
ival-mult: 4.0ms (26.3% of total)
ival-add: 2.0ms (13.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess14.0ms (1%)

Memory
24.0MiB live, 24.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
12113
26613
317313
426913
527813
628013
048
076
1116
2146
3176
0173
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)
Symmetry

(abs x)

Compiler

Compiled 8 to 4 computations (50% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune5.0ms (0.3%)

Memory
-35.2MiB live, 0.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.8%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Compiler

Compiled 8 to 4 computations (50% saved)

simplify2.0ms (0.2%)

Memory
3.8MiB live, 3.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff2
(+.f64 (*.f64 x x) (*.f64 x x))
cost-diff3
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0419
0715
11115
21415
31715
01712
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x x)
x
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 x x)
x

localize17.0ms (1.2%)

Memory
35.6MiB live, 35.6MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.01171875
(+.f64 (*.f64 x x) (*.f64 x x))
accuracy29.533043388199705
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Samples
13.0ms256×0valid
Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-hypot: 4.0ms (55.2% of total)
ival-mult: 2.0ms (27.6% of total)
ival-add: 1.0ms (13.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series8.0ms (0.5%)

Memory
-27.2MiB live, 7.5MiB allocated
Counts
3 → 4
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x x)
Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(* -1 (* x (sqrt 2)))
Calls

3 calls:

TimeVariablePointExpression
6.0ms
x
@0
((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms
x
@inf
((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms
x
@-inf
((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))

simplify4.0ms (0.3%)

Memory
10.9MiB live, 10.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
11517
23217
33817
44217
55417
66617
77717
89717
910217
010217
Stop Event
1×iter limit
1×saturated
Counts
4 → 4
Calls
Call 1
Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(* -1 (* x (sqrt 2)))
Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite28.0ms (2%)

Memory
13.0MiB live, 51.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0418
0714
12310
01609
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
3 → 33
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x x)
Outputs
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x (*.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval4.0ms (0.3%)

Memory
6.7MiB live, 6.7MiB allocated
Compiler

Compiled 370 to 110 computations (70.3% saved)

prune2.0ms (0.1%)

Memory
4.0MiB live, 4.0MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New38442
Fresh000
Picked101
Done000
Total39443
Accuracy
100.0%
Counts
43 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 x x)
▶99.5%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
▶53.8%
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
▶99.3%
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify12.0ms (0.8%)

Memory
-45.9MiB live, 5.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
cost-diff0
(hypot.f64 x x)
cost-diff0
(*.f64 #s(literal 2 binary64) x)
cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
cost-diff0
(sqrt.f64 x)
cost-diff0
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal 2 binary64))
cost-diff3
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff0
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01654
02551
13351
23451
03451
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
x
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(hypot.f64 x x)
x
Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(hypot.f64 x x)
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 x x)
x
#s(literal 2 binary64)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(sqrt.f64 x)
x
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(hypot.f64 x x)
x

localize40.0ms (2.8%)

Memory
11.6MiB live, 48.4MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.015625
(hypot.f64 x x)
accuracy0.0
(*.f64 #s(literal 2 binary64) x)
accuracy0.0
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy0.0
(sqrt.f64 x)
accuracy0.3287887695368841
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
accuracy0.0
(*.f64 x x)
accuracy0.01171875
(*.f64 (*.f64 x x) #s(literal 2 binary64))
accuracy29.533043388199705
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
accuracy0.0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.0
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy0.4609375
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
Samples
31.0ms256×0valid
Compiler

Compiled 61 to 14 computations (77% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-mult: 11.0ms (49.8% of total)
ival-sqrt: 6.0ms (27.2% of total)
ival-hypot: 4.0ms (18.1% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.4%)

Memory
12.1MiB live, 12.1MiB allocated
Counts
11 → 10
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(hypot.f64 x x)
Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))
1.0ms
x
@inf
((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))
1.0ms
x
@0
((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))

simplify132.0ms (9.2%)

Memory
-4.4MiB live, 33.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02246
15046
213646
326346
449146
585146
6120046
7132846
8139046
9142946
10161346
11191546
12196346
13199146
14200346
15200346
16223746
17242146
18373446
19385046
20387446
21388246
22388646
23389046
24400246
25405046
26405046
27426046
0426046
Stop Event
1×iter limit
1×saturated
Counts
10 → 10
Calls
Call 1
Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(sqrt x)
(sqrt.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 x)))

rewrite30.0ms (2.1%)

Memory
-4.3MiB live, 32.4MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01647
02540
15338
020338
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
11 → 83
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(hypot.f64 x x)
Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x (*.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) (-.f64 x x))
(+.f64 x x)
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))

eval6.0ms (0.4%)

Memory
11.9MiB live, 11.9MiB allocated
Compiler

Compiled 584 to 173 computations (70.4% saved)

prune3.0ms (0.2%)

Memory
6.9MiB live, 6.9MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New61263
Fresh000
Picked134
Done000
Total62567
Accuracy
100.0%
Counts
67 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
▶99.5%
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓53.8%
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
✓99.3%
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶99.1%
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
Compiler

Compiled 45 to 31 computations (31.1% saved)

simplify3.0ms (0.2%)

Memory
2.7MiB live, 2.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x x)
cost-diff0
(sqrt.f64 (+.f64 x x))
cost-diff0
(sqrt.f64 x)
cost-diff0
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
cost-diff0
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
cost-diff0
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
cost-diff3
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01554
02346
13243
24043
04040
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)

localize219.0ms (15.3%)

Memory
-4.4MiB live, 40.4MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x x)
accuracy0.0
(sqrt.f64 (+.f64 x x))
accuracy0.0
(sqrt.f64 x)
accuracy0.3287887695368841
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy0.0
(log.f64 #s(literal 2 binary64))
accuracy0.0
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy0.4609375
(*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy1.0
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
Samples
210.0ms256×0valid
Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-mult: 9.0ms (37.9% of total)
ival-hypot: 5.0ms (21.1% of total)
ival-exp: 3.0ms (12.6% of total)
ival-log: 3.0ms (12.6% of total)
ival-sqrt: 3.0ms (12.6% of total)
ival-add: 1.0ms (4.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.2%)

Memory
6.7MiB live, 6.7MiB allocated
Counts
9 → 8
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(log.f64 #s(literal 2 binary64))
Outputs
(* x (sqrt 2))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (log 2))
1.0ms
x
@inf
((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (log 2))
1.0ms
x
@0
((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (log 2))

simplify91.0ms (6.3%)

Memory
-15.4MiB live, 60.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02038
14638
213038
325738
449238
585138
6119638
7132438
8138338
9140838
10152938
11180838
12184838
13187638
14188838
15188838
16217238
17227638
18306138
19346438
20347638
0347638
Stop Event
1×iter limit
1×saturated
Counts
8 → 8
Calls
Call 1
Inputs
(* x (sqrt 2))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 x (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -2 binary64)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 x)))

rewrite28.0ms (1.9%)

Memory
3.9MiB live, 43.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01550
02339
15234
026131
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
9 → 71
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(log.f64 #s(literal 2 binary64))
Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (hypot.f64 x x) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (hypot.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 x x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (hypot.f64 x x) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (hypot.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 x x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (*.f64 x #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (*.f64 x (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(+.f64 (*.f64 x x) (*.f64 x x))
(+.f64 x x)
(log.f64 #s(literal 2 binary64))

eval6.0ms (0.4%)

Memory
12.9MiB live, 12.9MiB allocated
Compiler

Compiled 682 to 192 computations (71.8% saved)

prune10.0ms (0.7%)

Memory
-33.7MiB live, 10.0MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New61061
Fresh000
Picked022
Done033
Total61566
Accuracy
100.0%
Counts
66 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓99.5%
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓53.8%
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
✓99.3%
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓99.1%
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
Compiler

Compiled 105 to 58 computations (44.8% saved)

regimes10.0ms (0.7%)

Memory
12.5MiB live, 12.6MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
Outputs
(hypot.f64 x x)
Calls

4 calls:

3.0ms
x
2.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
2.0ms
(*.f64 x x)
2.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
100.0%1(+.f64 (*.f64 x x) (*.f64 x x))
100.0%1(*.f64 x x)
Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes8.0ms (0.5%)

Memory
17.2MiB live, 17.2MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
Outputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Calls

4 calls:

2.0ms
x
2.0ms
(*.f64 x x)
2.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
2.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
99.5%1(+.f64 (*.f64 x x) (*.f64 x x))
99.5%1(*.f64 x x)
Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes7.0ms (0.5%)

Memory
-24.5MiB live, 14.1MiB allocated
Accuracy

Total -29.3b remaining (-6360%)

Threshold costs -29.3b (-6360%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Calls

4 calls:

3.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
2.0ms
x
1.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
99.3%1x
99.3%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
99.3%1(+.f64 (*.f64 x x) (*.f64 x x))
99.3%1(*.f64 x x)
Compiler

Compiled 19 to 10 computations (47.4% saved)

simplify8.0ms (0.6%)

Memory
28.0MiB live, 28.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
11621
21921
32221
Stop Event
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Outputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

soundness45.0ms (3.1%)

Memory
-0.2MiB live, 39.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0418
0714
12310
01609
0817
11517
23217
33817
44217
55417
66617
77717
89717
910217
010217
01647
02540
15338
020338
Stop Event
1×done
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
1×iter limit
1×saturated
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Compiler

Compiled 67 to 40 computations (40.3% saved)

preprocess25.0ms (1.8%)

Memory
-3.3MiB live, 33.9MiB allocated
Remove

(abs x)

Compiler

Compiled 68 to 38 computations (44.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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