sqrt A (should all be same)

Time bar (total: 1.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB 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)

sample583.0ms (39.5%)

Memory
16.3MiB live, 599.1MiB allocated
Samples
324.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 185.0ms
ival-hypot: 176.0ms (95.2% of total)
ival-true: 6.0ms (3.2% of total)
ival-assert: 3.0ms (1.6% of total)
Bogosity

explain81.0ms (5.5%)

Memory
2.1MiB live, 83.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1300-2(-8.753556152764356e-162)(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-rescue740
↳(+.f64 (*.f64 x x) (*.f64 x x))underflow74
↳(*.f64 x x)underflow148
sqrt.f64(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))oflow-rescue540
↳(+.f64 (*.f64 x x) (*.f64 x x))overflow54
↳(*.f64 x x)overflow108
Confusion
Predicted +Predicted -
+1282
-0126
Precision
1.0
Recall
0.9846153846153847
Confusion?
Predicted +Predicted MaybePredicted -
+12802
-00126
Precision?
1.0
Recall?
0.9846153846153847
Freqs
test
numberfreq
0128
1128
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 (60% of total)
ival-mult: 4.0ms (26.7% of total)
ival-add: 2.0ms (13.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess15.0ms (1%)

Memory
13.4MiB live, 13.4MiB 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)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.9%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Compiler

Compiled 8 to 4 computations (50% saved)

simplify3.0ms (0.2%)

Memory
2.6MiB live, 2.6MiB 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

localize24.0ms (1.6%)

Memory
-8.7MiB live, 26.1MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.0078125
(+.f64 (*.f64 x x) (*.f64 x x))
accuracy30.134261068782713
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Samples
19.0ms256×0valid
Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-hypot: 4.0ms (49.2% of total)
ival-mult: 2.0ms (24.6% of total)
ival-add: 1.0ms (12.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.2%)

Memory
4.8MiB live, 4.8MiB 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
1.0ms
x
@inf
((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms
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))

simplify4.0ms (0.3%)

Memory
4.2MiB live, 4.2MiB 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)))

rewrite31.0ms (2.1%)

Memory
4.5MiB live, 39.5MiB 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
7.3MiB live, 7.3MiB allocated
Compiler

Compiled 370 to 110 computations (70.3% saved)

prune2.0ms (0.1%)

Memory
4.3MiB live, 4.3MiB 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)
▶99.3%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
▶52.9%
(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)

simplify3.0ms (0.2%)

Memory
4.6MiB live, 4.6MiB 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

localize45.0ms (3.1%)

Memory
-28.6MiB live, 54.5MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(hypot.f64 x x)
accuracy0.0
(*.f64 #s(literal 2 binary64) x)
accuracy0.0
(sqrt.f64 x)
accuracy0.2382803181639217
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy0.28125
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
accuracy0.0
(*.f64 x x)
accuracy0.0078125
(*.f64 (*.f64 x x) #s(literal 2 binary64))
accuracy30.134261068782713
(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))
accuracy0.4296875
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
Samples
35.0ms256×0valid
Compiler

Compiled 61 to 14 computations (77% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-mult: 12.0ms (52.4% of total)
ival-sqrt: 6.0ms (26.2% of total)
ival-hypot: 4.0ms (17.5% 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
11.1MiB live, 11.1MiB 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))))

simplify130.0ms (8.8%)

Memory
5.0MiB live, 41.8MiB 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)))

rewrite28.0ms (1.9%)

Memory
-7.4MiB live, 29.6MiB 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
19.5MiB live, 19.5MiB allocated
Compiler

Compiled 584 to 173 computations (70.4% saved)

prune29.0ms (2%)

Memory
-25.2MiB live, 26.9MiB allocated
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New60363
Fresh000
Picked134
Done000
Total61667
Accuracy
100.0%
Counts
67 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
▶99.2%
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶99.3%
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓52.9%
(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 53 to 37 computations (30.2% saved)

simplify5.0ms (0.3%)

Memory
14.5MiB live, 14.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 x)
cost-diff4
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
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
01873
02963
14258
25258
36758
49358
59758
69958
09955
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)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 x)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
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)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 x)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize47.0ms (3.2%)

Memory
-16.7MiB live, 59.8MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sqrt.f64 x)
accuracy0.0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.28125
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy0.4316788086106522
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy0.0
(+.f64 x x)
accuracy0.0
(sqrt.f64 x)
accuracy0.2382803181639217
(sqrt.f64 (+.f64 x x))
accuracy0.28125
(*.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))
accuracy0.4296875
(*.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
35.0ms256×0valid
Compiler

Compiled 67 to 17 computations (74.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-mult: 7.0ms (30.8% of total)
ival-hypot: 4.0ms (17.6% of total)
ival-sqrt: 4.0ms (17.6% of total)
ival-log: 3.0ms (13.2% of total)
ival-exp: 2.0ms (8.8% of total)
ival-add: 1.0ms (4.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.3%)

Memory
8.2MiB live, 8.2MiB allocated
Counts
12 → 10
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)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(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))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
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) (* (sqrt x) (* (sqrt x) (sqrt 2))) (* (sqrt x) (sqrt 2)) (sqrt 2) (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) (* (sqrt x) (* (sqrt x) (sqrt 2))) (* (sqrt x) (sqrt 2)) (sqrt 2) (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) (* (sqrt x) (* (sqrt x) (sqrt 2))) (* (sqrt x) (sqrt 2)) (sqrt 2) (log 2))

simplify73.0ms (4.9%)

Memory
9.9MiB live, 48.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02547
16347
221047
343547
4100247
5161347
6192247
7195947
8197047
9197947
10198147
11200147
12200947
13200947
14206147
15244547
16245347
0245347
Stop Event
1×iter limit
1×saturated
Counts
10 → 10
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))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))
Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt x)
(sqrt.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 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 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite34.0ms (2.3%)

Memory
-1.0MiB live, 46.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01865
02946
16744
028237
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
12 → 117
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)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(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))) (hypot.f64 x x))
(*.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 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #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 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.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 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #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 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(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 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #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 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 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 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 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 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 1 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 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 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 4 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 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.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)
(*.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 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #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 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 x #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 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #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 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 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 (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))))
(log.f64 #s(literal 2 binary64))

eval11.0ms (0.8%)

Memory
-21.4MiB live, 16.5MiB allocated
Compiler

Compiled 916 to 218 computations (76.2% saved)

prune4.0ms (0.3%)

Memory
10.8MiB live, 10.8MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New71071
Fresh000
Picked033
Done033
Total71677
Accuracy
100.0%
Counts
77 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓99.2%
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓99.3%
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓52.9%
(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 121 to 66 computations (45.5% saved)

regimes13.0ms (0.9%)

Memory
-15.6MiB live, 22.8MiB allocated
Counts
8 → 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)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(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:

4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
3.0ms
x
3.0ms
(*.f64 x x)
3.0ms
(+.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)

regimes9.0ms (0.6%)

Memory
19.7MiB live, 19.7MiB allocated
Accuracy

Total -30.1b remaining (-6998%)

Threshold costs -30.1b (-6998%)

Counts
6 → 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)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Calls

4 calls:

2.0ms
x
2.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
2.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
2.0ms
(*.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)

simplify10.0ms (0.7%)

Memory
-23.3MiB live, 16.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11214
21514
31814
Stop Event
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Outputs
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

soundness23.0ms (1.6%)

Memory
20.9MiB live, 20.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

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

Compiled 31 to 18 computations (41.9% saved)

preprocess246.0ms (16.7%)

Memory
-17.7MiB live, 22.6MiB allocated
Remove

(abs x)

Compiler

Compiled 54 to 30 computations (44.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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