sqrt C (should all be same)

Time bar (total: 1.4s)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%100%0%0%0%0%0%2
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.1s (76%)

Memory
-43.8MiB live, 841.6MiB allocated; 1.0s collecting garbage
Samples
829.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 189.0ms
ival-mult!: 102.0ms (53.8% of total)
ival-sqrt: 86.0ms (45.4% of total)
adjust: 1.0ms (0.5% of total)
Bogosity

preprocess76.0ms (5.4%)

Memory
-22.4MiB live, 23.0MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01019
13319
210519
321319
478019
5403919
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
52.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series3.0ms (0.2%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Counts
5 → 5
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x
Outputs
#s(approx (sqrt (* 2 (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* 2 (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* 2 (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
Calls

3 calls:

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

rewrite34.0ms (2.4%)

Memory
0.4MiB live, 47.2MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01961
02260
15057
017951
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
10 → 94
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x
#s(approx (sqrt (* 2 (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* 2 (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* 2 (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
Outputs
(*.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (pow.f64 (+.f64 x x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (fabs.f64 x)) x)
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (fabs.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (fabs.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (fabs.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) (neg.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 (neg.f64 x) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (fabs.f64 x)))
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x x) x)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (+.f64 x x) x)
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (+.f64 (fabs.f64 x) (fabs.f64 x)))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x (+.f64 x x))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 x x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) (pow.f64 (*.f64 x x) #s(literal 3 binary64))) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (*.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 x x (*.f64 x x))
(-.f64 (*.f64 x x) (*.f64 x (neg.f64 x)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 x x))
#s(literal 2 binary64)
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.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 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
x
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* 2 (* x x)) (*.f64 (+.f64 x x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval8.0ms (0.6%)

Memory
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 728 to 200 computations (72.5% saved)

prune4.0ms (0.3%)

Memory
8.4MiB live, 8.4MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New85590
Fresh000
Picked101
Done000
Total86591
Accuracy
100.0%
Counts
91 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
99.5%
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
52.9%
(sqrt.f64 (*.f64 (+.f64 x x) x))
99.3%
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
2.2%
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 78 to 60 computations (23.1% saved)

series7.0ms (0.5%)

Memory
9.4MiB live, 9.4MiB allocated; 0ms collecting garbage
Counts
15 → 14
Calls
Call 1
Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (* 2 (* 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)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(sqrt.f64 x)
Outputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#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 x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@inf
((sqrt (+ (* x x) (* x x))) x (sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* 2 (* x x))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))
2.0ms
x
@-inf
((sqrt (+ (* x x) (* x x))) x (sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* 2 (* x x))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))
2.0ms
x
@0
((sqrt (+ (* x x) (* x x))) x (sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* 2 (* x x))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

rewrite63.0ms (4.5%)

Memory
8.2MiB live, 54.6MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
062209
076162
1165102
0659102
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
29 → 175
Calls
Call 1
Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (* 2 (* 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)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(sqrt.f64 x)
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#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 x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
x
#s(approx (* (sqrt (+ x x)) (sqrt 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)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #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)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
#s(approx (* (sqrt (+ x x)) (sqrt x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(neg.f64 (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 x) (sqrt.f64 x))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) x)))
(neg.f64 (*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) x))
(neg.f64 x)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
#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)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #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)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #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)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx x x)
#s(approx (* (neg x) (sqrt 2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
#s(approx (neg x) (neg.f64 x))
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt x) (*.f64 #s(literal 1 binary64) x))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt x) (neg.f64 x))

eval15.0ms (1.1%)

Memory
-47.6MiB live, 8.6MiB allocated; 6ms collecting garbage
Compiler

Compiled 532 to 145 computations (72.7% saved)

prune3.0ms (0.2%)

Memory
3.6MiB live, 3.6MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New53154
Fresh000
Picked055
Done000
Total53659
Accuracy
100.0%
Counts
59 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
99.5%
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
52.9%
(sqrt.f64 (*.f64 (+.f64 x x) x))
5.3%
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
99.3%
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
2.2%
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 45 to 35 computations (22.2% saved)

series1.0ms (0.1%)

Memory
1.1MiB live, 1.1MiB allocated; 0ms collecting garbage
Counts
3 → 4
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
#s(approx (+ x x) #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
((sqrt (+ x x)) (+ x x) 2)
0.0ms
x
@inf
((sqrt (+ x x)) (+ x x) 2)
0.0ms
x
@0
((sqrt (+ x x)) (+ x x) 2)

rewrite30.0ms (2.2%)

Memory
11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01752
01849
15035
021135
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
7 → 10
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
#s(approx (+ x x) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
Outputs
(*.f64 (pow.f64 #s(approx (+ x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (+ x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (+ x x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ x x) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ x x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
#s(approx (sqrt (+ x x)) (*.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))

eval1.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 61 to 22 computations (63.9% saved)

prune2.0ms (0.1%)

Memory
1.5MiB live, 1.5MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New606
Fresh000
Picked011
Done055
Total6612
Accuracy
100.0%
Counts
12 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
99.5%
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
52.9%
(sqrt.f64 (*.f64 (+.f64 x x) x))
5.3%
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
99.3%
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
2.2%
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 45 to 35 computations (22.2% saved)

regimes39.0ms (2.8%)

Memory
-2.7MiB live, 44.2MiB allocated; 2ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
5 → 1
6 → 1
7 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
Outputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
Call 2
Inputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
Outputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
Call 3
Inputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
Call 4
Inputs
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(hypot.f64 x x)
Outputs
(hypot.f64 x x)
Calls

16 calls:

10.0ms
(*.f64 x x)
3.0ms
x
2.0ms
x
2.0ms
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
2.0ms
(*.f64 #s(literal 2 binary64) (*.f64 x x))
Results
AccuracySegmentsBranch
5.3%1(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
5.3%1(*.f64 #s(literal 2 binary64) (*.f64 x x))
5.3%1(*.f64 x x)
5.3%1x
99.3%1(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
99.3%1(*.f64 #s(literal 2 binary64) (*.f64 x x))
99.3%1(*.f64 x x)
99.3%1x
99.5%1(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
99.5%1(*.f64 #s(literal 2 binary64) (*.f64 x x))
99.5%1(*.f64 x x)
99.5%1x
100.0%1(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)))
100.0%1(*.f64 #s(literal 2 binary64) (*.f64 x x))
100.0%1(*.f64 x x)
100.0%1x
Compiler

Compiled 111 to 73 computations (34.2% saved)

derivations8.0ms (0.6%)

Memory
8.9MiB live, 8.9MiB allocated; 0ms collecting garbage
Stop Event
done
Compiler

Compiled 27 to 17 computations (37% saved)

preprocess41.0ms (2.9%)

Memory
-19.3MiB live, 68.3MiB allocated; 10ms collecting garbage
Remove

(abs x)

Compiler

Compiled 87 to 64 computations (26.4% saved)

end0.0ms (0%)

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

Profiling

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