Linear.Quaternion:$clog from linear-1.19.1.3

Time bar (total: 10.5s)

start0.0ms (0%)

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

analyze18.0ms (0.2%)

Memory
23.1MiB live, 23.1MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
50%50%50%0.1%0%0%0%3
50%50%50%0.1%0%0%0%4
62.5%62.4%37.5%0.1%0%0%0%5
66.7%62.4%31.2%0.1%0%6.2%0%6
75%65.6%21.9%0.1%0%12.5%0%7
80%68.7%17.2%0.1%0%14%0%8
85.7%70.2%11.7%0.1%0%18%0%9
88.9%71.8%9%0.1%0%19.1%0%10
92.3%72.6%6%0.1%0%21.3%0%11
94.1%73.4%4.6%0.1%0%22%0%12
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.0s (9.9%)

Memory
15.6MiB live, 910.9MiB allocated; 344ms collecting garbage
Samples
755.0ms8 256×0valid
14.0ms324×0invalid
Precisions
Click to see histograms. Total time spent on operations: 264.0ms
ival-sqrt: 110.0ms (41.6% of total)
ival-mult!: 91.0ms (34.4% of total)
ival-add!: 61.0ms (23.1% of total)
adjust: 2.0ms (0.8% of total)
Bogosity

preprocess239.0ms (2.3%)

Memory
-51.0MiB live, 64.9MiB allocated; 178ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01738
15138
214138
330438
476438
5358138
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series182.0ms (1.7%)

Memory
6.2MiB live, 155.2MiB allocated; 24ms collecting garbage
Counts
5 → 30
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (+.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx x x)
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (+ (* x x) y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 y (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (+ (* x x) y) (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (+ (* x x) y) (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y)) #s(literal 1 binary64)))))
Calls

6 calls:

TimeVariablePoint
1.0ms
x
inf
1.0ms
x
-inf
1.0ms
y
inf
1.0ms
y
-inf
1.0ms
x
0

rewrite206.0ms (2%)

Memory
-0.7MiB live, 226.5MiB allocated; 71ms collecting garbage
Counts
5 → 15
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
Outputs
(fabs.f64 (sqrt.f64 (fma.f64 x x y)))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(sqrt.f64 (fma.f64 x x y))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(-.f64 (*.f64 x x) (neg.f64 y))
(fma.f64 x x y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 (fabs.f64 x) (fabs.f64 x) y)
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(pow.f64 x #s(literal 2 binary64))
x
y

eval4.0ms (0%)

Memory
8.8MiB live, 8.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 849 to 179 computations (78.9% saved)

prune4.0ms (0%)

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New35641
Fresh000
Picked101
Done000
Total36642
Accuracy
100.0%
Counts
42 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.7%
(sqrt.f64 (fma.f64 x x y))
30.3%
(sqrt.f64 #s(approx (+ (* x x) y) y))
30.1%
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
72.9%
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
0.8%
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
1.1%
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
Compiler

Compiled 148 to 116 computations (21.6% saved)

series872.0ms (8.3%)

Memory
278.4MiB live, 371.5MiB allocated; 287ms collecting garbage
Counts
22 → 46
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
x
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(literal 1/2 binary64)
(/.f64 y (pow.f64 x #s(literal 2 binary64)))
y
(pow.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) x))
#s(approx x x)
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (/ y (pow x 2)) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (pow x 2) (pow.f64 x #s(literal 2 binary64)))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (+.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (* -1 x) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (+ (* x x) y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 y (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
#s(approx (sqrt (/ 1 y)) (/.f64 (sqrt.f64 y) y))
#s(approx (/ 1 y) (/.f64 #s(literal 1 binary64) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 x y))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 y (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (+ (* x x) y) (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y))))
#s(approx (sqrt (/ 1 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) y))))
#s(approx (+ (* x x) y) (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y)) #s(literal 1 binary64)))))
Calls

6 calls:

TimeVariablePoint
5.0ms
y
inf
5.0ms
y
-inf
2.0ms
x
0
2.0ms
y
0
1.0ms
x
-inf

rewrite935.0ms (8.9%)

Memory
0.2MiB live, 370.3MiB allocated; 812ms collecting garbage
Counts
22 → 552
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
x
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(literal 1/2 binary64)
(/.f64 y (pow.f64 x #s(literal 2 binary64)))
y
(pow.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
Outputs
#s(approx (sqrt (+ (* x x) y)) (+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x)))
(*.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 (*.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) x)
(*.f64 (+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(*.f64 x (*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x)))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(+.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)) x)
(+.f64 x (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)) (neg.f64 x))
(-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal -1/2 binary64)) x) (*.f64 x x)))
(/.f64 (*.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x) (*.f64 x x))
(/.f64 (*.f64 x (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 x x))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x #s(literal 1/2 binary64)) y)) (*.f64 x x))
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 x (*.f64 x x)) x)
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) (/.f64 x #s(literal 1 binary64)) x)
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) x x)
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (fabs.f64 x)) (/.f64 x (fabs.f64 x)) x)
(fma.f64 (/.f64 x (*.f64 x x)) (/.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (/.f64 x (neg.f64 x)) (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x)
(fma.f64 (/.f64 x (fabs.f64 x)) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (fabs.f64 x)) x)
(fma.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (neg.f64 y)) (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)
(fma.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) y x)
(fma.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) x)) (/.f64 y x) x)
(fma.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(fma.f64 (/.f64 y (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 x #s(literal -1 binary64)) x)
(fma.f64 (*.f64 x (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (/.f64 y x)) x)
(fma.f64 (/.f64 (*.f64 y x) (*.f64 x x)) #s(literal 1/2 binary64) x)
(fma.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) (/.f64 x (neg.f64 x)) x)
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) x) (/.f64 x x) x)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y x) (*.f64 x x)) x)
(fma.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) x)
(fma.f64 y (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) x)
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 y (*.f64 x x)) x)
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 x (*.f64 x x)) x)
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) x)
(fma.f64 (*.f64 x y) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (*.f64 y #s(literal -1/2 binary64)) (*.f64 x x)) x)
(fma.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) x)
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (/.f64 y x) x) x)
(fma.f64 (/.f64 x x) (/.f64 (*.f64 y #s(literal 1/2 binary64)) x) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) x)
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(fma.f64 x #s(literal 1 binary64) (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(fma.f64 #s(literal 1 binary64) x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (neg.f64 (fabs.f64 x))) (/.f64 x (neg.f64 (fabs.f64 x))) x)
(fma.f64 (/.f64 x (neg.f64 (*.f64 x x))) (/.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) x)
(fma.f64 (/.f64 x (neg.f64 (fabs.f64 x))) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (neg.f64 (fabs.f64 x))) x)
(fma.f64 (*.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64)) x x)
(fma.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) (fabs.f64 x))) (/.f64 y (fabs.f64 x)) x)
(fma.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)) #s(literal 1 binary64) x)
(fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (/.f64 x (neg.f64 (*.f64 x x))) x)
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 (neg.f64 (/.f64 y x)) x) x)
(fma.f64 (/.f64 #s(literal 1/2 binary64) (fabs.f64 x)) (*.f64 (/.f64 y (fabs.f64 x)) x) x)
(fma.f64 y (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x) x)
(fma.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x))) x)
(fma.f64 (neg.f64 y) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) x)
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)) x)
(fma.f64 #s(literal 1 binary64) x (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)))
(fma.f64 x #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) y) (*.f64 x x)))
(neg.f64 (*.f64 x (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(neg.f64 (*.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))
(neg.f64 (-.f64 (/.f64 (*.f64 (*.f64 y #s(literal -1/2 binary64)) x) (*.f64 x x)) x))
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 (neg.f64 x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 x))
(+.f64 x (*.f64 #s(literal 0 binary64) x))
(+.f64 x (*.f64 x #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (*.f64 #s(literal 0 binary64) x))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (*.f64 x #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 x #s(literal 0 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 x #s(literal 0 binary64)))
(neg.f64 (neg.f64 x))
(*.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)))
(+.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64))
(+.f64 (/.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)))
(+.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 y #s(literal -1/2 binary64)) (*.f64 x x))))
(+.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 x x))
(/.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (fma.f64 (neg.f64 x) x (*.f64 y #s(literal -1/2 binary64))) (neg.f64 (*.f64 x x)))
(/.f64 (+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x)) x)
(/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) (*.f64 #s(literal 2 binary64) (*.f64 y #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) (*.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(/.f64 (+.f64 (neg.f64 x) (/.f64 (*.f64 y #s(literal -1/2 binary64)) x)) (neg.f64 x))
(/.f64 (+.f64 (fabs.f64 x) (/.f64 (*.f64 y #s(literal 1/2 binary64)) (fabs.f64 x))) (fabs.f64 x))
(/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 #s(literal 2 binary64) (*.f64 y #s(literal -1/2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 (-.f64 (neg.f64 (*.f64 x x)) (*.f64 y #s(literal 1/2 binary64))) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) (neg.f64 (*.f64 x x))) #s(literal -1 binary64))
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) (neg.f64 (fabs.f64 x))) (neg.f64 (fabs.f64 x)))
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x) x)
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (fabs.f64 x)) #s(literal 2 binary64) (*.f64 (fabs.f64 x) #s(literal 2 binary64))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) (fabs.f64 x)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) #s(literal 2 binary64) (*.f64 (neg.f64 x) #s(literal 2 binary64))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) x) #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (*.f64 y #s(literal 1/2 binary64)) x) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) (*.f64 x #s(literal 2 binary64)))
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(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (/.f64 #s(literal 0 binary64) y))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) y))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(pow.f64 y #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))

eval79.0ms (0.8%)

Memory
0.1MiB live, 185.5MiB allocated; 19ms collecting garbage
Compiler

Compiled 13 400 to 2 885 computations (78.5% saved)

prune17.0ms (0.2%)

Memory
-13.3MiB live, 37.2MiB allocated; 8ms collecting garbage
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New6922694
Fresh011
Picked325
Done000
Total6955700
Accuracy
100.0%
Counts
700 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.7%
(sqrt.f64 (fma.f64 x x y))
30.3%
(sqrt.f64 #s(approx (+ (* x x) y) y))
72.7%
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
0.8%
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
1.1%
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
Compiler

Compiled 62 to 49 computations (21% saved)

series153.0ms (1.4%)

Memory
52.4MiB live, 132.0MiB allocated; 55ms collecting garbage
Counts
18 → 45
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(literal -1 binary64)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(literal 1/2 binary64)
(/.f64 y (pow.f64 x #s(literal 2 binary64)))
y
(pow.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
(*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (neg x) (*.f64 #s(literal -1 binary64) x))
#s(approx x x)
#s(approx (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (*.f64 #s(literal -1/2 binary64) (/.f64 y x)))
#s(approx (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) y)) x))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) x))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (/ y (pow x 2)) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (pow x 2) (pow.f64 x #s(literal 2 binary64)))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 y (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) (/.f64 y x))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
#s(approx y y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 x y))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 y (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 x y)))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) y))))
Calls

6 calls:

TimeVariablePoint
1.0ms
y
-inf
1.0ms
y
inf
1.0ms
x
inf
1.0ms
x
-inf
1.0ms
x
0

rewrite3.7s (35.5%)

Memory
-26.4MiB live, 2 078.2MiB allocated; 1.2s collecting garbage
Counts
18 → 5 415
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(literal -1 binary64)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(literal 1/2 binary64)
(/.f64 y (pow.f64 x #s(literal 2 binary64)))
y
(pow.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
(*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
Outputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(*.f64 x #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 8 binary64)) #s(literal 4 binary64))
(+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(+.f64 (neg.f64 x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(-.f64 (neg.f64 x) #s(literal 0 binary64))
(/.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 x x) #s(literal -2 binary64))
(/.f64 (neg.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) #s(literal -4 binary64))
(/.f64 (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))
(/.f64 (*.f64 (+.f64 x x) #s(literal -2 binary64)) #s(literal 4 binary64))
(/.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64)) #s(literal -4 binary64))
(/.f64 (*.f64 #s(literal -2 binary64) (+.f64 x x)) #s(literal 4 binary64))
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 x #s(literal -2 binary64))) #s(literal -4 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal -2 binary64))) #s(literal 4 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)) #s(literal -4 binary64))
(/.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(fma.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (+.f64 x x) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (+.f64 y y) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 x) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (/.f64 #s(literal 0 binary64) #s(literal 8 binary64)) #s(literal 4 binary64) (neg.f64 x))
(fma.f64 (/.f64 #s(literal -2 binary64) x) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 0 binary64) (neg.f64 x))
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 x) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))
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(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 x x) (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (fabs.f64 x))) #s(literal 0 binary64) #s(literal 2 binary64))
(fma.f64 (/.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x))) (/.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x))) #s(literal 1 binary64))
(fma.f64 (/.f64 (fabs.f64 x) (neg.f64 (*.f64 x x))) (/.f64 (fabs.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x))) (/.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x))) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) x) (/.f64 (neg.f64 (fabs.f64 x)) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) (neg.f64 x)) (/.f64 (neg.f64 (fabs.f64 x)) (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) #s(literal -1 binary64)) (/.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (*.f64 x x))) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (*.f64 x x))) (/.f64 (neg.f64 (fabs.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 x x) (neg.f64 (fabs.f64 x))) (/.f64 #s(literal -1 binary64) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (*.f64 x x)) (fabs.f64 x)) (/.f64 #s(literal -1 binary64) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (fabs.f64 x))) (/.f64 #s(literal 1 binary64) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (*.f64 x x)) x) (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (*.f64 x x)) (neg.f64 x)) (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (fabs.f64 x)) (*.f64 x x)) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 x x) (neg.f64 (*.f64 x x))) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 (*.f64 x x)) (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (*.f64 x x))) #s(literal 0 binary64) #s(literal 2 binary64))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x x) x)) #s(literal 2 binary64) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (/.f64 (neg.f64 (fabs.f64 x)) (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 x)) (/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (fabs.f64 x))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (neg.f64 (*.f64 x x)) (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (neg.f64 (*.f64 x x)) x) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (fabs.f64 x)) (/.f64 (*.f64 x x) (neg.f64 (fabs.f64 x))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (fabs.f64 x)) (/.f64 (neg.f64 (*.f64 x x)) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (fabs.f64 x) #s(literal -1 binary64)) (/.f64 (fabs.f64 x) (neg.f64 (*.f64 x x))) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (neg.f64 (*.f64 x x))) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (*.f64 x x)) (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (neg.f64 (fabs.f64 x))) #s(literal 2 binary64))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (neg.f64 (*.f64 x x))) #s(literal 2 binary64))
(hypot.f64 #s(literal -2 binary64) #s(literal 0 binary64))
(hypot.f64 #s(literal 2 binary64) #s(literal 0 binary64))
(hypot.f64 #s(literal 0 binary64) #s(literal -2 binary64))
(hypot.f64 #s(literal 0 binary64) #s(literal 2 binary64))
(neg.f64 #s(literal -2 binary64))
(sqrt.f64 #s(literal 4 binary64))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ (/ y (* 2 (* x x))) 1) #s(literal 1 binary64))))
(*.f64 x #s(approx (+ (/ y (* 2 (* x x))) 1) #s(literal 1 binary64)))
#s(approx (+ (/ y (* 2 (* x x))) 1) #s(literal 1 binary64))

eval2.2s (20.7%)

Memory
62.6MiB live, 1 585.6MiB allocated; 579ms collecting garbage
Compiler

Compiled 158 183 to 27 866 computations (82.4% saved)

prune121.0ms (1.1%)

Memory
10.1MiB live, 255.5MiB allocated; 39ms collecting garbage
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New5 95615 957
Fresh000
Picked123
Done022
Total5 95755 962
Accuracy
100.0%
Counts
5 962 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.7%
(sqrt.f64 (fma.f64 x x y))
30.3%
(sqrt.f64 #s(approx (+ (* x x) y) y))
0.8%
#s(approx (sqrt (+ (* x x) y)) (-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x))
72.7%
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
1.1%
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
Compiler

Compiled 56 to 43 computations (23.2% saved)

series189.0ms (1.8%)

Memory
-14.7MiB live, 77.0MiB allocated; 41ms collecting garbage
Counts
7 → 32
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x))
(-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x)
(/.f64 (*.f64 y #s(literal -1/2 binary64)) x)
(*.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
x
Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (- (/ (* y -1/2) x) x) (*.f64 #s(literal -1/2 binary64) (/.f64 y x)))
#s(approx (- (/ (* y -1/2) x) x) (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) y)) x))
#s(approx x x)
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (- (/ (* y -1/2) x) x) (*.f64 #s(literal -1 binary64) x))
#s(approx (- (/ (* y -1/2) x) x) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 y (fma.f64 y (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (- (/ (* y -1/2) x) x) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) x))
#s(approx (* y -1/2) (*.f64 #s(literal -1/2 binary64) y))
#s(approx y y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (- (/ (* y -1/2) x) x) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (- (/ (* y -1/2) x) x) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 x y)))))
Calls

6 calls:

TimeVariablePoint
1.0ms
y
inf
1.0ms
y
-inf
1.0ms
y
0
1.0ms
x
inf
1.0ms
x
-inf

rewrite228.0ms (2.2%)

Memory
43.2MiB live, 87.2MiB allocated; 11ms collecting garbage
Counts
7 → 15
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x))
(-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x)
(/.f64 (*.f64 y #s(literal -1/2 binary64)) x)
(*.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
x
Outputs
#s(approx (sqrt (+ (* x x) y)) (-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x))
(+.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) (neg.f64 x))
(-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x)
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x) (neg.f64 x))
(fma.f64 y (/.f64 #s(literal -1/2 binary64) x) (neg.f64 x))
(neg.f64 (-.f64 x (/.f64 (*.f64 y #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 y (/.f64 #s(literal -1/2 binary64) x))
(/.f64 (*.f64 y #s(literal -1/2 binary64)) x)
(/.f64 (neg.f64 (*.f64 y #s(literal -1/2 binary64))) (neg.f64 x))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) y)
y
#s(literal -1/2 binary64)
x

eval5.0ms (0%)

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

Compiled 1 012 to 203 computations (79.9% saved)

prune63.0ms (0.6%)

Memory
-67.2MiB live, 3.6MiB allocated; 75ms collecting garbage
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New40040
Fresh000
Picked011
Done044
Total40545
Accuracy
100.0%
Counts
45 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.7%
(sqrt.f64 (fma.f64 x x y))
30.3%
(sqrt.f64 #s(approx (+ (* x x) y) y))
0.8%
#s(approx (sqrt (+ (* x x) y)) (-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x))
72.7%
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
1.1%
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
Compiler

Compiled 56 to 43 computations (23.2% saved)

regimes97.0ms (0.9%)

Memory
27.3MiB live, 77.8MiB allocated; 10ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
3 → 1
4 → 2
10 → 2
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
Outputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
Call 2
Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
Outputs
(sqrt.f64 #s(approx (+ (* x x) y) y))
Call 3
Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
Outputs
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
Call 4
Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 x x) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
Outputs
(sqrt.f64 (fma.f64 x x y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x #s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
Calls

19 calls:

7.0ms
(+.f64 (*.f64 x x) y)
7.0ms
(sqrt.f64 (+.f64 (*.f64 x x) y))
6.0ms
(+.f64 (*.f64 x x) y)
5.0ms
(*.f64 x x)
4.0ms
y
Results
AccuracySegmentsBranch
1.1%1(*.f64 x x)
1.1%1(+.f64 (*.f64 x x) y)
1.1%1(sqrt.f64 (+.f64 (*.f64 x x) y))
1.1%1y
1.1%1x
30.3%1(+.f64 (*.f64 x x) y)
30.3%1(sqrt.f64 (+.f64 (*.f64 x x) y))
30.3%1y
30.3%1(*.f64 x x)
30.3%1x
92.0%2(*.f64 x x)
77.1%2(+.f64 (*.f64 x x) y)
77.1%2(sqrt.f64 (+.f64 (*.f64 x x) y))
92.0%2x
100.0%2(*.f64 x x)
100.0%2(+.f64 (*.f64 x x) y)
100.0%2(sqrt.f64 (+.f64 (*.f64 x x) y))
100.0%2x
78.7%2y
Compiler

Compiled 186 to 109 computations (41.4% saved)

bsearch2.0ms (0%)

Memory
2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
predicate-same
Steps
TimeLeftRight
1.0ms
4.3956833131040795e+113
9.643998643871816e+117
Samples
1.0ms16×0valid
0.0ms0invalid
Compiler

Compiled 34 to 32 computations (5.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0% of total)
ival-add!: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
ival-mult!: 0.0ms (0% of total)

bsearch52.0ms (0.5%)

Memory
11.4MiB live, 11.4MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
50.0ms
9.050636018726025e-40
5.839729262176638e-38
Samples
43.0ms112×0valid
1.0ms31×0invalid
Compiler

Compiled 205 to 178 computations (13.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sqrt: 1.0ms (37.5% of total)
ival-mult!: 1.0ms (37.5% of total)
adjust: 0.0ms (0% of total)
ival-add!: 0.0ms (0% of total)

derivations11.0ms (0.1%)

Memory
-44.5MiB live, 2.2MiB allocated; 15ms collecting garbage
Stop Event
done
Compiler

Compiled 78 to 28 computations (64.1% saved)

preprocess94.0ms (0.9%)

Memory
3.3MiB live, 48.6MiB allocated; 8ms collecting garbage
Remove

(abs x)

Compiler

Compiled 240 to 143 computations (40.4% saved)

end0.0ms (0%)

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

Profiling

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