Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

Time bar (total: 6.6s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze50.0ms (0.8%)

Memory
-5.8MiB live, 112.6MiB allocated
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
0%0%99.9%0.1%0%0%0%3
50%49.9%49.9%0.1%0%0%0%4
50%49.9%49.9%0.1%0%0%0%5
50%49.9%49.9%0.1%0%0%0%6
66.7%49.9%25%0.1%0%25%0%7
66.7%49.9%25%0.1%0%25%0%8
66.7%49.9%25%0.1%0%25%0%9
80%49.9%12.5%0.1%0%37.4%0%10
80%49.9%12.5%0.1%0%37.4%0%11
80%49.9%12.5%0.1%0%37.4%0%12
Compiler

Compiled 12 to 12 computations (0% saved)

sample1.4s (20.6%)

Memory
36.1MiB live, 1 666.3MiB allocated
Samples
826.0ms8 256×0valid
172.0ms2 129×0invalid
Precisions
Click to see histograms. Total time spent on operations: 574.0ms
ival-mult: 294.0ms (51.2% of total)
ival-sqrt: 108.0ms (18.8% of total)
ival-div: 79.0ms (13.8% of total)
ival-add: 69.0ms (12% of total)
exact: 10.0ms (1.7% of total)
ival-true: 9.0ms (1.6% of total)
ival-assert: 5.0ms (0.9% of total)
Bogosity

explain145.0ms (2.2%)

Memory
-15.4MiB live, 103.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
00-0-z
00-0-(sqrt.f64 z)
00-0-(+.f64 x (*.f64 y (sqrt.f64 z)))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
00-0-y
00-0-#s(literal 2 binary64)
00-0-(*.f64 y (sqrt.f64 z))
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
73.0ms512×0valid
Compiler

Compiled 104 to 44 computations (57.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-sqrt: 43.0ms (76.4% of total)
ival-mult: 6.0ms (10.7% of total)
ival-div: 3.0ms (5.3% of total)
ival-add: 2.0ms (3.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess96.0ms (1.5%)

Memory
0.6MiB live, 38.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03578
111274
231174
360074
493274
5134874
6174474
7205574
8216874
9225274
10228874
11229274
12229274
0108
0168
1278
2378
3398
0397
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
Compiler

Compiled 10 to 10 computations (0% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
Compiler

Compiled 10 to 10 computations (0% saved)

simplify3.0ms (0%)

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

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y (sqrt.f64 z))
cost-diff0
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
cost-diff128
(+.f64 x (*.f64 y (sqrt.f64 z)))
cost-diff704
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
01626
12726
23726
33926
03924
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x (*.f64 y (sqrt.f64 z)))
x
(*.f64 y (sqrt.f64 z))
y
(sqrt.f64 z)
z
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x (*.f64 y (sqrt.f64 z)))
(fma.f64 (sqrt.f64 z) y x)
x
(*.f64 y (sqrt.f64 z))
(*.f64 (sqrt.f64 z) y)
y
(sqrt.f64 z)
z

localize41.0ms (0.6%)

Memory
-6.6MiB live, 30.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
accuracy0
(sqrt.f64 z)
accuracy0.00390625
(+.f64 x (*.f64 y (sqrt.f64 z)))
accuracy0.19921875
(*.f64 y (sqrt.f64 z))
Samples
17.0ms256×0valid
Compiler

Compiled 62 to 22 computations (64.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 3.0ms (35.3% of total)
ival-div: 2.0ms (23.5% of total)
ival-sqrt: 2.0ms (23.5% of total)
ival-add: 1.0ms (11.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
12.9MiB live, 12.9MiB allocated
Counts
5 → 108
Calls
Call 1
Inputs
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())
#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())
Outputs
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
2.0ms
z
@-inf
((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z))
1.0ms
y
@-inf
((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z))
1.0ms
z
@0
((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z))
1.0ms
z
@inf
((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z))
1.0ms
y
@inf
((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z))

simplify144.0ms (2.2%)

Memory
-8.0MiB live, 110.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075646
1251646
2797646
32298622
45069622
57549622
08141566
Stop Event
iter limit
node limit
Counts
108 → 105
Calls
Call 1
Inputs
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
Outputs
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 (sqrt.f64 z) y)
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 (sqrt.f64 z) y)
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 (sqrt.f64 z) y)
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 (sqrt.f64 z) y)
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 (sqrt.f64 z) y)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
x
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (+ (sqrt z) (/ x y)))
(fma.f64 (sqrt.f64 z) y x)
(* y (+ (sqrt z) (/ x y)))
(fma.f64 (sqrt.f64 z) y x)
(* y (+ (sqrt z) (/ x y)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(fma.f64 (sqrt.f64 z) y x)
(* x (+ 1 (* (/ y x) (sqrt z))))
(fma.f64 (sqrt.f64 z) y x)
(* x (+ 1 (* (/ y x) (sqrt z))))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))

rewrite220.0ms (3.3%)

Memory
38.1MiB live, 112.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01021
01621
14121
223421
3200121
0816219
Stop Event
iter limit
node limit
iter limit
Counts
5 → 272
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
(+.f64 x (*.f64 y (sqrt.f64 z)))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
(*.f64 y (sqrt.f64 z))
(sqrt.f64 z)
Outputs
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eval185.0ms (2.8%)

Memory
-33.0MiB live, 93.5MiB allocated
Compiler

Compiled 9 397 to 942 computations (90% saved)

prune13.0ms (0.2%)

Memory
25.9MiB live, 25.9MiB allocated
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New36710377
Fresh000
Picked101
Done000
Total36810378
Accuracy
100.0%
Counts
378 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(fma.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64)))
46.2%
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
38.7%
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))))
99.9%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
87.6%
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
93.8%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
49.3%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))
51.9%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 266 to 212 computations (20.3% saved)

simplify181.0ms (2.7%)

Memory
-26.7MiB live, 55.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
cost-diff128
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
cost-diff704
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
cost-diff2240
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
cost-diff0
(neg.f64 z)
cost-diff0
(fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x))
cost-diff0
(*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
cost-diff0
(*.f64 z y)
cost-diff0
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
cost-diff0
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
cost-diff0
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(sqrt.f64 z)
cost-diff0
(fma.f64 (sqrt.f64 z) y x)
cost-diff0
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036203
062179
1111179
2187179
3336179
4630179
51065179
61954179
74694179
86040179
96345179
106643179
116974179
126994179
137932179
08145179
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(fma.f64 (sqrt.f64 z) y x)
(sqrt.f64 z)
z
y
x
#s(literal 1/2 binary64)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(*.f64 z y)
z
y
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(/.f64 #s(literal 1 binary64) z)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x))
(neg.f64 z)
z
(*.f64 y y)
y
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 x (*.f64 (sqrt.f64 z) y))
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
x
(*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
y
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
(sqrt.f64 (sqrt.f64 z))
(sqrt.f64 z)
z
Outputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x))
(fma.f64 (sqrt.f64 z) y x)
(fma.f64 y (sqrt.f64 z) x)
(sqrt.f64 z)
z
y
x
#s(literal 1/2 binary64)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z) x) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z) x)
(*.f64 z y)
(*.f64 y z)
z
y
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(/.f64 #s(literal 1 binary64) z)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)))
(*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)))
(fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x))
(fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x))
(neg.f64 z)
z
(*.f64 y y)
y
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 x (*.f64 (sqrt.f64 z) y))
(-.f64 x (*.f64 y (sqrt.f64 z)))
(*.f64 (sqrt.f64 z) y)
(*.f64 y (sqrt.f64 z))
(sqrt.f64 z)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
(fma.f64 y (sqrt.f64 z) x)
x
(*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
(*.f64 y (sqrt.f64 z))
y
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
(sqrt.f64 z)
(sqrt.f64 (sqrt.f64 z))
(sqrt.f64 z)
z

localize208.0ms (3.2%)

Memory
-0.8MiB live, 110.6MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
accuracy0.1484375
(sqrt.f64 (sqrt.f64 z))
accuracy0.19921875
(*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
accuracy0.4912300293053261
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
accuracy0.19921875
(*.f64 (sqrt.f64 z) y)
accuracy0.2089486125993
(*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))
accuracy10.615156354235214
(fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x))
accuracy33.66454661504442
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
accuracy0
(*.f64 z y)
accuracy0
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
accuracy0.13671875
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy3.9661309417996202
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy30.794266345110078
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
accuracy0
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
accuracy0
(sqrt.f64 z)
accuracy0.09375
(fma.f64 (sqrt.f64 z) y x)
Samples
137.0ms256×0valid
Compiler

Compiled 395 to 67 computations (83% saved)

Precisions
Click to see histograms. Total time spent on operations: 82.0ms
ival-mult: 63.0ms (76.9% of total)
ival-add: 6.0ms (7.3% of total)
ival-div: 5.0ms (6.1% of total)
ival-sqrt: 5.0ms (6.1% of total)
ival-sub: 1.0ms (1.2% of total)
ival-neg: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series141.0ms (2.1%)

Memory
1.9MiB live, 124.6MiB allocated
Counts
21 → 540
Calls
Call 1
Inputs
#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) (patch (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (neg.f64 z) (patch (neg.f64 z) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) (patch (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (patch (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())
#s(alt (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))) (patch (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (sqrt.f64 z)) (patch (sqrt.f64 (sqrt.f64 z)) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))) (taylor 0 z) (#s(alt (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))) (taylor 0 z) (#s(alt (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))) (taylor 0 z) (#s(alt (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))) (taylor 0 z) (#s(alt (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) (patch (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (pow y 2) z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) (patch (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (pow y 2) z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) (patch (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (pow y 2) z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) (patch (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 z) (taylor 0 z) (#s(alt (neg.f64 z) (patch (neg.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 z) (taylor 0 z) (#s(alt (neg.f64 z) (patch (neg.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 z) (taylor 0 z) (#s(alt (neg.f64 z) (patch (neg.f64 z) #<representation binary64>) () ())) ())
#s(alt (* -1 z) (taylor 0 z) (#s(alt (neg.f64 z) (patch (neg.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) (patch (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) (patch (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (patch (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (patch (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (patch (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
59.0ms
z
@0
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (neg z) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (sqrt (/ 1 z)) (* (sqrt z) y) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)))
28.0ms
z
@-inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (neg z) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (sqrt (/ 1 z)) (* (sqrt z) y) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)))
10.0ms
z
@inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (neg z) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (sqrt (/ 1 z)) (* (sqrt z) y) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)))
9.0ms
y
@-inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (neg z) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (sqrt (/ 1 z)) (* (sqrt z) y) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)))
2.0ms
y
@inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (neg z) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (sqrt (/ 1 z)) (* (sqrt z) y) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)))

simplify193.0ms (2.9%)

Memory
24.2MiB live, 176.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01944063
16493927
225363786
360663785
084113503
Stop Event
iter limit
node limit
Counts
540 → 531
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y z)
(* y z)
(* y z)
(* y z)
(* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(* 1/2 (pow x 2))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(pow x 2)
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(* -1 z)
(* -1 z)
(* -1 z)
(* -1 z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(pow (* 1 z) 1/4)
(pow (* 1 z) 1/4)
(pow (* 1 z) 1/4)
(pow (* 1 z) 1/4)
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* y z)
(* y z)
(* y z)
(* y z)
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))))
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (+ (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) (* (pow y 2) (pow z 2)))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))))
(* -1/2 (* (pow y 2) z))
(* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))
(* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))
(* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))
(* -1 (* (pow y 2) z))
(* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))
(* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))
(* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))
(* -1 z)
(* -1 z)
(* -1 z)
(* -1 z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(pow (* 1 z) 1/4)
(pow (* 1 z) 1/4)
(pow (* 1 z) 1/4)
(pow (* 1 z) 1/4)
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* -1 (* z (+ (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* (* y (pow (sqrt -1) 2)) (sqrt z))
(* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(* -1 (* z (+ (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(* y z)
(* y z)
(* y z)
(* y z)
(* -1/2 (* y (sqrt z)))
(+ (* -1/2 (* y (sqrt z))) (* -1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2)))) z)))
(+ (* -1 (/ (+ (* -1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2))))) y) (sqrt (/ 1 z)))) (* 1/2 (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2)))))) z)) (* -1/2 (* y (sqrt z))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2))))) y) (sqrt z))) (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2))))) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* 1/2 (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2)))))) z)) (* -1/2 (* y (sqrt z))))
(* -1/2 (* (pow y 2) z))
(* -1 (* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))))
(* -1 (* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))))
(* -1 (* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))))
(* -1 (* (pow y 2) z))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))))
(* -1 z)
(* -1 z)
(* -1 z)
(* -1 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* (pow (* -1 z) 1/4) (sqrt (sqrt -1)))
(* (pow (* -1 z) 1/4) (sqrt (sqrt -1)))
(* (pow (* -1 z) 1/4) (sqrt (sqrt -1)))
(* (pow (* -1 z) 1/4) (sqrt (sqrt -1)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y z)
(* y z)
(* y z)
(* y z)
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (pow x 2))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(pow x 2)
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y z)
(* y z)
(* y z)
(* y z)
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* -1/2 (* (pow y 2) z))
(* (pow y 2) (+ (* -1/2 z) (* 1/2 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ (* -1/2 z) (* 1/2 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ (* -1/2 z) (* 1/2 (/ (pow x 2) (pow y 2)))))
(* -1 (* (pow y 2) z))
(* (pow y 2) (+ (* -1 z) (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ (* -1 z) (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ (* -1 z) (/ (pow x 2) (pow y 2))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* y z)
(* y z)
(* y z)
(* y z)
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1/2 (* (pow y 2) z))
(* (pow y 2) (+ (* -1/2 z) (* 1/2 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ (* -1/2 z) (* 1/2 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ (* -1/2 z) (* 1/2 (/ (pow x 2) (pow y 2)))))
(* -1 (* (pow y 2) z))
(* (pow y 2) (+ (* -1 z) (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ (* -1 z) (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ (* -1 z) (/ (pow x 2) (pow y 2))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* -1/2 (* (pow y 2) z))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(* -1 (* (pow y 2) z))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
Outputs
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(pow x 2)
(*.f64 x x)
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(* -1 z)
(neg.f64 z)
(* -1 z)
(neg.f64 z)
(* -1 z)
(neg.f64 z)
(* -1 z)
(neg.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(pow (* 1 z) 1/4)
(pow.f64 z #s(literal 1/4 binary64))
(pow (* 1 z) 1/4)
(pow.f64 z #s(literal 1/4 binary64))
(pow (* 1 z) 1/4)
(pow.f64 z #s(literal 1/4 binary64))
(pow (* 1 z) 1/4)
(pow.f64 z #s(literal 1/4 binary64))
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z y) x))
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(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))

rewrite198.0ms (3%)

Memory
-4.7MiB live, 308.8MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036164
062121
1204119
21126116
08871116
Stop Event
iter limit
node limit
iter limit
Counts
21 → 1 514
Calls
Call 1
Inputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(fma.f64 (sqrt.f64 z) y x)
(sqrt.f64 z)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(*.f64 z y)
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x))
(neg.f64 z)
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(*.f64 (sqrt.f64 z) y)
(*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
(sqrt.f64 (sqrt.f64 z))
Outputs
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eval973.0ms (14.8%)

Memory
-132.2MiB live, 554.9MiB allocated
Compiler

Compiled 54 541 to 3 834 computations (93% saved)

prune54.0ms (0.8%)

Memory
16.5MiB live, 215.1MiB allocated
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2 25872 265
Fresh505
Picked325
Done000
Total2 26692 275
Accuracy
100.0%
Counts
2 275 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
21.5%
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
93.8%
(*.f64 (fma.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 y z) x) #s(literal 1/2 binary64))
99.7%
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
90.5%
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
99.9%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
49.3%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
87.6%
#s(approx (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))))))
93.8%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
51.9%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 191 to 159 computations (16.8% saved)

simplify134.0ms (2%)

Memory
-11.9MiB live, 66.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (*.f64 (neg.f64 y) z) y)
cost-diff0
#s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y))
cost-diff0
(*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
cost-diff0
(*.f64 z y)
cost-diff0
(*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))
cost-diff0
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
cost-diff320
(fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x)
cost-diff0
(sqrt.f64 z)
cost-diff0
(/.f64 y (sqrt.f64 z))
cost-diff0
(fma.f64 (/.f64 y (sqrt.f64 z)) z x)
cost-diff0
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 z)
cost-diff0
(*.f64 (sqrt.f64 z) y)
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 z)
cost-diff0
(/.f64 z (sqrt.f64 z))
cost-diff0
(fma.f64 (/.f64 z (sqrt.f64 z)) y x)
cost-diff0
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040229
063225
1118220
2199220
3319220
4457220
5533220
6768220
7913220
81130220
91469220
101996220
112465220
122561220
132585220
142598220
152598220
162598220
172638220
182872220
02872217
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 z (sqrt.f64 z)) y x)
(/.f64 z (sqrt.f64 z))
z
(sqrt.f64 z)
y
x
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
z
y
#s(literal 1/2 binary64)
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 y (sqrt.f64 z)) z x)
(/.f64 y (sqrt.f64 z))
y
(sqrt.f64 z)
z
x
#s(literal 1/2 binary64)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x)
(*.f64 z y)
z
y
(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
#s(literal 1 binary64)
(sqrt.f64 z)
x
#s(literal 1/2 binary64)
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y))
(*.f64 (*.f64 (neg.f64 y) z) y)
(*.f64 (neg.f64 y) z)
(neg.f64 y)
y
z
#s(literal 1/2 binary64)
(-.f64 x (*.f64 (sqrt.f64 z) y))
x
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
Outputs
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 z (sqrt.f64 z)) x))
(fma.f64 (/.f64 z (sqrt.f64 z)) y x)
(fma.f64 y (/.f64 z (sqrt.f64 z)) x)
(/.f64 z (sqrt.f64 z))
z
(sqrt.f64 z)
y
x
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 y (sqrt.f64 z))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
#s(approx (+ (* (sqrt z) y) x) (*.f64 y (sqrt.f64 z)))
(*.f64 (sqrt.f64 z) y)
(*.f64 y (sqrt.f64 z))
(sqrt.f64 z)
z
y
#s(literal 1/2 binary64)
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 z (sqrt.f64 z)) x))
(fma.f64 (/.f64 y (sqrt.f64 z)) z x)
(fma.f64 y (/.f64 z (sqrt.f64 z)) x)
(/.f64 y (sqrt.f64 z))
y
(sqrt.f64 z)
z
x
#s(literal 1/2 binary64)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 z (sqrt.f64 z)) x)))
(*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 y (/.f64 z (sqrt.f64 z)) x))
(fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x)
(fma.f64 y (/.f64 z (sqrt.f64 z)) x)
(*.f64 z y)
(*.f64 y z)
z
y
(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
#s(literal 1 binary64)
(sqrt.f64 z)
x
#s(literal 1/2 binary64)
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 z) x)) #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)))
(*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y))
(*.f64 (*.f64 (neg.f64 y) z) y)
(*.f64 (neg.f64 y) z)
(neg.f64 y)
y
z
#s(literal 1/2 binary64)
(-.f64 x (*.f64 (sqrt.f64 z) y))
(fma.f64 (neg.f64 y) (sqrt.f64 z) x)
x
(*.f64 (sqrt.f64 z) y)
(*.f64 y (sqrt.f64 z))
(sqrt.f64 z)

localize102.0ms (1.5%)

Memory
28.2MiB live, 181.9MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.19921875
(*.f64 (sqrt.f64 z) y)
accuracy0.2089486125993
(*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64))
accuracy29.82234604070481
#s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y))
accuracy33.66454661504442
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
accuracy0
(sqrt.f64 z)
accuracy0
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
accuracy0.234375
(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
accuracy3.9661309417996202
(fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x)
accuracy0
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
accuracy0
(sqrt.f64 z)
accuracy0.1796875
(/.f64 y (sqrt.f64 z))
accuracy6.034514640766774
(fma.f64 (/.f64 y (sqrt.f64 z)) z x)
accuracy0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
accuracy0
(sqrt.f64 z)
accuracy0.19921875
(*.f64 (sqrt.f64 z) y)
accuracy32.33177760235102
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
accuracy0
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
accuracy0
(sqrt.f64 z)
accuracy0.09375
(fma.f64 (/.f64 z (sqrt.f64 z)) y x)
accuracy0.47265625
(/.f64 z (sqrt.f64 z))
Samples
74.0ms256×0valid
Compiler

Compiled 375 to 67 computations (82.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-mult: 27.0ms (51.2% of total)
ival-add: 12.0ms (22.8% of total)
ival-div: 8.0ms (15.2% of total)
ival-sqrt: 2.0ms (3.8% of total)
ival-neg: 2.0ms (3.8% of total)
ival-sub: 1.0ms (1.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series44.0ms (0.7%)

Memory
-23.1MiB live, 70.9MiB allocated
Counts
19 → 564
Calls
Call 1
Inputs
#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())
#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())
#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) (patch (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) (patch #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (neg.f64 y) z) y) (patch (*.f64 (*.f64 (neg.f64 y) z) y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 z (sqrt.f64 z)) y x) (patch (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) (patch (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) (patch (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) (patch (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) (patch (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) (patch #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) (patch #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) (patch #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) (patch #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
8.0ms
z
@inf
((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (* z y) (/ 1 (sqrt z))) x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (/ 1 (sqrt z))) x) 1/2) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (* (* (neg y) z) y) (/ 1 (sqrt z)))
4.0ms
z
@-inf
((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (* z y) (/ 1 (sqrt z))) x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (/ 1 (sqrt z))) x) 1/2) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (* (* (neg y) z) y) (/ 1 (sqrt z)))
2.0ms
y
@-inf
((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (* z y) (/ 1 (sqrt z))) x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (/ 1 (sqrt z))) x) 1/2) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (* (* (neg y) z) y) (/ 1 (sqrt z)))
2.0ms
z
@0
((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (* z y) (/ 1 (sqrt z))) x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (/ 1 (sqrt z))) x) 1/2) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (* (* (neg y) z) y) (/ 1 (sqrt z)))
2.0ms
y
@0
((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (* z y) (/ 1 (sqrt z))) x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (/ 1 (sqrt z))) x) 1/2) (* z y) (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (+ (* (neg z) (* y y)) (* x x)) (* (* (neg y) z) y) (/ 1 (sqrt z)))

simplify158.0ms (2.4%)

Memory
10.3MiB live, 202.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01864349
16354266
221494132
364714101
090933780
Stop Event
iter limit
node limit
Counts
564 → 552
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(+ x (* y (sqrt z)))
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(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
Outputs
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(+ (* -1/2 (* (pow y 2) z)) (* 1/2 (pow x 2)))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(pow x 2)
(*.f64 x x)
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(+ (* -1 (* (pow y 2) z)) (pow x 2))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 z)) (/.f64 (/.f64 (*.f64 x x) y) z) (fma.f64 (sqrt.f64 z) y x)) #s(literal 1/2 binary64))
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (*.f64 (fma.f64 (/.f64 (sqrt.f64 z) y) (*.f64 (neg.f64 x) x) (*.f64 z x)) (/.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 z)) (/.f64 (/.f64 (*.f64 x x) y) z) (fma.f64 (sqrt.f64 z) y x))))
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (+ (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) (* (pow y 2) (pow z 2)))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x (fma.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 z) y) (*.f64 (neg.f64 x) x) (*.f64 z x)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (*.f64 x (/.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) (/.f64 x y)) (/.f64 (sqrt.f64 z) z) x) z) (*.f64 y y)))) (fma.f64 (neg.f64 (sqrt.f64 z)) (/.f64 (/.f64 (*.f64 x x) y) z) (fma.f64 (sqrt.f64 z) y x))))
(* -1/2 (* (pow y 2) z))
(*.f64 (*.f64 (*.f64 y y) z) #s(literal -1/2 binary64))
(* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))
(fma.f64 (*.f64 (*.f64 y y) #s(literal -1/2 binary64)) z (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))
(fma.f64 (*.f64 (neg.f64 y) z) y (*.f64 x x))
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(* -1 (* (pow y 2) z))
(*.f64 (*.f64 (neg.f64 y) z) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
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(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
x
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(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(fma.f64 (sqrt.f64 z) y x)
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(fma.f64 (sqrt.f64 z) y x)
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(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 x)
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(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
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(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 x)
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(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(fma.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal -1/2 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(fma.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal -1/2 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/2 (/ (* (pow y 2) z) (pow x 2)))))
(fma.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal -1/2 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(fma.f64 (*.f64 (*.f64 (neg.f64 y) z) y) #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
(fma.f64 (*.f64 (*.f64 (neg.f64 y) z) y) #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (* (pow y 2) z) (pow x 2)))))
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rewrite173.0ms (2.6%)

Memory
-1.2MiB live, 319.7MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040185
063177
1223173
21150156
09412156
Stop Event
iter limit
node limit
iter limit
Counts
19 → 980
Calls
Call 1
Inputs
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 z (sqrt.f64 z)) y x)
(/.f64 z (sqrt.f64 z))
(sqrt.f64 z)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
(*.f64 (sqrt.f64 z) y)
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 y (sqrt.f64 z)) z x)
(/.f64 y (sqrt.f64 z))
(fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x)
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64))
(*.f64 z y)
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y))
(*.f64 (*.f64 (neg.f64 y) z) y)
(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
Outputs
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eval234.0ms (3.6%)

Memory
28.0MiB live, 492.3MiB allocated
Compiler

Compiled 30 332 to 2 484 computations (91.8% saved)

prune55.0ms (0.8%)

Memory
-12.0MiB live, 148.8MiB allocated
Pruning

10 alts after pruning (5 fresh and 5 done)

PrunedKeptTotal
New1 78951 794
Fresh202
Picked235
Done022
Total1 793101 803
Accuracy
100.0%
Counts
1 803 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
21.5%
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
99.9%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
43.6%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
49.2%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
42.6%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
49.3%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
42.0%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
49.3%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
93.8%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
51.9%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 136 to 139 computations (-2.2% saved)

simplify60.0ms (0.9%)

Memory
-5.4MiB live, 33.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(neg.f64 y)
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
cost-diff1216
(/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
cost-diff0
(/.f64 (sqrt.f64 z) y)
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y)))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
cost-diff384
(/.f64 z (/.f64 (sqrt.f64 z) y))
cost-diff0
(*.f64 y z)
cost-diff0
(/.f64 (*.f64 y z) (sqrt.f64 z))
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
cost-diff0
(/.f64 y (sqrt.f64 z))
cost-diff0
(*.f64 (/.f64 y (sqrt.f64 z)) z)
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
cost-diff0
(pow.f64 z #s(literal -1/2 binary64))
cost-diff0
(/.f64 y (pow.f64 z #s(literal -1/2 binary64)))
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031215
048215
167215
284212
3118206
4161206
5444206
6976206
71755206
82057206
92228206
102337206
112406206
122554206
132554206
02554196
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))
(/.f64 y (pow.f64 z #s(literal -1/2 binary64)))
y
(pow.f64 z #s(literal -1/2 binary64))
z
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(/.f64 y (sqrt.f64 z))
y
(sqrt.f64 z)
z
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
(/.f64 (*.f64 y z) (sqrt.f64 z))
(*.f64 y z)
y
z
(sqrt.f64 z)
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y)))
(/.f64 z (/.f64 (sqrt.f64 z) y))
z
(/.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
y
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))))
(/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(neg.f64 y)
y
(/.f64 #s(literal -1 binary64) (sqrt.f64 z))
#s(literal -1 binary64)
(sqrt.f64 z)
z
#s(literal 1/2 binary64)
Outputs
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))
#s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))
(/.f64 y (pow.f64 z #s(literal -1/2 binary64)))
y
(pow.f64 z #s(literal -1/2 binary64))
z
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(/.f64 y (sqrt.f64 z))
y
(sqrt.f64 z)
z
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(/.f64 (*.f64 y z) (sqrt.f64 z))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(*.f64 y z)
(*.f64 z y)
y
z
(sqrt.f64 z)
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y)))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(/.f64 z (/.f64 (sqrt.f64 z) y))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
z
(/.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
y
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
(/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(*.f64 (sqrt.f64 z) y)
(neg.f64 y)
y
(/.f64 #s(literal -1 binary64) (sqrt.f64 z))
#s(literal -1 binary64)
(sqrt.f64 z)
z
#s(literal 1/2 binary64)

localize81.0ms (1.2%)

Memory
1.8MiB live, 129.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0
(neg.f64 y)
accuracy0.234375
(/.f64 #s(literal -1 binary64) (sqrt.f64 z))
accuracy0.2421875
(/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
accuracy32.33177760235102
#s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))))
accuracy0
(sqrt.f64 z)
accuracy0.26171875
(/.f64 (sqrt.f64 z) y)
accuracy7.545479225712871
(/.f64 z (/.f64 (sqrt.f64 z) y))
accuracy32.33177760235102
#s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y)))
accuracy0
(*.f64 y z)
accuracy0
(sqrt.f64 z)
accuracy8.631230618261146
(/.f64 (*.f64 y z) (sqrt.f64 z))
accuracy32.33177760235102
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
accuracy0
(sqrt.f64 z)
accuracy0.1796875
(/.f64 y (sqrt.f64 z))
accuracy7.806797391806421
(*.f64 (/.f64 y (sqrt.f64 z)) z)
accuracy32.33177760235102
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
accuracy0
(pow.f64 z #s(literal -1/2 binary64))
accuracy0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
accuracy0.2421875
(/.f64 y (pow.f64 z #s(literal -1/2 binary64)))
accuracy32.33177760235102
#s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))
Samples
58.0ms256×0valid
Compiler

Compiled 302 to 51 computations (83.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-div: 11.0ms (39.2% of total)
ival-mult: 6.0ms (21.4% of total)
ival-pow: 6.0ms (21.4% of total)
ival-sqrt: 2.0ms (7.1% of total)
ival-add: 1.0ms (3.6% of total)
ival-neg: 1.0ms (3.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series43.0ms (0.7%)

Memory
-27.3MiB live, 53.4MiB allocated
Counts
22 → 600
Calls
Call 1
Inputs
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (patch (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 z #s(literal -1/2 binary64)) (patch (pow.f64 z #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())
#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 y z) (sqrt.f64 z)) (patch (/.f64 (*.f64 y z) (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (*.f64 y z) (patch (*.f64 y z) #<representation binary64>) () ())
#s(alt (/.f64 z (/.f64 (sqrt.f64 z) y)) (patch (/.f64 z (/.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 z) y) (patch (/.f64 (sqrt.f64 z) y) #<representation binary64>) () ())
#s(alt (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))) (patch (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
10.0ms
z
@-inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ y (pow z -1/2)) (pow z -1/2) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ z (/ (sqrt z) y)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (sqrt z) y) (/ (neg y) (/ -1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (neg y) (sqrt z) (/ -1 (sqrt z)))
2.0ms
z
@0
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ y (pow z -1/2)) (pow z -1/2) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ z (/ (sqrt z) y)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (sqrt z) y) (/ (neg y) (/ -1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (neg y) (sqrt z) (/ -1 (sqrt z)))
2.0ms
y
@-inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ y (pow z -1/2)) (pow z -1/2) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ z (/ (sqrt z) y)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (sqrt z) y) (/ (neg y) (/ -1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (neg y) (sqrt z) (/ -1 (sqrt z)))
2.0ms
z
@inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ y (pow z -1/2)) (pow z -1/2) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ z (/ (sqrt z) y)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (sqrt z) y) (/ (neg y) (/ -1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (neg y) (sqrt z) (/ -1 (sqrt z)))
1.0ms
y
@0
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ y (pow z -1/2)) (pow z -1/2) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ z (/ (sqrt z) y)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (sqrt z) y) (/ (neg y) (/ -1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (neg y) (sqrt z) (/ -1 (sqrt z)))

simplify136.0ms (2.1%)

Memory
36.9MiB live, 143.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0853634
12783586
28333586
326973466
461063466
082983186
Stop Event
iter limit
node limit
Counts
600 → 585
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* y (sqrt z)))
(* -1 (* y (sqrt z)))
(* -1 (* y (sqrt z)))
(* -1 (* y (sqrt z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z)))
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z)))
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z)))
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* -1 (sqrt (/ 1 z)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
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(* 1/2 x)
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(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
Outputs
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(* (/ 1 y) (sqrt z))
(/.f64 (sqrt.f64 z) y)
(* (/ 1 y) (sqrt z))
(/.f64 (sqrt.f64 z) y)
(* (/ 1 y) (sqrt z))
(/.f64 (sqrt.f64 z) y)
(* (/ 1 y) (sqrt z))
(/.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(+ x (* y (sqrt z)))
(fma.f64 (sqrt.f64 z) y x)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* -1 (sqrt (/ 1 z)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* -1 (sqrt (/ 1 z)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* -1 (sqrt (/ 1 z)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* -1 (sqrt (/ 1 z)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* y (sqrt (/ 1 z)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* (/ 1 y) (sqrt z))
(/.f64 (sqrt.f64 z) y)
(* (/ 1 y) (sqrt z))
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(* (/ 1 y) (sqrt z))
(/.f64 (sqrt.f64 z) y)
(* (/ 1 y) (sqrt z))
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(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* 1/2 (* y (sqrt z)))
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
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rewrite147.0ms (2.2%)

Memory
16.4MiB live, 174.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031192
048176
1127161
2552161
34269161
09143151
Stop Event
iter limit
node limit
iter limit
Counts
22 → 1 142
Calls
Call 1
Inputs
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))
(/.f64 y (pow.f64 z #s(literal -1/2 binary64)))
(pow.f64 z #s(literal -1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(/.f64 y (sqrt.f64 z))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
(/.f64 (*.f64 y z) (sqrt.f64 z))
(*.f64 y z)
(/.f64 z (/.f64 (sqrt.f64 z) y))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y)))
(/.f64 (sqrt.f64 z) y)
(/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z))))
(neg.f64 y)
(sqrt.f64 z)
(/.f64 #s(literal -1 binary64) (sqrt.f64 z))
Outputs
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eval369.0ms (5.6%)

Memory
-3.8MiB live, 378.8MiB allocated
Compiler

Compiled 23 389 to 3 253 computations (86.1% saved)

prune97.0ms (1.5%)

Memory
8.2MiB live, 135.5MiB allocated
Pruning

9 alts after pruning (1 fresh and 8 done)

PrunedKeptTotal
New1 99011 991
Fresh000
Picked235
Done055
Total1 99292 001
Accuracy
100.0%
Counts
2 001 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
21.5%
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
99.9%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
43.6%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
42.6%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
49.3%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y #s(approx (pow z -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))) #s(literal 1/2 binary64))
42.0%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
49.3%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
93.8%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
51.9%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 371 to 189 computations (49.1% saved)

regimes53.0ms (0.8%)

Memory
9.9MiB live, 85.9MiB allocated
Counts
24 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) x) #s(literal 1/2 binary64)))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y #s(approx (pow z -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 z (/.f64 (sqrt.f64 z) y))) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))))
(/.f64 (*.f64 #s(approx (+ (* (neg z) (* y y)) (* x x)) (*.f64 (*.f64 (neg.f64 y) z) y)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/.f64 (*.f64 (fma.f64 (neg.f64 z) (*.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
#s(approx (/ (* (+ (* (neg z) (* y y)) (* x x)) 1/2) (- x (* (sqrt z) y))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) z) y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 y z) x) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64)))
Outputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
Calls

7 calls:

9.0ms
(sqrt.f64 z)
9.0ms
z
7.0ms
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
7.0ms
x
7.0ms
y
Results
AccuracySegmentsBranch
99.9%1x
99.9%1y
99.9%1z
99.9%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
99.9%1(+.f64 x (*.f64 y (sqrt.f64 z)))
99.9%1(*.f64 y (sqrt.f64 z))
99.9%1(sqrt.f64 z)
Compiler

Compiled 25 to 34 computations (-36% saved)

regimes17.0ms (0.3%)

Memory
-38.2MiB live, 43.2MiB allocated
Counts
3 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
Outputs
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))
Calls

7 calls:

4.0ms
x
3.0ms
(sqrt.f64 z)
2.0ms
y
2.0ms
(+.f64 x (*.f64 y (sqrt.f64 z)))
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
Results
AccuracySegmentsBranch
76.1%3x
76.9%3y
66.0%2z
59.9%3(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
59.9%3(+.f64 x (*.f64 y (sqrt.f64 z)))
81.4%3(*.f64 y (sqrt.f64 z))
66.0%2(sqrt.f64 z)
Compiler

Compiled 25 to 34 computations (-36% saved)

regimes11.0ms (0.2%)

Memory
32.6MiB live, 32.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

7 calls:

2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
1.0ms
(+.f64 x (*.f64 y (sqrt.f64 z)))
1.0ms
x
1.0ms
(sqrt.f64 z)
1.0ms
(*.f64 y (sqrt.f64 z))
Results
AccuracySegmentsBranch
51.9%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
51.9%1(+.f64 x (*.f64 y (sqrt.f64 z)))
51.9%1z
51.9%1(sqrt.f64 z)
51.9%1x
51.9%1y
51.9%1(*.f64 y (sqrt.f64 z))
Compiler

Compiled 25 to 34 computations (-36% saved)

bsearch1.0ms (0%)

Memory
3.2MiB live, 3.2MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
3.166490006828065e+77
7.956581506615147e+87
0.0ms
-5.979556023776784e+52
-2.1769448714949027e+48
Compiler

Compiled 13 to 16 computations (-23.1% saved)

simplify24.0ms (0.4%)

Memory
-22.5MiB live, 55.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02675
13375
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal -49999999999999999661047433718081398823085422097203200 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) (if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal 500000000000000004246810716844851488074434962299380307947499551351398452953088 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Outputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 z) y x))
(if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal -49999999999999999661047433718081398823085422097203200 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) (if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal 500000000000000004246810716844851488074434962299380307947499551351398452953088 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))))
(if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal -49999999999999999661047433718081398823085422097203200 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64))) (if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal 500000000000000004246810716844851488074434962299380307947499551351398452953088 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

soundness399.0ms (6.1%)

Memory
-10.0MiB live, 256.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075646
1251646
2797646
32298622
45069622
57549622
08141566
01021
01621
14121
223421
3200121
0816219
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 91 to 50 computations (45.1% saved)

preprocess31.0ms (0.5%)

Memory
-3.1MiB live, 71.1MiB allocated
Compiler

Compiled 106 to 56 computations (47.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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