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

Time bar (total: 6.6s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze45.0ms (0.7%)

Memory
27.4MiB live, 104.7MiB 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)

sample1.0s (15.8%)

Memory
27.5MiB live, 1 729.8MiB allocated
Samples
478.0ms8 256×0valid
124.0ms2 047×0invalid
Precisions
Click to see histograms. Total time spent on operations: 342.0ms
ival-mult: 120.0ms (35.1% of total)
ival-div: 82.0ms (24% of total)
ival-sqrt: 71.0ms (20.7% of total)
ival-add: 48.0ms (14% of total)
exact: 9.0ms (2.6% of total)
ival-true: 8.0ms (2.3% of total)
ival-assert: 4.0ms (1.2% of total)
Bogosity

explain138.0ms (2.1%)

Memory
-28.1MiB live, 131.5MiB 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
32.0ms512×0valid
Compiler

Compiled 74 to 34 computations (54.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-mult: 6.0ms (36.1% of total)
ival-sqrt: 4.0ms (24.1% of total)
ival-div: 3.0ms (18.1% of total)
ival-add: 2.0ms (12% of total)
exact: 1.0ms (6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess71.0ms (1.1%)

Memory
11.0MiB live, 45.4MiB allocated
Algorithm
egg-herbie
Rules
482×unsub-neg
354×distribute-lft-neg-in
312×cancel-sign-sub-inv
270×distribute-rgt-in
236×associate-*r*
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
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.1MiB live, 1.1MiB 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)

simplify4.0ms (0.1%)

Memory
4.7MiB live, 4.7MiB 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))
Rules
32×lower-*.f32
28×lower-*.f64
20×lower-fma.f64
20×lower-fma.f32
16×*-commutative
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

localize31.0ms (0.5%)

Memory
-9.2MiB live, 36.4MiB 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)))
accuracy0.23828125
(*.f64 y (sqrt.f64 z))
Samples
25.0ms256×0valid
Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-sqrt: 11.0ms (64.4% of total)
ival-mult: 3.0ms (17.6% of total)
ival-div: 2.0ms (11.7% of total)
ival-add: 1.0ms (5.9% 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
19.9MiB live, 19.9MiB 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))

simplify129.0ms (2%)

Memory
-13.0MiB live, 144.4MiB allocated
Algorithm
egg-herbie
Rules
5 642×lower-fma.f64
5 642×lower-fma.f32
3 660×lower-*.f64
3 660×lower-*.f32
1 856×lower-/.f32
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))

rewrite213.0ms (3.2%)

Memory
13.7MiB live, 170.7MiB allocated
Rules
7 460×lower-fma.f64
7 460×lower-fma.f32
4 298×lower-*.f32
4 294×lower-*.f64
4 222×lower-/.f64
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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eval50.0ms (0.8%)

Memory
1.5MiB live, 113.3MiB allocated
Compiler

Compiled 9 397 to 942 computations (90% saved)

prune17.0ms (0.3%)

Memory
3.3MiB live, 49.4MiB 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)))
54.1%
(/.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))
54.0%
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sqrt.f64 z) y) x) (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))))
99.8%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
87.5%
(*.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)))))))
70.7%
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
95.2%
#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)))
52.2%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)))
49.5%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 266 to 216 computations (18.8% saved)

simplify269.0ms (4.1%)

Memory
-21.6MiB live, 92.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.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)))))))
cost-diff128
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))
cost-diff704
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
cost-diff1728
(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))))))
cost-diff0
(*.f64 z y)
cost-diff0
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
cost-diff0
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
cost-diff0
(/.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))
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))
Rules
3 560×lower-fma.f32
3 552×lower-fma.f64
2 480×lower-*.f32
2 462×lower-*.f64
1 280×unsub-neg
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037263
065254
1125254
2257252
3586246
41145246
52094246
63955246
74750246
85091246
95272246
105284246
115296246
125871246
136078246
146096246
156100246
166100246
176100246
186154246
196285246
206382246
216382246
06382246
Stop Event
iter limit
saturated
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 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
(*.f64 z y)
z
y
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
#s(literal 1/2 binary64)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
(*.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(literal 1 binary64) #s(literal 2 binary64))
#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))))))
x
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
(-.f64 x (*.f64 (sqrt.f64 z) y))
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
z
y
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))
(*.f64 z y)
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
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 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (fma.f64 y (sqrt.f64 z) (neg.f64 x))))
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (*.f64 y z) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
(fma.f64 (*.f64 y z) y (*.f64 (neg.f64 x) x))
(*.f64 z y)
(*.f64 y z)
z
y
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
#s(literal 1/2 binary64)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(fma.f64 y (sqrt.f64 z) (neg.f64 x))
(*.f64 (sqrt.f64 z) y)
(*.f64 y (sqrt.f64 z))
(sqrt.f64 z)
(*.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 (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (fma.f64 y (sqrt.f64 z) (neg.f64 x))))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1/2 binary64)
#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 (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)) (-.f64 x (*.f64 y (sqrt.f64 z))))
x
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/.f64 x (-.f64 x (*.f64 y (sqrt.f64 z))))
(-.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)
z
y
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(*.f64 (/.f64 z (fma.f64 y (sqrt.f64 z) (neg.f64 x))) (*.f64 y y))
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))
(*.f64 (/.f64 z (-.f64 x (*.f64 y (sqrt.f64 z)))) (*.f64 y y))
(*.f64 z y)
(*.f64 y z)
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/.f64 y (-.f64 x (*.f64 y (sqrt.f64 z))))

localize170.0ms (2.6%)

Memory
1.0MiB live, 201.6MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.23828125
(*.f64 (sqrt.f64 z) y)
accuracy1.8625433899550892
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
accuracy4.416924135229649
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))
accuracy4.947040889273882
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
accuracy0.01171875
(-.f64 (*.f64 (sqrt.f64 z) y) x)
accuracy0.23828125
(*.f64 (sqrt.f64 z) y)
accuracy1.5820257452111206
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
accuracy28.80863559915213
(/.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))
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)))
accuracy0.14453125
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy3.0415992012567914
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy32.313986461195164
#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)
accuracy0.12890625
(fma.f64 (sqrt.f64 z) y x)
Samples
83.0ms256×0valid
Compiler

Compiled 266 to 38 computations (85.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 59.0ms
ival-div: 24.0ms (40.9% of total)
ival-mult: 20.0ms (34.1% of total)
ival-add: 5.0ms (8.5% of total)
ival-sqrt: 4.0ms (6.8% of total)
ival-neg: 3.0ms (5.1% of total)
ival-sub: 2.0ms (3.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series401.0ms (6.1%)

Memory
12.5MiB live, 88.2MiB allocated
Counts
22 → 660
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 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) (patch (/.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)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ())
#s(alt (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)))))) (patch (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)))))) #<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 (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) (patch (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) #<representation binary64>) () ())
#s(alt (*.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))))))) (patch (*.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))))))) #<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 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())
#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())
#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<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) (- (* y (sqrt z)) x))) (taylor 0 z) (#s(alt (/.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)) (patch (/.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)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) (taylor 0 z) (#s(alt (/.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)) (patch (/.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)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 y) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x)) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* (pow y 2) (sqrt z)) (/ (* (pow y 3) z) x)) x))) x)) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 4) x) (sqrt (pow z 3)))) (* -1 (* (pow y 3) z))) x)) (* (pow y 2) (sqrt z))) x))) x)) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow y 2) z) x) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (* (pow y 2) z))) x)) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* (pow y 3) (sqrt (pow z 3))) (/ (* (pow y 4) (pow z 2)) x)) x))) x)) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 5) x) (sqrt (pow z 5)))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x))) x)) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (/ y x) (sqrt z))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y (sqrt z))) x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) (* y (sqrt z))) x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
17.0ms
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) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y))))
11.0ms
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) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y))))
9.0ms
x
@-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) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y))))
6.0ms
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) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y))))
6.0ms
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) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y))))

simplify241.0ms (3.7%)

Memory
0.4MiB live, 281.5MiB allocated
Algorithm
egg-herbie
Rules
10 772×lower-fma.f64
10 772×lower-fma.f32
6 546×lower-*.f64
6 546×lower-*.f32
3 324×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08688527
129407807
084347444
Stop Event
iter limit
node limit
Counts
660 → 651
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) (- (* y (sqrt z)) x)))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(* -1/2 (pow x 2))
(+ (* -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 (pow x 2))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(/ (pow x 2) (- x (* y (sqrt z))))
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z)))))
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z)))))
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z)))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(* -1 (/ (* (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 y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 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)) x)
(- (* y (sqrt z)) x)
(- (* y (sqrt z)) x)
(- (* y (sqrt z)) x)
(/ y (- x (* y (sqrt z))))
(/ y (- x (* y (sqrt z))))
(/ y (- x (* y (sqrt z))))
(/ y (- x (* y (sqrt z))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(/ x (- x (* y (sqrt z))))
(/ x (- x (* y (sqrt z))))
(/ x (- x (* y (sqrt z))))
(/ x (- x (* 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)
(* 1/2 (* 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 x 2) z)) (* 1/2 (pow y 2))))
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2))))
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2))))
(* (pow y 2) z)
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* y (sqrt z))
(- (+ x (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z))))) (* -1 (* y (sqrt z))))
(- (+ x (+ (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z)))) (* (/ (pow x 2) y) (sqrt (/ 1 z))))) (+ (* -1 (* y (sqrt z))) (/ (pow x 3) (* (pow y 2) z))))
(- (+ x (+ (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z)))) (* (/ (pow x 2) y) (sqrt (/ 1 z))))) (+ (* -1 (* y (sqrt z))) (* (/ (pow x 4) (pow y 3)) (sqrt (/ 1 (pow z 3))))))
(* y (sqrt z))
(- x (* -1 (* y (sqrt z))))
(- (+ x (* (/ (pow x 2) y) (sqrt (/ 1 z)))) (* -1 (* y (sqrt z))))
(- (+ x (+ (* (/ (pow x 2) y) (sqrt (/ 1 z))) (/ (pow x 3) (* (pow y 2) z)))) (* -1 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (+ (* -1 (* (/ (pow x 2) y) (sqrt z))) (* x z)) z)))
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (/ (+ (* -1 (* (/ (pow x 2) y) (sqrt z))) (* x z)) z)) (* 1/2 (/ (- (* (/ (pow x 2) y) (sqrt (pow z 3))) (/ (* (pow x 3) z) (pow y 2))) (pow z 2)))))
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (/ (+ (* -1 (* (/ (pow x 2) y) (sqrt z))) (* x z)) z)) (+ (* 1/2 (/ (- (* (/ (pow x 2) y) (sqrt (pow z 3))) (/ (* (pow x 3) z) (pow y 2))) (pow z 2))) (* 1/2 (/ (- (/ (* (pow x 3) (pow z 2)) (pow y 2)) (* (/ (pow x 4) (pow y 3)) (sqrt (pow z 3)))) (pow z 3))))))
(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))
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z)))))
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z)))))
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z)))))
(* -1 (sqrt (/ 1 z)))
(/ (+ (* -1 (sqrt z)) (* -1 (/ x y))) z)
(/ (- (+ (* -1 (sqrt z)) (* -1 (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 z))))) (/ x y)) z)
(/ (- (+ (* -1 (sqrt z)) (* -1 (/ (pow x 3) (* (pow y 3) z)))) (+ (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 z))) (/ x y))) z)
(* -1 (* y (sqrt z)))
(+ (* -1 x) (* -1 (* y (sqrt z))))
(- (+ (* -1 (* y (sqrt z))) (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z))))) x)
(- (+ (* -1 (* y (sqrt z))) (* -1 (/ (pow x 3) (* (pow y 2) z)))) (+ x (* (/ (pow x 2) y) (sqrt (/ 1 z)))))
(* -1 (* (/ x y) (sqrt (/ 1 z))))
(/ (+ (* -1 (* (/ x y) (sqrt z))) (* -1 (/ (pow x 2) (pow y 2)))) z)
(/ (- (+ (* -1 (* (/ x y) (sqrt z))) (* -1 (* (/ (pow x 3) (pow y 3)) (sqrt (/ 1 z))))) (/ (pow x 2) (pow y 2))) z)
(/ (- (+ (* -1 (* (/ x y) (sqrt z))) (* -1 (/ (pow x 4) (* (pow y 4) z)))) (+ (* (/ (pow x 3) (pow y 3)) (sqrt (/ 1 z))) (/ (pow x 2) (pow y 2)))) 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)))
(* -1/2 (* (* 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)
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(+ (* -1 (sqrt (/ 1 z))) (* x (- (* x (- (* -1 (/ x (* (pow y 3) (pow z 2)))) (* (/ 1 (pow y 2)) (sqrt (/ 1 (pow z 3)))))) (/ 1 (* y z)))))
(* -1 (* y (sqrt z)))
(+ (* -1 x) (* -1 (* y (sqrt z))))
(+ (* -1 (* y (sqrt z))) (* x (- (* -1 (* (/ x y) (sqrt (/ 1 z)))) 1)))
(+ (* -1 (* y (sqrt z))) (* x (- (* x (- (* -1 (/ x (* (pow y 2) z))) (* (/ 1 y) (sqrt (/ 1 z))))) 1)))
(* -1 (* (/ x y) (sqrt (/ 1 z))))
(* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* -1 (/ x (* (pow y 2) z)))))
(* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* x (- (* -1 (* (/ x (pow y 3)) (sqrt (/ 1 (pow z 3))))) (/ 1 (* (pow y 2) z))))))
(* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* x (- (* x (- (* -1 (/ x (* (pow y 4) (pow z 2)))) (* (/ 1 (pow y 3)) (sqrt (/ 1 (pow z 3)))))) (/ 1 (* (pow y 2) 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 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2)))) (* -1 (* (/ y x) (sqrt z)))))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2)))) (* -1 (* (/ y x) (sqrt z)))))
(* -1 (/ (* (pow y 2) z) x))
(/ (- (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* (pow y 2) z)) x)
(/ (- (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (/ (* (pow y 4) (pow z 2)) (pow x 2)))) (* (pow y 2) z)) x)
(/ (- (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (+ (* -1 (* (/ (pow y 5) (pow x 3)) (sqrt (pow z 5)))) (* -1 (/ (* (pow y 4) (pow z 2)) (pow x 2))))) (* (pow y 2) z)) x)
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (+ (* -1/2 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2))) (* 1/2 (* (/ y x) (sqrt z))))))
(* x (+ 1/2 (+ (* -1/2 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2))) (* 1/2 (* (/ y x) (sqrt z))))))
(* -1 x)
(* x (- (* (/ y x) (sqrt z)) 1))
(* x (- (* (/ y x) (sqrt z)) 1))
(* x (- (* (/ y x) (sqrt z)) 1))
(/ y x)
(/ (+ y (* (/ (pow y 2) x) (sqrt z))) x)
(/ (- (+ y (/ (* (pow y 3) z) (pow x 2))) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x)
(/ (- (+ y (* (/ (pow y 4) (pow x 3)) (sqrt (pow z 3)))) (+ (* -1 (* (/ (pow y 2) x) (sqrt z))) (* -1 (/ (* (pow y 3) z) (pow x 2))))) x)
(/ (* (pow y 2) z) x)
(/ (+ (* (/ (pow y 3) x) (sqrt (pow z 3))) (* (pow y 2) z)) x)
(/ (- (+ (* (pow y 2) z) (/ (* (pow y 4) (pow z 2)) (pow x 2))) (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3))))) x)
(/ (- (+ (* (/ (pow y 5) (pow x 3)) (sqrt (pow z 5))) (* (pow y 2) z)) (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (/ (* (pow y 4) (pow z 2)) (pow x 2))))) x)
1
(+ 1 (* (/ y x) (sqrt z)))
(- (+ 1 (/ (* (pow y 2) z) (pow x 2))) (* -1 (* (/ y x) (sqrt z))))
(- (+ 1 (* (/ (pow y 3) (pow x 3)) (sqrt (pow z 3)))) (+ (* -1 (* (/ y x) (sqrt z))) (* -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)))
(* 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 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 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 (/ (* (pow y 2) z) x))
(* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (* (pow y 4) (pow z 2)) x)) (* (pow y 3) (sqrt (pow z 3)))) x)) (* -1 (* (pow y 2) z))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 5) x) (sqrt (pow z 5))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x)) (* -1 (* (pow y 2) z))) 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 x)
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z))))))
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z))))))
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z))))))
(/ y x)
(* -1 (/ (+ (* -1 y) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x))
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* (pow y 2) (sqrt z)) (/ (* (pow y 3) z) x)) x))) x))
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 4) x) (sqrt (pow z 3)))) (* -1 (* (pow y 3) z))) x)) (* (pow y 2) (sqrt z))) x))) x))
(/ (* (pow y 2) z) x)
(* -1 (/ (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (* (pow y 2) z))) x))
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* (pow y 3) (sqrt (pow z 3))) (/ (* (pow y 4) (pow z 2)) x)) x))) x))
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 5) x) (sqrt (pow z 5)))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x))) x))
1
(+ 1 (* (/ y x) (sqrt z)))
(+ 1 (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y (sqrt z))) x)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) (* y (sqrt z))) x)))
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) (- (* y (sqrt z)) x)))
(/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (-.f64 (*.f64 (sqrt.f64 z) y) x)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (-.f64 (*.f64 (sqrt.f64 z) y) x)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (-.f64 (*.f64 (sqrt.f64 z) y) x)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z)))
(fma.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z)))
(fma.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z)))
(fma.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z))
(/ (pow x 2) (- x (* y (sqrt z))))
(/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y)))
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z)))))
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y))))
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z)))))
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y))))
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z)))))
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z)))))
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))
(/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) 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 y y) #s(literal -1/2 binary64)) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) 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 y y) #s(literal -1/2 binary64)) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) 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 y y) #s(literal -1/2 binary64)) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) x) (-.f64 x (*.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))
(* 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)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(- (* y (sqrt z)) x)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(- (* y (sqrt z)) x)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(- (* y (sqrt z)) x)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(/ y (- x (* y (sqrt z))))
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ y (- x (* y (sqrt z))))
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ y (- x (* y (sqrt z))))
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ y (- x (* y (sqrt z))))
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(*.f64 (*.f64 y y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(*.f64 (*.f64 y y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(*.f64 (*.f64 y y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(/ (* (pow y 2) z) (- x (* y (sqrt z))))
(*.f64 (*.f64 y y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))))
(/ x (- x (* y (sqrt z))))
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ x (- x (* y (sqrt z))))
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ x (- x (* y (sqrt z))))
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
(/ x (- x (* y (sqrt z))))
(/.f64 x (-.f64 x (*.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 (*.f64 z #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y (/.f64 x z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y (/.f64 x z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y (/.f64 x z)))
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y (/.f64 x z)) z)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y (/.f64 x z)) z)
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y (/.f64 x z)) z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
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(* -1 (/ (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (* (pow y 2) z))) x))
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (*.f64 (*.f64 y y) z)) x)
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* (pow y 3) (sqrt (pow z 3))) (/ (* (pow y 4) (pow z 2)) x)) x))) x))
(/.f64 (fma.f64 (*.f64 y y) z (/.f64 (neg.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 z z) x) (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 x))) x)
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 5) x) (sqrt (pow z 5)))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x))) x))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) z (/.f64 (fma.f64 (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)) (/.f64 (neg.f64 (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) z) z (*.f64 (/.f64 (pow.f64 y #s(literal 5 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 5 binary64)))))) (neg.f64 x))) x))) x)
1
#s(literal 1 binary64)
(+ 1 (* (/ y x) (sqrt z)))
(fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64))
(+ 1 (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y (sqrt z))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 y (*.f64 y (/.f64 z x)) (*.f64 (sqrt.f64 z) y))) x))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) (* y (sqrt z))) x)))
(+.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (*.f64 (*.f64 y y) z)) x) (*.f64 (sqrt.f64 z) y)) x) #s(literal 1 binary64))

rewrite195.0ms (3%)

Memory
-0.3MiB live, 269.8MiB allocated
Rules
6 688×lower-fma.f32
6 680×lower-fma.f64
4 894×lower-/.f32
4 886×lower-/.f64
4 100×lower-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037214
065157
1227155
21548152
08808152
Stop Event
iter limit
node limit
iter limit
Counts
22 → 1 966
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 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
(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(literal 1 binary64) #s(literal 2 binary64))
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.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)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(*.f64 (sqrt.f64 z) y)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))
Outputs
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eval388.0ms (5.9%)

Memory
74.1MiB live, 632.7MiB allocated
Compiler

Compiled 96 289 to 5 545 computations (94.2% saved)

prune83.0ms (1.3%)

Memory
-70.2MiB live, 173.0MiB allocated
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2 82362 829
Fresh505
Picked235
Done000
Total2 83092 839
Accuracy
100.0%
Counts
2 839 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.8%
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
25.0%
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
92.2%
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
99.8%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
91.8%
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x))
92.1%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
52.2%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
95.2%
#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)))
49.5%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 185 to 146 computations (21.1% saved)

simplify136.0ms (2.1%)

Memory
23.3MiB live, 98.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 z y)
cost-diff0
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
cost-diff0
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
cost-diff0
(*.f64 (*.f64 y y) z)
cost-diff0
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z))
cost-diff0
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
cost-diff0
(+.f64 (/.f64 x y) (sqrt.f64 z))
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
cost-diff832
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)
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 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))
Rules
5 074×lower-fma.f32
5 070×lower-fma.f64
3 326×lower-*.f32
3 302×lower-*.f64
1 026×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039266
065266
199266
2140266
3226266
4419266
5676260
61458260
73761260
85305260
96454260
107151260
117506260
127741260
08009253
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.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)
(*.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 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y))
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)
(+.f64 (/.f64 x y) (sqrt.f64 z))
(/.f64 x y)
x
y
(sqrt.f64 z)
z
#s(literal 1/2 binary64)
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z))
(*.f64 (*.f64 y y) z)
(*.f64 y y)
y
z
#s(literal 1/2 binary64)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
x
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
(*.f64 z y)
z
y
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
#s(literal 1/2 binary64)
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)
(/.f64 (*.f64 y z) (sqrt.f64 z))
(*.f64 y z)
(sqrt.f64 z)
Outputs
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 y (sqrt.f64 z)) z x))
(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)
(*.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 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y))
#s(approx (+ (* (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x))
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)
(fma.f64 (sqrt.f64 z) y x)
(+.f64 (/.f64 x y) (sqrt.f64 z))
(/.f64 x y)
x
y
(sqrt.f64 z)
z
#s(literal 1/2 binary64)
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (sqrt.f64 z) y) x)) #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 z y) y)))
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 z y) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z))
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 z y) y))
(*.f64 (*.f64 y y) z)
(*.f64 (*.f64 z y) y)
(*.f64 y y)
y
z
#s(literal 1/2 binary64)
(-.f64 (*.f64 (sqrt.f64 z) y) x)
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
x
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 y (sqrt.f64 z)) z (neg.f64 x))) (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)))
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
(*.f64 z y)
z
y
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
#s(literal 1/2 binary64)
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)
(fma.f64 (/.f64 y (sqrt.f64 z)) z (neg.f64 x))
(/.f64 (*.f64 y z) (sqrt.f64 z))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(*.f64 y z)
(*.f64 z y)
(sqrt.f64 z)

localize89.0ms (1.4%)

Memory
4.1MiB live, 120.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.01171875
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)
accuracy1.5820257452111206
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
accuracy6.486491170645028
(/.f64 (*.f64 y z) (sqrt.f64 z))
accuracy28.80863559915213
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
accuracy0.23828125
(*.f64 (sqrt.f64 z) y)
accuracy7.4748743680171135
(*.f64 (*.f64 y y) z)
accuracy27.212899386633868
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z))
accuracy28.80863559915213
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
accuracy0
(sqrt.f64 z)
accuracy0
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y))
accuracy0.0078125
(+.f64 (/.f64 x y) (sqrt.f64 z))
accuracy5.075735930260777
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)
accuracy0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
accuracy0
(sqrt.f64 z)
accuracy0.23828125
(*.f64 (sqrt.f64 z) y)
accuracy30.49993912766908
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
accuracy0
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
accuracy0
(sqrt.f64 z)
accuracy0.17578125
(/.f64 y (sqrt.f64 z))
accuracy4.983146049881451
(fma.f64 (/.f64 y (sqrt.f64 z)) z x)
Samples
68.0ms256×0valid
Compiler

Compiled 230 to 31 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-mult: 20.0ms (50.6% of total)
ival-div: 10.0ms (25.3% of total)
ival-add: 4.0ms (10.1% of total)
ival-sub: 2.0ms (5.1% of total)
ival-sqrt: 2.0ms (5.1% of total)
ival-neg: 1.0ms (2.5% 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
-12.2MiB live, 63.6MiB allocated
Counts
21 → 672
Calls
Call 1
Inputs
#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 (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 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) (patch (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #<representation binary64>) () ())
#s(alt (+.f64 (/.f64 x y) (sqrt.f64 z)) (patch (+.f64 (/.f64 x y) (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) (patch (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) (patch #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 y y) z) (patch (*.f64 (*.f64 y y) z) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) (patch (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ())
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 y z) (sqrt.f64 z)) (patch (/.f64 (*.f64 y z) (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) (patch (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) #<representation binary64>) () ())
Outputs
#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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#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 (* y (sqrt z))) (taylor 0 z) (#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 (* y (sqrt z))) (taylor 0 z) (#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 (* y (sqrt z))) (taylor 0 z) (#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 (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 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 (* 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>) () ())) ())
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#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) (patch (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) (patch (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) (patch (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) (patch (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
7.0ms
z
@-inf
((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x))
3.0ms
y
@-inf
((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x))
2.0ms
z
@0
((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x))
2.0ms
y
@0
((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x))
2.0ms
y
@inf
((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x))

simplify181.0ms (2.7%)

Memory
25.6MiB live, 216.0MiB allocated
Algorithm
egg-herbie
Rules
7 848×lower-fma.f64
7 848×lower-fma.f32
5 248×lower-*.f64
5 248×lower-*.f32
3 290×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02535866
18345663
229695484
370965482
081515203
Stop Event
iter limit
node limit
Counts
672 → 660
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 (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 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))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* 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) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x)))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(* -1/2 (pow x 2))
(+ (* -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 (pow x 2))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) z)
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x)))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x))))
(* -1/2 (pow x 2))
(+ (* -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 (pow x 2))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(* y z)
(* y z)
(* y z)
(* y z)
(* 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)) x)
(* 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 (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 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))))
(* 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 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))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(sqrt z)
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(* z (+ (sqrt (/ 1 z)) (/ x (* 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 x 2) z)) (* 1/2 (pow y 2))))
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2))))
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2))))
(* (pow y 2) z)
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) 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 x 2) z)) (* 1/2 (pow y 2))))
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2))))
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2))))
(* (pow y 2) z)
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2)))
(* y z)
(* y z)
(* y z)
(* y z)
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z)))))
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z)))))
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* y (sqrt z))
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (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 (* (* 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 (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 (* 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 (* 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 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(* -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 y 2)) (* 1/2 (/ (pow x 2) z)))))
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z)))))
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z)))))
(* (pow y 2) z)
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z))))
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z))))
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z))))
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) z)
(* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
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(+ (* -1 (/ (+ (* 1/2 (* (/ (* x (* (pow (sqrt -1) 2) (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) y) (sqrt (/ 1 z)))) (* 1/2 (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))))
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x
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
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x
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(+ x (* y (sqrt z)))
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(/ x y)
(/ (+ x (* y (sqrt z))) y)
(/ (+ x (* y (sqrt z))) y)
(/ (+ x (* y (sqrt z))) y)
(* 1/2 x)
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* -1/2 (pow x 2))
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(* y z)
(* y z)
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(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* (pow y 2) z))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
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(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
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(* y z)
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(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
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(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* 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 (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))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(sqrt z)
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ 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 (* (pow y 2) z))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) z)
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) z)
(* (pow y 2) 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 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z)))
(* (pow y 2) z)
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2)))))
(* y z)
(* y z)
(* y z)
(* y z)
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(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (/ x y))))
(* -1 (* y (+ (* -1 (sqrt z)) (/ x y))))
(* -1 (* y (+ (* -1 (sqrt z)) (/ x 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)))
(* 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)))
(sqrt z)
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x 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))))
(* 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)) (* 1/2 (* (pow y 2) z)))
(* (pow y 2) z)
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
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(+ (* -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)))
(* (pow y 2) z)
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
(+ (* -1 (pow x 2)) (* (pow y 2) z))
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(+ (* -1 x) (* y (sqrt z)))
(+ (* -1 x) (* y (sqrt z)))
(* 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
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(* 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))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 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))))
(/ x y)
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(* 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 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* 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)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
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(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
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(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* -1 x)
(* x (- (* (/ y x) (sqrt z)) 1))
(* x (- (* (/ y x) (sqrt z)) 1))
(* x (- (* (/ 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
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(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
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(* -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)))
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 y)
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(* 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 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 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 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z))))))
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z))))))
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z))))))
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 (/ 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)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
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(*.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))
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(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
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(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x))
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(-.f64 (*.f64 (sqrt.f64 z) y) x)

rewrite195.0ms (3%)

Memory
1.2MiB live, 229.7MiB allocated
Rules
5 310×lower-fma.f32
5 306×lower-fma.f64
4 446×lower-/.f32
4 436×lower-/.f64
4 422×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039214
065201
1198201
21316196
09205189
Stop Event
iter limit
node limit
iter limit
Counts
21 → 876
Calls
Call 1
Inputs
(*.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))
(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 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y))
(+.f64 (/.f64 x y) (sqrt.f64 z))
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64))
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z))
(*.f64 (*.f64 y y) z)
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))
(*.f64 z y)
(/.f64 (*.f64 y z) (sqrt.f64 z))
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)
Outputs
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eval234.0ms (3.6%)

Memory
27.8MiB live, 418.8MiB allocated
Compiler

Compiled 35 020 to 3 349 computations (90.4% saved)

prune110.0ms (1.7%)

Memory
7.3MiB live, 122.2MiB allocated
Pruning

8 alts after pruning (3 fresh and 5 done)

PrunedKeptTotal
New1 75231 755
Fresh101
Picked325
Done033
Total1 75681 764
Accuracy
100.0%
Counts
1 764 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
47.8%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
47.4%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64))
46.8%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
92.1%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
52.2%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
95.2%
#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)))
49.5%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 72 to 72 computations (0% saved)

simplify29.0ms (0.4%)

Memory
-23.9MiB live, 33.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 z y)
cost-diff0
(/.f64 (*.f64 z y) (sqrt.f64 z))
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z)))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))))
cost-diff0
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64))
cost-diff320
(*.f64 z #s(literal 1 binary64))
cost-diff1088
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 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))
Rules
148×times-frac
116×lower-*.f32
108×lower-*.f64
90×lower-/.f32
80×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023152
035136
154136
281136
3102136
4123136
5124136
6165136
7235136
8317136
9318136
0318130
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))
#s(literal 1 binary64)
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))
(/.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
z
y
(*.f64 z #s(literal 1 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z)))
(/.f64 (*.f64 z y) (sqrt.f64 z))
(*.f64 z y)
z
y
(sqrt.f64 z)
#s(literal 1/2 binary64)
Outputs
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)))
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
#s(literal 1 binary64)
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))
(/.f64 (/.f64 (sqrt.f64 z) y) z)
(/.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
z
y
(*.f64 z #s(literal 1 binary64))
z
#s(literal 1/2 binary64)
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z)))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
(/.f64 (*.f64 z y) (sqrt.f64 z))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(*.f64 z y)
(*.f64 y z)
z
y
(sqrt.f64 z)
#s(literal 1/2 binary64)

localize52.0ms (0.8%)

Memory
6.9MiB live, 79.0MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 z y)
accuracy0
(sqrt.f64 z)
accuracy6.486491170645028
(/.f64 (*.f64 z y) (sqrt.f64 z))
accuracy30.49993912766908
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z)))
accuracy0.2421875
(/.f64 (sqrt.f64 z) y)
accuracy0.5019902531452896
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))
accuracy7.113432028837478
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))
accuracy30.49993912766908
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))))
accuracy0
(sqrt.f64 z)
accuracy0.17578125
(/.f64 y (sqrt.f64 z))
accuracy7.598177951658053
(*.f64 (/.f64 y (sqrt.f64 z)) z)
accuracy30.49993912766908
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))
Samples
39.0ms256×0valid
Compiler

Compiled 104 to 19 computations (81.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-div: 7.0ms (31% of total)
ival-mult: 7.0ms (31% of total)
ival-sqrt: 7.0ms (31% of total)
ival-add: 1.0ms (4.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series103.0ms (1.6%)

Memory
-7.6MiB live, 29.8MiB allocated
Counts
15 → 408
Calls
Call 1
Inputs
#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(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 z y) (sqrt.f64 z)) (patch (/.f64 (*.f64 z y) (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) (patch (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 z) y) (patch (/.f64 (sqrt.f64 z) y) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#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 (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#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 (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#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 (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#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 (+ x (* y (sqrt z))) (taylor 0 z) (#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 (+ x (* y (sqrt z))) (taylor 0 z) (#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 (+ x (* y (sqrt z))) (taylor 0 z) (#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 (+ x (* y (sqrt z))) (taylor 0 z) (#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 (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #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 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #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 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #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 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #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 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (*.f64 z y) (sqrt.f64 z)) (patch (/.f64 (*.f64 z y) (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (*.f64 z y) (sqrt.f64 z)) (patch (/.f64 (*.f64 z y) (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (*.f64 z y) (sqrt.f64 z)) (patch (/.f64 (*.f64 z y) (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (*.f64 z y) (sqrt.f64 z)) (patch (/.f64 (*.f64 z y) (sqrt.f64 z)) #<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 (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>) () ())) ())
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#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 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #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 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (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 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
81.0ms
y
@0
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y))
3.0ms
z
@-inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y))
2.0ms
y
@-inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y))
2.0ms
z
@0
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y))
1.0ms
y
@inf
((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y))

simplify145.0ms (2.2%)

Memory
10.8MiB live, 133.3MiB allocated
Algorithm
egg-herbie
Rules
4 106×lower-*.f64
4 106×lower-*.f32
3 286×lower-fma.f64
3 286×lower-fma.f32
1 958×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0842454
12792358
28742358
328282286
462472286
082752118
Stop Event
iter limit
node limit
Counts
408 → 387
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))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt (/ 1 z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
z
z
z
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)))
(* 1/2 (+ 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)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 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)))
(* 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)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
z
z
z
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)))
(* 1/2 (* 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)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 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))))))
(* 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)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
z
z
z
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))))))
(* -1/2 (* (* 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)
(* -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 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))))
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))))
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z))))
(* -1 (* (/ (pow (sqrt -1) 2) y) (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)))
(* 1/2 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)))
(* 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)))
(* 1/2 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)
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 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)))
(* 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))))
(* 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)
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 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)))
(* 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)))))
(* 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)
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 y) (sqrt z))
(* (/ 1 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))))
(* 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)))
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)
(* 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)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
(* y (sqrt z))
(*.f64 (sqrt.f64 z) y)
z
z
z
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)
(* 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)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)
(* (/ 1 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))))
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x
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rewrite390.0ms (5.9%)

Memory
-15.9MiB live, 143.3MiB allocated
Rules
3 958×lower-fma.f64
3 958×lower-fma.f32
3 634×lower-*.f32
3 626×lower-*.f64
2 688×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023138
035122
197122
2433103
33215103
0814997
Stop Event
iter limit
node limit
iter limit
Counts
15 → 704
Calls
Call 1
Inputs
(*.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(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))
(*.f64 z #s(literal 1 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z)))
(/.f64 (*.f64 z y) (sqrt.f64 z))
(*.f64 z y)
(sqrt.f64 z)
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))
(/.f64 (sqrt.f64 z) y)
Outputs
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eval617.0ms (9.4%)

Memory
-172.7MiB live, 223.5MiB allocated
Compiler

Compiled 16 474 to 2 741 computations (83.4% saved)

prune53.0ms (0.8%)

Memory
31.4MiB live, 106.8MiB allocated
Pruning

8 alts after pruning (1 fresh and 7 done)

PrunedKeptTotal
New1 20611 207
Fresh000
Picked123
Done055
Total1 20781 215
Accuracy
100.0%
Counts
1 215 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
47.8%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
52.1%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
46.8%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
92.1%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
52.2%
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
95.2%
#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)))
49.5%
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 334 to 164 computations (50.9% saved)

regimes85.0ms (1.3%)

Memory
-9.1MiB live, 73.7MiB allocated
Counts
21 → 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 z y) (sqrt.f64 z))) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #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)))
(*.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 (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))
(/.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 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sqrt.f64 z) y) x) (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x))
(*.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 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 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:

34.0ms
(*.f64 y (sqrt.f64 z))
18.0ms
z
7.0ms
(sqrt.f64 z)
7.0ms
y
6.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1y
99.8%1z
99.8%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
99.8%1(+.f64 x (*.f64 y (sqrt.f64 z)))
99.8%1(*.f64 y (sqrt.f64 z))
99.8%1(sqrt.f64 z)
Compiler

Compiled 25 to 34 computations (-36% saved)

regimes22.0ms (0.3%)

Memory
-4.1MiB live, 33.8MiB 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:

10.0ms
z
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
2.0ms
(sqrt.f64 z)
2.0ms
(*.f64 y (sqrt.f64 z))
2.0ms
y
Results
AccuracySegmentsBranch
76.1%3x
75.4%3y
65.5%2z
66.1%5(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
66.1%5(+.f64 x (*.f64 y (sqrt.f64 z)))
76.8%3(*.f64 y (sqrt.f64 z))
65.5%2(sqrt.f64 z)
Compiler

Compiled 25 to 34 computations (-36% saved)

regimes13.0ms (0.2%)

Memory
-3.4MiB live, 30.8MiB 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:

4.0ms
(+.f64 x (*.f64 y (sqrt.f64 z)))
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
1.0ms
(sqrt.f64 z)
1.0ms
x
1.0ms
z
Results
AccuracySegmentsBranch
49.5%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
49.5%1(+.f64 x (*.f64 y (sqrt.f64 z)))
49.5%1z
49.5%1(sqrt.f64 z)
49.5%1y
49.5%1x
49.5%1(*.f64 y (sqrt.f64 z))
Compiler

Compiled 25 to 34 computations (-36% saved)

bsearch1.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
2.109919871678362e-93
1.1254345654938374e-89
0.0ms
-1.7159403214766657e-15
-6.5161860743525674e-21
Compiler

Compiled 13 to 16 computations (-23.1% saved)

simplify24.0ms (0.4%)

Memory
31.7MiB live, 68.9MiB allocated
Algorithm
egg-herbie
Rules
*-commutative-binary64-*.f64
1-exp-binary32-exp.f32
1-exp-binary64-exp.f64
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 -2535301200456459/2535301200456458802993406410752 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 2348542582773833/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 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 -2535301200456459/2535301200456458802993406410752 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 2348542582773833/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 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 -2535301200456459/2535301200456458802993406410752 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 2348542582773833/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 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))

soundness527.0ms (8%)

Memory
-21.8MiB live, 292.5MiB allocated
Rules
7 460×lower-fma.f64
7 460×lower-fma.f32
5 642×lower-fma.f64
5 642×lower-fma.f32
4 298×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

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

Compiled 91 to 50 computations (45.1% saved)

preprocess47.0ms (0.7%)

Memory
-11.2MiB live, 51.5MiB 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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