Numeric.Interval.Internal:bisect from intervals-0.7.1, A

Time bar (total: 5.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.6s (47.8%)

Memory
-172.1MiB live, 836.7MiB allocated
Samples
1.3s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 192.0ms
ival-div: 73.0ms (37.9% of total)
ival-sub: 59.0ms (30.7% of total)
ival-add: 47.0ms (24.4% of total)
ival-true: 6.0ms (3.1% of total)
exact: 5.0ms (2.6% of total)
ival-assert: 3.0ms (1.6% of total)
Bogosity

explain93.0ms (1.7%)

Memory
11.6MiB live, 126.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
00-0-(-.f64 y x)
00-0-y
00-0-#s(literal 2 binary64)
00-0-(/.f64 (-.f64 y x) #s(literal 2 binary64))
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
25.0ms512×0valid
Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-div: 4.0ms (41.2% of total)
ival-sub: 3.0ms (30.9% of total)
ival-add: 2.0ms (20.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess367.0ms (6.7%)

Memory
-11.2MiB live, 301.9MiB allocated
Algorithm
1×egg-herbie
Rules
9 566×lower-fma.f64
9 566×lower-fma.f32
1 665×associate-+r+
1 004×associate-+r-
970×lower-+.f32
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
01641
14435
213735
338029
464425
594225
6232525
7310025
8341725
9351625
10358125
11358425
12360025
13360925
14360925
15360925
16360925
067
097
1157
2267
3467
4877
51507
63267
75326
812675
919835
1023945
1124125
1224265
1324265
1433665
1539095
1640655
1741245
1845325
1963725
2070365
2179685
083225
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Outputs
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
Symmetry

(sort x y)

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify272.0ms (5%)

Memory
18.1MiB live, 215.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 y x)
cost-diff192
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
cost-diff384
(/.f64 (-.f64 y x) #s(literal 2 binary64))
Rules
9 566×lower-fma.f64
9 566×lower-fma.f32
970×lower-+.f32
969×lower-+.f64
942×lower--.f32
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
0618
0918
11518
22618
34618
48718
515018
632618
753217
8126716
9198316
10239416
11241216
12242616
13242616
14336616
15390916
16406516
17412416
18453216
19637216
20703616
21796816
0832216
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
x
(/.f64 (-.f64 y x) #s(literal 2 binary64))
(-.f64 y x)
y
#s(literal 2 binary64)
Outputs
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
x
(/.f64 (-.f64 y x) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 y x))
(-.f64 y x)
y
#s(literal 2 binary64)

localize42.0ms (0.8%)

Memory
-3.8MiB live, 40.8MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 (-.f64 y x) #s(literal 2 binary64))
accuracy0
(-.f64 y x)
accuracy0.0234375
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Samples
36.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-sub: 7.0ms (71.2% of total)
ival-div: 2.0ms (20.3% of total)
ival-add: 1.0ms (10.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
5.3MiB live, 5.3MiB allocated
Counts
3 → 72
Calls
Call 1
Inputs
#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())
Outputs
#s(alt (* -1/2 x) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 x) (* 1/2 y)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 x) (* 1/2 y)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 x) (* 1/2 y)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (* -1/2 (/ x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (* -1/2 (/ x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (* -1/2 (/ x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* 1/2 (/ x y)) 1/2))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* 1/2 (/ x y)) 1/2))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* 1/2 (/ x y)) 1/2))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 (/ y x)) 1/2)) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 (/ y x)) 1/2)) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 (/ y x)) 1/2)) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/2 (* -1/2 (/ y x))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/2 (* -1/2 (/ y x))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/2 (* -1/2 (/ y x))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) #s(literal 2 binary64)) (patch (/.f64 (-.f64 y x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 x)) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
Calls

18 calls:

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

simplify225.0ms (4.1%)

Memory
-32.4MiB live, 215.4MiB allocated
Algorithm
1×egg-herbie
Rules
6 300×lower-fma.f64
6 300×lower-fma.f32
917×lower-*.f64
917×lower-*.f32
801×lower--.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057315
1177315
2498279
31491279
45234279
57541279
08288279
Stop Event
1×iter limit
1×node limit
Counts
72 → 69
Calls
Call 1
Inputs
(* -1/2 x)
(+ (* -1/2 x) (* 1/2 y))
(+ (* -1/2 x) (* 1/2 y))
(+ (* -1/2 x) (* 1/2 y))
(* 1/2 y)
(* y (+ 1/2 (* -1/2 (/ x y))))
(* y (+ 1/2 (* -1/2 (/ x y))))
(* y (+ 1/2 (* -1/2 (/ x y))))
(* 1/2 y)
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(* 1/2 y)
(+ (* -1/2 x) (* 1/2 y))
(+ (* -1/2 x) (* 1/2 y))
(+ (* -1/2 x) (* 1/2 y))
(* -1/2 x)
(* x (- (* 1/2 (/ y x)) 1/2))
(* x (- (* 1/2 (/ y x)) 1/2))
(* x (- (* 1/2 (/ y x)) 1/2))
(* -1/2 x)
(* -1 (* x (+ 1/2 (* -1/2 (/ y x)))))
(* -1 (* x (+ 1/2 (* -1/2 (/ y x)))))
(* -1 (* x (+ 1/2 (* -1/2 (/ y x)))))
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(+ x (* -1/2 x))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(* 1/2 y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* 1/2 y)
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 x)
(- y x)
(- y x)
(- y x)
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
Outputs
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(+ (* -1/2 x) (* 1/2 y))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(+ (* -1/2 x) (* 1/2 y))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(+ (* -1/2 x) (* 1/2 y))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* y (+ 1/2 (* -1/2 (/ x y))))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* y (+ 1/2 (* -1/2 (/ x y))))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* y (+ 1/2 (* -1/2 (/ x y))))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* -1/2 x) (* 1/2 y))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(+ (* -1/2 x) (* 1/2 y))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(+ (* -1/2 x) (* 1/2 y))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/2 (/ y x)) 1/2))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ y x)) 1/2))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ y x)) 1/2))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (+ 1/2 (* -1/2 (/ y x)))))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (+ 1/2 (* -1/2 (/ y x)))))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (+ 1/2 (* -1/2 (/ y x)))))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+ x (* -1/2 x))
(*.f64 #s(literal 1/2 binary64) x)
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(* -1 x)
(neg.f64 x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
y
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y x)
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y x)
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y x)
y
(* -1 (* y (- (/ x y) 1)))
(-.f64 y x)
(* -1 (* y (- (/ x y) 1)))
(-.f64 y x)
(* -1 (* y (- (/ x y) 1)))
(-.f64 y x)
y
(+ y (* -1 x))
(-.f64 y x)
(+ y (* -1 x))
(-.f64 y x)
(+ y (* -1 x))
(-.f64 y x)
(* -1 x)
(neg.f64 x)
(* x (- (/ y x) 1))
(-.f64 y x)
(* x (- (/ y x) 1))
(-.f64 y x)
(* x (- (/ y x) 1))
(-.f64 y x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 y x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 y x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 y x)

rewrite220.0ms (4%)

Memory
47.4MiB live, 225.2MiB allocated
Rules
2 040×lower-fma.f64
2 040×lower-fma.f32
1 920×lower-*.f64
1 920×lower-*.f32
1 299×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
14815
240015
3508215
0821114
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 344
Calls
Call 1
Inputs
(/.f64 (-.f64 y x) #s(literal 2 binary64))
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(-.f64 y x)
Outputs
(*.f64 (/.f64 (*.f64 (+.f64 x y) (*.f64 #s(literal -1/2 binary64) (-.f64 x y))) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (fma.f64 (-.f64 x y) x (*.f64 y y)))
(*.f64 (/.f64 (*.f64 (+.f64 x y) (*.f64 #s(literal -1/2 binary64) (-.f64 x y))) (*.f64 (+.f64 x y) (-.f64 y x))) (-.f64 y x))
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 (*.f64 y y) (*.f64 (+.f64 x y) x)))) (-.f64 (*.f64 y y) (*.f64 (+.f64 x y) x)))
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (fma.f64 (*.f64 (*.f64 (+.f64 x y) x) (*.f64 (+.f64 x y) x)) (*.f64 (+.f64 x y) x) (*.f64 (*.f64 (*.f64 y y) (*.f64 y y)) (*.f64 y y)))) (fma.f64 (*.f64 (+.f64 x y) x) (-.f64 (*.f64 (+.f64 x y) x) (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 y y))))
(*.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 x y)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 x y)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (+.f64 x y) #s(literal 2 binary64)) (/.f64 (-.f64 y x) (+.f64 x y)))
(*.f64 (/.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) #s(literal 2 binary64)) (/.f64 (-.f64 y x) (fma.f64 (+.f64 x y) x (*.f64 y y))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 (+.f64 x y) (-.f64 x y)))) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y))))
(*.f64 (*.f64 (+.f64 x y) (*.f64 #s(literal -1/2 binary64) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y))))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 #s(literal -1/2 binary64) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x y))))
(*.f64 #s(literal -1/2 binary64) (-.f64 x y))
(*.f64 (fma.f64 (*.f64 (*.f64 y y) y) #s(literal 1/8 binary64) (neg.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 (*.f64 y y) #s(literal 1/4 binary64)))))
(*.f64 (fma.f64 #s(literal 2 binary64) y (*.f64 #s(literal -2 binary64) x)) #s(literal 1/4 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 y x)))
(*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (*.f64 (+.f64 x y) #s(literal 2 binary64))))
(*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 2 binary64)))
(*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) #s(literal 2 binary64))))
(*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) (+.f64 x y)))
(*.f64 #s(literal 1/2 binary64) (-.f64 y x))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 x y)))
(*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (/.f64 (-.f64 y x) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) #s(literal 2 binary64))))
(*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y))) #s(literal 2 binary64)))
(*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y))) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) #s(literal 2 binary64))))
(*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y))))
(*.f64 (-.f64 x y) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 x y)) #s(literal 1 binary64))
(*.f64 (-.f64 y x) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (neg.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 x y))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 x y)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (+.f64 x y) (*.f64 (+.f64 x y) (*.f64 #s(literal -1/2 binary64) (-.f64 x y)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 #s(literal -1/2 binary64) (-.f64 x y)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 (*.f64 y y) #s(literal 1/4 binary64))) (fma.f64 (*.f64 (*.f64 y y) y) #s(literal 1/8 binary64) (neg.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) y (*.f64 #s(literal -2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -4 binary64) (-.f64 y x)) (-.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (-.f64 x y)) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 x y)) #s(literal 1 binary64))
(/.f64 (*.f64 (*.f64 (+.f64 x y) (*.f64 #s(literal -1/2 binary64) (-.f64 x y))) #s(literal 1 binary64)) (+.f64 x y))
(/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) #s(literal 1 binary64)) (fma.f64 (+.f64 x y) x (*.f64 y y)))
(/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 #s(literal -1/2 binary64) (-.f64 x y))) #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 y y) y) #s(literal 1/8 binary64) (neg.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)))) #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 (*.f64 y y) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) y (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 4 binary64))
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1/2 binary64)) (+.f64 x y))
(/.f64 (*.f64 (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y)) #s(literal -1/2 binary64)) (fma.f64 (+.f64 x y) x (*.f64 y y)))
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) #s(literal -1/2 binary64)) (neg.f64 (+.f64 x y)))
(/.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) #s(literal -1/2 binary64)) (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y))))
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) #s(literal 1/2 binary64)) (neg.f64 (+.f64 x y)))
(/.f64 (*.f64 (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 x y) (-.f64 x y))) (neg.f64 (+.f64 x y)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y))) (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (*.f64 #s(literal -1/2 binary64) (-.f64 x y)))) (+.f64 x y))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)))) (fma.f64 (+.f64 x y) x (*.f64 y y)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 #s(literal -1/2 binary64) (-.f64 x y)))) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 y y) y) #s(literal 1/8 binary64) (neg.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64))))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)) (*.f64 (*.f64 y y) #s(literal 1/4 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) y (*.f64 #s(literal -2 binary64) x))) #s(literal 4 binary64))
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) #s(literal 1 binary64)) (*.f64 (+.f64 x y) #s(literal 2 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) #s(literal 1 binary64)) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 y x))) (*.f64 (+.f64 x y) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 y y) #s(literal 1/4 binary64)) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 x #s(literal -1/2 binary64))))
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(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (+.f64 x y))) (fma.f64 (*.f64 y y) (*.f64 y y) (*.f64 (*.f64 x x) (fma.f64 x x (*.f64 y y)))))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y)))) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)))
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(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) #s(literal 1 binary64)) (+.f64 x y))
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(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 x y))) (neg.f64 (+.f64 x y)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y))) (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 y x))) (+.f64 x y))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (fma.f64 (+.f64 x y) x (*.f64 y y)))
(/.f64 (-.f64 (*.f64 (*.f64 y (/.f64 y (+.f64 x y))) (*.f64 y (/.f64 y (+.f64 x y)))) (*.f64 (*.f64 x (/.f64 x (+.f64 x y))) (*.f64 x (/.f64 x (+.f64 x y))))) (fma.f64 y (/.f64 y (+.f64 x y)) (*.f64 x (/.f64 x (+.f64 x y)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y))))) (*.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))))) (fma.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (-.f64 (neg.f64 x) y))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 y (/.f64 y (+.f64 x y))) (*.f64 y (/.f64 y (+.f64 x y)))) (*.f64 y (/.f64 y (+.f64 x y)))) (*.f64 (*.f64 (*.f64 x (/.f64 x (+.f64 x y))) (*.f64 x (/.f64 x (+.f64 x y)))) (*.f64 x (/.f64 x (+.f64 x y))))) (fma.f64 (*.f64 y (/.f64 y (+.f64 x y))) (*.f64 y (/.f64 y (+.f64 x y))) (fma.f64 (*.f64 x (/.f64 x (+.f64 x y))) (*.f64 x (/.f64 x (+.f64 x y))) (*.f64 (*.f64 y (/.f64 y (+.f64 x y))) (*.f64 x (/.f64 x (+.f64 x y)))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y))))) (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y))))) (*.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))))) (fma.f64 (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))) (*.f64 (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (neg.f64 (neg.f64 (+.f64 x y))))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (+.f64 x y))
(/.f64 (neg.f64 (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y))) (neg.f64 (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y))) (fma.f64 (+.f64 x y) x (*.f64 y y)))
(/.f64 (-.f64 (*.f64 (*.f64 y y) (+.f64 x y)) (*.f64 (+.f64 x y) (*.f64 x x))) (*.f64 (+.f64 x y) (+.f64 x y)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 y y) y) (fma.f64 (+.f64 x y) x (*.f64 y y))) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (fma.f64 (+.f64 x y) x (*.f64 y y))))
(/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 y x))) (*.f64 (+.f64 x y) (fma.f64 x x (*.f64 y y))))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 y y) (*.f64 y y)) (*.f64 y y)) (*.f64 (*.f64 y y) y) (neg.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x)))) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (fma.f64 (*.f64 (*.f64 y y) (*.f64 (*.f64 y y) y)) y (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))))))
(/.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (*.f64 (+.f64 x y) (fma.f64 (*.f64 y y) (*.f64 y y) (*.f64 (*.f64 x x) (fma.f64 x x (*.f64 y y))))))
(/.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))))
(/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (neg.f64 (+.f64 x y)))
(/.f64 (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 x y)) (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
(/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (neg.f64 (neg.f64 (+.f64 x y))))
(/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (+.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 x y)))
(/.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (fma.f64 x x (-.f64 (*.f64 y y) (*.f64 (neg.f64 x) y))))
(/.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (neg.f64 (neg.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(/.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (fma.f64 (+.f64 x y) x (*.f64 y y)))
(neg.f64 (-.f64 x y))
(fma.f64 (/.f64 (*.f64 (*.f64 y y) y) (*.f64 (fma.f64 (+.f64 x y) x (*.f64 y y)) (-.f64 (*.f64 y y) (*.f64 (+.f64 x y) x)))) (-.f64 (*.f64 y y) (*.f64 (+.f64 x y) x)) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(fma.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 (*.f64 (*.f64 (+.f64 x y) x) (*.f64 (+.f64 x y) x)) (*.f64 (+.f64 x y) x) (*.f64 (*.f64 (*.f64 y y) (*.f64 y y)) (*.f64 y y)))) (fma.f64 (*.f64 (+.f64 x y) x) (-.f64 (*.f64 (+.f64 x y) x) (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 y y))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(fma.f64 (/.f64 (*.f64 y y) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))) (fma.f64 (-.f64 x y) x (*.f64 y y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (-.f64 y x))) (-.f64 y x) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (pow.f64 y #s(literal 3/2 binary64)) (fma.f64 (+.f64 x y) x (*.f64 y y))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(fma.f64 #s(literal -1 binary64) x y)
(fma.f64 (neg.f64 x) #s(literal 1 binary64) (*.f64 y #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) (*.f64 #s(literal 1 binary64) y))
(fma.f64 #s(literal 1 binary64) y (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(fma.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 (*.f64 (*.f64 y y) y) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x y) x (*.f64 y y))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(fma.f64 x #s(literal -1 binary64) y)
(fma.f64 y (/.f64 (*.f64 y y) (fma.f64 (+.f64 x y) x (*.f64 y y))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(fma.f64 y (/.f64 y (+.f64 x y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 y #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 (+.f64 y #s(literal 0 binary64)) x)
(-.f64 (*.f64 y (/.f64 y (+.f64 x y))) (*.f64 x (/.f64 x (+.f64 x y))))
(-.f64 (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y))))
(-.f64 #s(literal 0 binary64) (-.f64 x y))
(-.f64 y x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #s(literal -1 binary64)))
(+.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 y #s(literal 1 binary64)))
(+.f64 (*.f64 y #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) y))
(+.f64 (*.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(+.f64 (neg.f64 (neg.f64 y)) (neg.f64 x))
(+.f64 (*.f64 y (/.f64 y (+.f64 x y))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(+.f64 (*.f64 (*.f64 y y) (/.f64 y (fma.f64 (+.f64 x y) x (*.f64 y y)))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (+.f64 x y) x (*.f64 y y)))))
(+.f64 (neg.f64 x) y)
(+.f64 y (neg.f64 x))

eval71.0ms (1.3%)

Memory
-15.9MiB live, 153.6MiB allocated
Compiler

Compiled 8 747 to 1 088 computations (87.6% saved)

prune56.0ms (1%)

Memory
5.3MiB live, 125.1MiB allocated
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4103413
Fresh000
Picked101
Done000
Total4113414
Accuracy
100.0%
Counts
414 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
▶51.1%
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
▶49.7%
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 20 to 13 computations (35% saved)

simplify230.0ms (4.2%)

Memory
-7.7MiB live, 192.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 y x)
cost-diff0
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 y #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
Rules
9 026×lower-fma.f64
9 026×lower-fma.f32
1 172×lower--.f64
1 172×lower--.f32
914×lower-*.f32
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
01456
01856
12856
24156
36156
410256
517156
636856
760950
8151450
9218850
10256550
11258150
12259350
13259350
14355250
15410450
16426050
17431850
18472650
19657050
20723450
0807650
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)
y
x
#s(literal 1/2 binary64)
Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
y
#s(literal 1/2 binary64)
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)
y
x
#s(literal 1/2 binary64)

localize53.0ms (1%)

Memory
3.5MiB live, 83.4MiB allocated
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 y x)
accuracy0
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
accuracy0
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
accuracy0
(*.f64 y #s(literal 1/2 binary64))
accuracy31.265303177340627
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy32.16218127241832
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
Samples
37.0ms256×0valid
Compiler

Compiled 44 to 13 computations (70.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-div: 18.0ms (63.1% of total)
ival-add: 4.0ms (14% of total)
ival-mult: 4.0ms (14% of total)
ival-sub: 1.0ms (3.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
-23.0MiB live, 13.8MiB allocated
Counts
7 → 144
Calls
Call 1
Inputs
#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.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 (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 y) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 x)) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 x)) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 x)) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (+ (* -1/2 x) (* 1/2 y))) (taylor 0 y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2))) (taylor -inf y) (#s(alt #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (patch #s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1/2 (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 (/ x y)) 1/2))) (taylor -inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 (/ x y)) 1/2))) (taylor -inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 (/ x y)) 1/2))) (taylor -inf y) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 y)) (taylor 0 x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (/ y x)))) (taylor inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y x)) 1/2))) (taylor -inf x) (#s(alt (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (*.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
Calls

36 calls:

TimeVariablePointExpression
1.0ms
x
@0
(* (+ y x) 1/2)
0.0ms
x
@0
(* 1/2 x)
0.0ms
x
@-inf
(* 1/2 x)
0.0ms
x
@inf
(* 1/2 x)
0.0ms
y
@inf
(* (+ y x) 1/2)

simplify178.0ms (3.2%)

Memory
38.7MiB live, 265.1MiB allocated
Algorithm
1×egg-herbie
Rules
8 011×lower-fma.f64
8 011×lower-fma.f32
1 213×lower-*.f64
1 213×lower-*.f32
827×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050564
1153564
2370564
31193564
44180564
56758564
08288564
Stop Event
1×iter limit
1×node limit
Counts
144 → 138
Calls
Call 1
Inputs
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(+ x (* -1/2 x))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(* 1/2 y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* 1/2 y)
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(+ x (* -1/2 x))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(* 1/2 y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* 1/2 y)
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(+ x (* -1/2 x))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(* 1/2 y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* 1/2 y)
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* 1/2 y)
(* y (+ 1/2 (* 1/2 (/ x y))))
(* y (+ 1/2 (* 1/2 (/ x y))))
(* y (+ 1/2 (* 1/2 (/ x y))))
(* 1/2 y)
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
Outputs
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (* -1/2 x))
(*.f64 x #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (* -1/2 x))
(*.f64 x #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (* -1/2 x))
(*.f64 x #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ x (+ (* -1/2 x) (* 1/2 y)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* y (+ 1/2 (* 1/2 (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (* 1/2 (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* y (+ 1/2 (* 1/2 (/ x y))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+ (* 1/2 x) (* 1/2 y))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/2 (/ y x))))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)

rewrite192.0ms (3.5%)

Memory
-6.8MiB live, 288.2MiB allocated
Rules
2 158×lower-fma.f64
2 158×lower-fma.f32
1 916×lower-*.f32
1 913×lower-*.f64
1 712×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01449
01849
16449
247649
3630649
0808346
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 213
Calls
Call 1
Inputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 y #s(literal 1/2 binary64))
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)
Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 (neg.f64 y) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 y #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) y) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 y)) #s(literal 2 binary64))
(/.f64 (neg.f64 y) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y))
(/.f64 y #s(literal 2 binary64))
(neg.f64 (/.f64 y #s(literal -2 binary64)))
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) (-.f64 (*.f64 y y) (*.f64 (-.f64 x y) x)))) (-.f64 (*.f64 y y) (*.f64 (-.f64 x y) x)))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 y y) y) (*.f64 y y)) y (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x y) x) x) (-.f64 x y)) (*.f64 (-.f64 x y) x)))) (fma.f64 (*.f64 (-.f64 x y) x) (-.f64 (*.f64 (-.f64 x y) x) (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 y y))))
(*.f64 (/.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 x y))) (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))))
(*.f64 (/.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (+.f64 y x)))
(*.f64 (/.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 y x))) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) y) (*.f64 y y)))
(*.f64 (/.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 y x))) (fma.f64 (+.f64 y x) x (*.f64 y y)))
(*.f64 (/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 y x)))
(*.f64 (/.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x y)))
(*.f64 (/.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (+.f64 y x) (-.f64 y x))) (+.f64 y x))
(*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))) (fma.f64 (+.f64 y x) x (*.f64 y y)))
(*.f64 (/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (+.f64 y x) (/.f64 (-.f64 y x) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 x y) x (*.f64 y y))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (/.f64 (-.f64 y x) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))))) (/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (fma.f64 (-.f64 x y) x (*.f64 y y))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 y x))) (/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(*.f64 (*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) x (*.f64 y y))))
(*.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x y)))
(*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) (-.f64 y x)))
(*.f64 #s(literal 1 binary64) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) x (*.f64 y y))) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 x y) x (*.f64 y y))))
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(fma.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 x y))) (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 (*.f64 y y) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x y)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 y (-.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 y (*.f64 (+.f64 y x) (/.f64 (-.f64 y x) (fma.f64 (*.f64 y y) y (*.f64 (*.f64 x x) x))))) (/.f64 y (fma.f64 (-.f64 x y) x (*.f64 y y))) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 y (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 y x))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) x (*.f64 y y)))) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 y (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 y (/.f64 #s(literal 1 binary64) (+.f64 y x))) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 y x))) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) y) (*.f64 y y)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) (-.f64 y x))) (fma.f64 (+.f64 y x) x (*.f64 y y)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 y x) (-.f64 y x))) (+.f64 y x) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (fma.f64 y y (*.f64 x x)) (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 y x)))
(fma.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (+.f64 y x) x) (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 y y)))
(fma.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 y y) (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (+.f64 y x) x)))
(fma.f64 (fma.f64 y y (*.f64 x x)) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (*.f64 y x) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 y #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 #s(literal 1 binary64) y))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) y)
(fma.f64 #s(literal 1 binary64) y x)
(fma.f64 #s(literal 1 binary64) x (*.f64 y #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1 binary64) y))
(fma.f64 #s(literal 1 binary64) x y)
(fma.f64 (*.f64 (+.f64 y x) x) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (*.f64 y y) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))))
(fma.f64 (*.f64 y y) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 y x) x) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))))
(fma.f64 (*.f64 y y) (/.f64 #s(literal -1 binary64) (-.f64 x y)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 y (/.f64 y (-.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 y #s(literal 1 binary64) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 y #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) y))
(fma.f64 x #s(literal 1 binary64) y)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (/.f64 (*.f64 y y) (-.f64 x y)))
(-.f64 (*.f64 y (/.f64 y (-.f64 y x))) (*.f64 x (/.f64 x (-.f64 y x))))
(-.f64 y (neg.f64 x))
(+.f64 (-.f64 y #s(literal 0 binary64)) x)
(+.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))) (*.f64 (*.f64 y x) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))))
(+.f64 (*.f64 (*.f64 (+.f64 y x) x) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))) (*.f64 (*.f64 y y) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))))
(+.f64 (*.f64 (*.f64 y y) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))) (*.f64 (*.f64 (+.f64 y x) x) (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64))))
(+.f64 (*.f64 y #s(literal 1 binary64)) x)
(+.f64 (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (fma.f64 y y (*.f64 x x))) (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 y x)))
(+.f64 (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (+.f64 y x) x)) (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 y y)))
(+.f64 (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 y y)) (*.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (+.f64 y x) x)))
(+.f64 (*.f64 #s(literal 1 binary64) y) x)
(+.f64 (*.f64 y (/.f64 y (-.f64 y x))) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(+.f64 y x)
(+.f64 x (*.f64 y #s(literal 1 binary64)))
(+.f64 x (*.f64 #s(literal 1 binary64) y))
(+.f64 x y)

eval146.0ms (2.7%)

Memory
3.3MiB live, 84.5MiB allocated
Compiler

Compiled 5 208 to 578 computations (88.9% saved)

prune40.0ms (0.7%)

Memory
-8.3MiB live, 68.5MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3510351
Fresh000
Picked033
Done000
Total3513354
Accuracy
100.0%
Counts
354 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
✓51.1%
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
✓49.7%
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 43 to 24 computations (44.2% saved)

regimes7.0ms (0.1%)

Memory
11.9MiB live, 11.9MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
Calls

3 calls:

2.0ms
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
2.0ms
x
2.0ms
y
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory
-37.5MiB live, 8.2MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
Calls

3 calls:

3.0ms
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
2.0ms
y
1.0ms
x
Results
AccuracySegmentsBranch
80.6%2x
89.3%2y
97.4%2(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory
8.0MiB live, 8.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

3 calls:

1.0ms
y
1.0ms
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
1.0ms
x
Results
AccuracySegmentsBranch
49.7%1x
49.7%1y
49.7%1(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-9.891714592114946e-267
1.011844926893908e-268
Compiler

Compiled 12 to 11 computations (8.3% saved)

simplify7.0ms (0.1%)

Memory
10.7MiB live, 10.7MiB allocated
Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
4×+-commutative_binary64
2×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02056
12756
23256
33456
43556
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
(if (<=.f64 (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #s(literal -1452164949685335/290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224570063240272065048916911180770489396052896597871561450348236492274894506629430939420761276732468592926240515079310107169312085954718183386786847281838290059659012482973391669690368 binary64)) #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))
Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) (+.f64 y x)))
(if (<=.f64 (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #s(literal -1452164949685335/290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224570063240272065048916911180770489396052896597871561450348236492274894506629430939420761276732468592926240515079310107169312085954718183386786847281838290059659012482973391669690368 binary64)) #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64))))
(if (<=.f64 (+.f64 (/.f64 (-.f64 y x) #s(literal 2 binary64)) x) #s(literal -1452164949685335/290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224570063240272065048916911180770489396052896597871561450348236492274894506629430939420761276732468592926240515079310107169312085954718183386786847281838290059659012482973391669690368 binary64)) #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y)))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) x))

soundness605.0ms (11%)

Memory
-18.0MiB live, 137.8MiB allocated
Rules
6 300×lower-fma.f64
6 300×lower-fma.f32
917×lower-*.f64
917×lower-*.f32
801×lower--.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057315
1177315
2498279
31491279
45234279
57541279
08288279
Stop Event
1×done
1×iter limit
1×node limit
Compiler

Compiled 47 to 28 computations (40.4% saved)

preprocess35.0ms (0.6%)

Memory
13.9MiB live, 86.2MiB allocated
Remove

(sort x y)

Compiler

Compiled 124 to 70 computations (43.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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