Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B

Time bar (total: 5.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze80.0ms (1.6%)

Memory
-1.0MiB live, 49.6MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
50%50%50%0.1%0%0%0%3
50%50%50%0.1%0%0%0%4
62.5%62.4%37.5%0.1%0%0%0%5
68.8%68.7%31.2%0.1%0%0%0%6
78.1%78%21.9%0.1%0%0%0%7
82.8%82.7%17.2%0.1%0%0%0%8
88.3%88.2%11.7%0.1%0%0%0%9
91%90.9%9%0.1%0%0%0%10
93.9%93.9%6%0.1%0%0%0%11
95.4%95.3%4.6%0.1%0%0%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.8s (34.9%)

Memory
27.3MiB live, 967.6MiB allocated
Samples
1.3s8 255×0valid
0.0ms2valid
Precisions
Click to see histograms. Total time spent on operations: 888.0ms
ival-mult: 298.0ms (33.6% of total)
ival-div: 231.0ms (26% of total)
ival-add: 175.0ms (19.7% of total)
ival-sub: 166.0ms (18.7% of total)
exact: 8.0ms (0.9% of total)
ival-true: 7.0ms (0.8% of total)
ival-assert: 3.0ms (0.3% of total)
adjust: 0.0ms (0% of total)
Bogosity

explain149.0ms (3%)

Memory
-31.6MiB live, 292.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
400-0-(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
00-0-(/.f64 (*.f64 x y) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
00-0-(*.f64 x y)
00-0-(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
00-0-(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
00-0-#s(literal 2 binary64)
00-0-y
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
33.0ms512×0valid
Compiler

Compiled 93 to 31 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-div: 8.0ms (44.5% of total)
ival-mult: 4.0ms (22.2% of total)
ival-sub: 2.0ms (11.1% of total)
ival-add: 2.0ms (11.1% of total)
exact: 1.0ms (5.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess68.0ms (1.3%)

Memory
22.5MiB live, 101.1MiB allocated
Algorithm
egg-herbie
Rules
384×lower-fma.f64
384×lower-fma.f32
272×lower-*.f32
270×lower-*.f64
224×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02363
15761
212157
325355
454155
588855
699555
7101955
8102955
9103355
0911
01411
12211
23311
34811
49011
516311
628411
737911
858911
967911
1080111
1183711
12100011
13100911
0100910
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Outputs
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(-.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64))))
Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory
2.3MiB live, 2.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify27.0ms (0.5%)

Memory
-1.3MiB live, 37.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
cost-diff0
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
cost-diff128
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
cost-diff384
(/.f64 (*.f64 x y) #s(literal 2 binary64))
Rules
384×lower-fma.f64
384×lower-fma.f32
272×lower-*.f32
270×lower-*.f64
224×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0939
01439
12239
23339
34839
49039
516339
628439
737939
858939
967939
1080139
1183739
12100039
13100939
0100936
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
x
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
y
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
#s(literal 1 binary64)
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
#s(literal 2 binary64)
Outputs
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(-.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64))))
x
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
(/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64)))
y
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 y x))
(*.f64 x y)
(*.f64 y x)
#s(literal 2 binary64)

localize27.0ms (0.5%)

Memory
-13.7MiB live, 67.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
accuracy0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
accuracy0
(*.f64 x y)
accuracy9.380609132041245
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
Samples
17.0ms256×0valid
Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-div: 3.0ms (38.8% of total)
ival-mult: 2.0ms (25.9% of total)
ival-sub: 1.0ms (12.9% of total)
ival-add: 1.0ms (12.9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory
-10.9MiB live, 27.2MiB allocated
Counts
5 → 120
Calls
Call 1
Inputs
#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify147.0ms (2.9%)

Memory
41.2MiB live, 229.7MiB allocated
Algorithm
egg-herbie
Rules
13 558×lower-fma.f64
13 558×lower-fma.f32
4 930×lower-*.f64
4 930×lower-*.f32
1 854×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02311053
17381018
21944987
36075981
08419934
Stop Event
iter limit
node limit
Counts
120 → 115
Calls
Call 1
Inputs
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(* x y)
(* x y)
(* x y)
(* x y)
Outputs
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
y
(* y (+ 1 (* -1/2 (* x y))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal 1 binary64)) y)
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(fma.f64 (*.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal -1/8 binary64))) y)) y #s(literal 1 binary64)) y)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* y (+ (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* y (+ (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* y (+ (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x)) x) x)
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x) #s(literal -2 binary64)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(-.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x)) x))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x)) x) x)
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x) #s(literal -2 binary64)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(-.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x)) x))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 y)
(neg.f64 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(fma.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(fma.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal 1/8 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/4 binary64))) x (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64))) x (neg.f64 y))
y
(+ y (* -1/2 (* x (pow y 2))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal 1 binary64)) y)
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(fma.f64 (*.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y y) #s(literal -1/2 binary64) (*.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/4 binary64) (*.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal -1/8 binary64))) x)) x y)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x) #s(literal -2 binary64)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -16 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x))) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 (*.f64 y y) x))) x) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x)) (/.f64 #s(literal 8 binary64) (*.f64 y y))) x)) x) #s(literal -2 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)

rewrite199.0ms (4%)

Memory
-23.5MiB live, 306.7MiB allocated
Rules
5 754×lower-fma.f64
5 754×lower-fma.f32
4 124×lower-*.f32
4 122×lower-*.f64
2 962×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0935
01435
16335
250035
3687335
0852732
Stop Event
iter limit
node limit
iter limit
Counts
5 → 279
Calls
Call 1
Inputs
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
(*.f64 x y)
Outputs
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 y x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 y x)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 (neg.f64 x) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 (neg.f64 x) (/.f64 y #s(literal -2 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 x) y))
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(neg.f64 (*.f64 (/.f64 y (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))) #s(literal 1 binary64)))
(neg.f64 (/.f64 y (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))))
(fma.f64 (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 y x))))
(fma.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64))) (*.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(fma.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64))) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 y x)) (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64))) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))) (/.f64 y (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 y (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))))
(exp.f64 (*.f64 (-.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) (log.f64 y)) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 y x)) (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(+.f64 (*.f64 (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64))) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64))) (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(+.f64 (*.f64 (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 y x))))
(+.f64 (*.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64)))) (*.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 (*.f64 y x) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal 1/2 binary64)))))
(*.f64 (neg.f64 (neg.f64 x)) y)
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (*.f64 y x))
(*.f64 (*.f64 y x) #s(literal 1 binary64))
(*.f64 y (neg.f64 (neg.f64 x)))
(*.f64 y x)
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) y))

eval50.0ms (1%)

Memory
18.9MiB live, 142.7MiB allocated
Compiler

Compiled 9 214 to 1 087 computations (88.2% saved)

prune11.0ms (0.2%)

Memory
-42.6MiB live, 41.8MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3895394
Fresh000
Picked101
Done000
Total3905395
Accuracy
100.0%
Counts
395 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
62.5%
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
64.7%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
74.4%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
28.9%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
Compiler

Compiled 66 to 60 computations (9.1% saved)

simplify82.0ms (1.6%)

Memory
29.8MiB live, 69.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y x)
cost-diff0
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
cost-diff0
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
cost-diff0
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
cost-diff0
(/.f64 #s(literal 2 binary64) x)
cost-diff0
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
cost-diff0
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
cost-diff0
(-.f64 x y)
cost-diff0
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
cost-diff0
(neg.f64 y)
cost-diff0
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
cost-diff0
(*.f64 y x)
cost-diff0
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff0
(/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
cost-diff0
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
Rules
1 384×lower-fma.f32
1 378×lower-fma.f64
664×lower-*.f32
662×lower-*.f64
278×associate-/l*
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
025144
037144
159144
297144
3179144
4368144
5697141
61091139
71434139
81620139
91752139
101839139
111985139
122002139
132011139
142018139
152019139
02019139
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
x
(/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
y
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(*.f64 y x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
(neg.f64 y)
y
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
(-.f64 x y)
x
y
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
x
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(*.f64 y x)
y
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
Outputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64))))
x
(/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64)))
y
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64))
(*.f64 y x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
(neg.f64 y)
y
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
(-.f64 x y)
x
y
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
x
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) y x))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) y x)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64))
(*.f64 y x)
y
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)

localize55.0ms (1.1%)

Memory
-0.1MiB live, 118.7MiB allocated
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
accuracy0
(*.f64 y x)
accuracy0.0234375
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
accuracy22.593334628147005
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
accuracy0
(/.f64 #s(literal 2 binary64) x)
accuracy0
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
accuracy31.824672121297063
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
accuracy0
(-.f64 x y)
accuracy16.354940042735667
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
accuracy0
(neg.f64 y)
accuracy45.49942069783688
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
accuracy0
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy0
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
accuracy0
(*.f64 y x)
accuracy9.380609132041245
(/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
Samples
39.0ms256×0valid
Compiler

Compiled 127 to 24 computations (81.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-div: 7.0ms (30.1% of total)
ival-mult: 6.0ms (25.8% of total)
ival-sub: 4.0ms (17.2% of total)
ival-add: 4.0ms (17.2% of total)
exact: 1.0ms (4.3% of total)
ival-neg: 1.0ms (4.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series17.0ms (0.3%)

Memory
0.6MiB live, 39.6MiB allocated
Counts
14 → 312
Calls
Call 1
Inputs
#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #<representation binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())
#s(alt (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (patch (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@0
((- x (/ y (+ (* (* y x) 1/2) 1))) (/ y (+ (* (* y x) 1/2) 1)) (+ (* (* y x) 1/2) 1) (* y x) (- x (/ y (+ 1 (/ (* x y) 2)))) (neg y) (- x (/ y (+ 1 (/ (* x y) 2)))) (- x y) (- x (/ y (+ 1 (/ (* x y) 2)))) (/ y (+ 1 (/ (* x y) 2))) (/ 2 x) (- x (/ y (+ 1 (/ (* x y) 2)))) (+ (* (+ (* (* y x) 1/2) -1) y) x) (+ (* (* y x) 1/2) -1))
1.0ms
x
@-inf
((- x (/ y (+ (* (* y x) 1/2) 1))) (/ y (+ (* (* y x) 1/2) 1)) (+ (* (* y x) 1/2) 1) (* y x) (- x (/ y (+ 1 (/ (* x y) 2)))) (neg y) (- x (/ y (+ 1 (/ (* x y) 2)))) (- x y) (- x (/ y (+ 1 (/ (* x y) 2)))) (/ y (+ 1 (/ (* x y) 2))) (/ 2 x) (- x (/ y (+ 1 (/ (* x y) 2)))) (+ (* (+ (* (* y x) 1/2) -1) y) x) (+ (* (* y x) 1/2) -1))
1.0ms
y
@-inf
((- x (/ y (+ (* (* y x) 1/2) 1))) (/ y (+ (* (* y x) 1/2) 1)) (+ (* (* y x) 1/2) 1) (* y x) (- x (/ y (+ 1 (/ (* x y) 2)))) (neg y) (- x (/ y (+ 1 (/ (* x y) 2)))) (- x y) (- x (/ y (+ 1 (/ (* x y) 2)))) (/ y (+ 1 (/ (* x y) 2))) (/ 2 x) (- x (/ y (+ 1 (/ (* x y) 2)))) (+ (* (+ (* (* y x) 1/2) -1) y) x) (+ (* (* y x) 1/2) -1))
1.0ms
y
@inf
((- x (/ y (+ (* (* y x) 1/2) 1))) (/ y (+ (* (* y x) 1/2) 1)) (+ (* (* y x) 1/2) 1) (* y x) (- x (/ y (+ 1 (/ (* x y) 2)))) (neg y) (- x (/ y (+ 1 (/ (* x y) 2)))) (- x y) (- x (/ y (+ 1 (/ (* x y) 2)))) (/ y (+ 1 (/ (* x y) 2))) (/ 2 x) (- x (/ y (+ 1 (/ (* x y) 2)))) (+ (* (+ (* (* y x) 1/2) -1) y) x) (+ (* (* y x) 1/2) -1))
1.0ms
x
@inf
((- x (/ y (+ (* (* y x) 1/2) 1))) (/ y (+ (* (* y x) 1/2) 1)) (+ (* (* y x) 1/2) 1) (* y x) (- x (/ y (+ 1 (/ (* x y) 2)))) (neg y) (- x (/ y (+ 1 (/ (* x y) 2)))) (- x y) (- x (/ y (+ 1 (/ (* x y) 2)))) (/ y (+ 1 (/ (* x y) 2))) (/ 2 x) (- x (/ y (+ 1 (/ (* x y) 2)))) (+ (* (+ (* (* y x) 1/2) -1) y) x) (+ (* (* y x) 1/2) -1))

simplify173.0ms (3.4%)

Memory
-15.3MiB live, 304.3MiB allocated
Algorithm
egg-herbie
Rules
12 856×lower-fma.f64
12 856×lower-fma.f32
4 554×lower-*.f64
4 554×lower-*.f32
2 528×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02783177
18753073
223692971
370722957
083012778
Stop Event
iter limit
node limit
Counts
312 → 289
Calls
Call 1
Inputs
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* 1/2 (* x y)) 1)))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* x y)
(* x y)
(* x y)
(* x y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* 1/2 (* x y))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* x y)
(* x y)
(* x y)
(* x y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(* -1 y)
(- x y)
(- x y)
(- x y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(* -1 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(* x (+ 1 (* 1/2 (pow y 2))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* 1/2 (* x y))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* x y)
(* x y)
(* x y)
(* x y)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
Outputs
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
y
(* y (+ 1 (* -1/2 (* x y))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) y #s(literal 1 binary64)) y)
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(fma.f64 (*.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal -1/8 binary64))) y)) y #s(literal 1 binary64)) y)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
y
(* y (+ 1 (* -1/2 (* x y))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) y #s(literal 1 binary64)) y)
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(fma.f64 (*.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal -1/8 binary64))) y)) y #s(literal 1 binary64)) y)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
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(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))

rewrite333.0ms (6.6%)

Memory
28.9MiB live, 221.8MiB allocated
Rules
4 952×lower-/.f32
4 948×lower-/.f64
4 560×lower-fma.f32
4 554×lower-fma.f64
4 288×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025128
037123
1178123
21175123
08323123
Stop Event
iter limit
node limit
iter limit
Counts
14 → 316
Calls
Call 1
Inputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(*.f64 y x)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
(neg.f64 y)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
(-.f64 x y)
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
Outputs
(*.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x)) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (/.f64 (*.f64 x x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (fma.f64 (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (*.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (fma.f64 (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x)))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (*.f64 x x) (*.f64 (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (*.f64 (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (*.f64 (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)))) (*.f64 (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64))) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))) (-.f64 (*.f64 x x) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))))
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 y (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64))) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (/.f64 y (pow.f64 (fma.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (/.f64 y (pow.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 y (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64))) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 y (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) x)
(fma.f64 (/.f64 y (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) x)
(fma.f64 #s(literal -1 binary64) (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)
(fma.f64 (neg.f64 y) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -1 binary64)) x)
(fma.f64 y (neg.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -1 binary64))) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))) (/.f64 (pow.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x) (*.f64 x x))))
(-.f64 x (/.f64 y (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))
(+.f64 (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) x)
(+.f64 x (/.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))
(*.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64))) #s(literal -1 binary64))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (+.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) y)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) y))))
(/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) y))) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (*.f64 y x)) #s(literal 1/2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64))
(fma.f64 (*.f64 (neg.f64 y) x) #s(literal -1/2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 y x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64))
(fma.f64 y (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))
(fma.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))
(expm1.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) y)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 (*.f64 (*.f64 y x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))

eval184.0ms (3.7%)

Memory
-30.4MiB live, 128.2MiB allocated
Compiler

Compiled 11 658 to 1 355 computations (88.4% saved)

prune68.0ms (1.3%)

Memory
6.1MiB live, 44.8MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New6301631
Fresh000
Picked145
Done000
Total6315636
Accuracy
100.0%
Counts
636 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
62.5%
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
74.4%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
28.9%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
29.6%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
Compiler

Compiled 33 to 31 computations (6.1% saved)

simplify118.0ms (2.3%)

Memory
23.6MiB live, 70.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
cost-diff0
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
cost-diff0
#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))
cost-diff0
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
Rules
1 304×lower-fma.f32
1 302×lower-fma.f64
616×lower-*.f32
612×lower-*.f64
246×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02171
02571
13971
26471
311971
418971
535871
666471
7113071
8145071
9152571
10161171
11167971
12180071
13181271
14182071
15182771
16182871
0182868
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(*.f64 y x)
y
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
Outputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(*.f64 y x)
y
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)

localize40.0ms (0.8%)

Memory
-1.9MiB live, 34.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y x)
accuracy0.0546875
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
accuracy22.49188893404826
#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))
accuracy22.593334628147005
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
Samples
32.0ms256×0valid
Compiler

Compiled 47 to 18 computations (61.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 13.0ms (61% of total)
ival-div: 3.0ms (14.1% of total)
ival-add: 3.0ms (14.1% of total)
ival-sub: 1.0ms (4.7% of total)
exact: 1.0ms (4.7% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series15.0ms (0.3%)

Memory
-27.8MiB live, 8.8MiB allocated
Counts
5 → 120
Calls
Call 1
Inputs
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 y) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (* 1/2 (* x (pow y 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (* 1/2 (* x (pow y 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (* 1/2 (* x (pow y 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<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 y) (taylor 0 x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (pow y 2)))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x (pow y 2))) (taylor inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (pow y 2)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify427.0ms (8.5%)

Memory
7.6MiB live, 159.1MiB allocated
Algorithm
egg-herbie
Rules
16 400×lower-fma.f64
16 400×lower-fma.f32
4 314×lower-*.f64
4 314×lower-*.f32
3 250×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01751010
15331004
21502992
34273980
08382893
Stop Event
iter limit
node limit
Counts
120 → 116
Calls
Call 1
Inputs
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(* -1 y)
(* y (- (* 1/2 (* x y)) 1))
(* y (- (* 1/2 (* x y)) 1))
(* y (- (* 1/2 (* x y)) 1))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(* x y)
(* x y)
(* x y)
(* x y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* x y)
(* x y)
(* x y)
(* x y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(* -1 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(* -1 y)
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(* x y)
(* x y)
(* x y)
(* x y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(* x (+ 1 (* 1/2 (pow y 2))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* 1/2 (* x (pow y 2)))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* 1/2 (* x y))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* 1/2 (* x (pow y 2)))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* x y)
(* x y)
(* x y)
(* x y)
Outputs
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (*.f64 x (fma.f64 (*.f64 #s(literal -1/4 binary64) y) x #s(literal 1/2 binary64))) y #s(literal -1 binary64)) y x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 y)
(neg.f64 y)
(* y (- (* 1/2 (* x y)) 1))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* y (- (* 1/2 (* x y)) 1))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* y (- (* 1/2 (* x y)) 1))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
-1
#s(literal -1 binary64)
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) y)) x) (/.f64 #s(literal 2 binary64) x))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(-.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 y y) x))) x) x) (-.f64 (/.f64 #s(literal 2 binary64) x) x))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) y)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(* 1/2 (* x (pow y 2)))
(*.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 x (*.f64 y y))) y #s(literal -1 binary64)) y)
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 x (*.f64 y y))) y #s(literal -1 binary64)) y)
(* 1/2 (* x (pow y 2)))
(*.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* 1/2 (* x y))
(*.f64 (*.f64 y x) #s(literal 1/2 binary64))
(* y (- (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* y (- (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* y (- (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) y)) x) (/.f64 #s(literal 2 binary64) x))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 y y) x))) x) x) (-.f64 (/.f64 #s(literal 2 binary64) x) x))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) y)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(* 1/2 (* x (pow y 2)))
(*.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) y) y)
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) y) y)
(* 1/2 (* x (pow y 2)))
(*.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* 1/2 (* x y))
(*.f64 (*.f64 y x) #s(literal 1/2 binary64))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* -1 y)
(neg.f64 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(fma.f64 (fma.f64 (*.f64 x (fma.f64 (*.f64 #s(literal -1/4 binary64) y) x #s(literal 1/2 binary64))) y #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(fma.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal 1/8 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/4 binary64))) x (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64))) x (neg.f64 y))
(* -1 y)
(neg.f64 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 y)
(neg.f64 y)
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
-1
#s(literal -1 binary64)
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (-.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (+ 1 (* 1/2 (pow y 2))))
(*.f64 (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* 1/2 (* x (pow y 2)))
(*.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* 1/2 (* x y))
(*.f64 (*.f64 y x) #s(literal 1/2 binary64))
(* x (- (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x (- (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x (- (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (-.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(*.f64 (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* 1/2 (* x (pow y 2)))
(*.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* 1/2 (* x y))
(*.f64 (*.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)

rewrite186.0ms (3.7%)

Memory
25.3MiB live, 144.1MiB allocated
Rules
11 116×lower-fma.f32
11 114×lower-fma.f64
5 460×lower-*.f32
5 456×lower-*.f64
3 210×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02167
02567
110867
278167
0908164
Stop Event
iter limit
node limit
iter limit
Counts
5 → 194
Calls
Call 1
Inputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))
(*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(*.f64 y x)
Outputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) y)))
#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) y))
(*.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64)))) (/.f64 y (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)))))
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(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(fma.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64)))) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(fma.f64 (/.f64 y (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (pow.f64 (fma.f64 (*.f64 y x) (fma.f64 #s(literal 1/4 binary64) (*.f64 y x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 y x)) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(fma.f64 (neg.f64 y) (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 (neg.f64 x) y) #s(literal -1/2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 y x)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 x) (*.f64 y #s(literal -1 binary64))) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal -1 binary64))
(fma.f64 y (*.f64 (neg.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(fma.f64 y (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 y (neg.f64 (*.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64))
(fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))
(fma.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 (*.f64 y #s(literal -1/2 binary64))) #s(literal -1 binary64))
(fma.f64 x (*.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))
(expm1.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 y x))) #s(literal -1 binary64)))
(-.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))))
(-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 y x)))
(+.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
(*.f64 (neg.f64 (neg.f64 x)) y)
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) y))
(*.f64 (*.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 y x))
(*.f64 y (neg.f64 (neg.f64 x)))
(*.f64 y x)
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) y))

eval122.0ms (2.4%)

Memory
-19.4MiB live, 55.7MiB allocated
Compiler

Compiled 5 624 to 1 050 computations (81.3% saved)

prune8.0ms (0.2%)

Memory
20.1MiB live, 20.1MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New3100310
Fresh000
Picked011
Done044
Total3105315
Accuracy
100.0%
Counts
315 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
62.5%
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
74.4%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
28.9%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
29.6%
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
Compiler

Compiled 87 to 59 computations (32.2% saved)

regimes9.0ms (0.2%)

Memory
13.2MiB live, 13.2MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Outputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
Calls

3 calls:

3.0ms
y
3.0ms
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 13 computations (0% saved)

regimes55.0ms (1.1%)

Memory
-36.8MiB live, 11.6MiB allocated
Counts
5 → 3
Calls
Call 1
Inputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (*.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
Outputs
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
Calls

3 calls:

49.0ms
y
2.0ms
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
2.0ms
x
Results
AccuracySegmentsBranch
89.3%3x
93.9%3y
87.0%3(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 13 computations (0% saved)

regimes5.0ms (0.1%)

Memory
8.6MiB live, 8.6MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
Outputs
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
Calls

3 calls:

2.0ms
x
2.0ms
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
2.0ms
y
Results
AccuracySegmentsBranch
74.4%1(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
74.4%1x
74.4%1y
Compiler

Compiled 13 to 13 computations (0% saved)

regimes4.0ms (0.1%)

Memory
7.7MiB live, 7.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

3 calls:

1.0ms
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
1.0ms
x
1.0ms
y
Results
AccuracySegmentsBranch
28.9%1y
28.9%1(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
28.9%1x
Compiler

Compiled 13 to 13 computations (0% saved)

bsearch71.0ms (1.4%)

Memory
-6.0MiB live, 32.5MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
54.0ms
6.393941847882692e+48
1.5738036054382421e+56
14.0ms
-7.712722695001175e+98
-1.543442669891281e+87
Samples
57.0ms304×0valid
Compiler

Compiled 204 to 242 computations (-18.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-add: 43.0ms (84.8% of total)
ival-div: 4.0ms (7.9% of total)
ival-mult: 2.0ms (3.9% of total)
ival-sub: 1.0ms (2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify61.0ms (1.2%)

Memory
-1.9MiB live, 36.8MiB allocated
Algorithm
egg-herbie
Rules
14×+-commutative-binary64-+.f64
14×sub-neg-binary64-neg.f64-+.f64--.f64
10×*-commutative-binary64-*.f64
neg-sub0-binary64--.f64-neg.f64
neg-mul-1-binary64-*.f64-neg.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02792
13992
25192
35892
46292
56392
Stop Event
saturated
Calls
Call 1
Inputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -280000000000000005424143956845641588573833593202227332235080591143009246246676874572229302206595072 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 145000000000000003525778919484870697476661272552818081792 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
Outputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -280000000000000005424143956845641588573833593202227332235080591143009246246676874572229302206595072 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 145000000000000003525778919484870697476661272552818081792 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

soundness438.0ms (8.7%)

Memory
24.8MiB live, 334.2MiB allocated
Rules
13 558×lower-fma.f64
13 558×lower-fma.f32
5 754×lower-fma.f64
5 754×lower-fma.f32
4 930×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0935
01435
16335
250035
3687335
0852732
02311053
17381018
21944987
36075981
08419934
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 75 to 50 computations (33.3% saved)

preprocess35.0ms (0.7%)

Memory
13.1MiB live, 90.4MiB allocated
Compiler

Compiled 104 to 62 computations (40.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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