arccos

Time bar (total: 4.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze94.0ms (2.1%)

Memory
-28.3MiB live, 11.2MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
33.3%25%50%0%0%25%0%4
60%37.5%25%0%0%37.5%0%5
77.8%43.7%12.5%0%0%43.7%0%6
88.2%46.9%6.2%0%0%46.9%0%7
93.9%48.4%3.1%0%0%48.4%0%8
96.9%49.2%1.6%0%0%49.2%0%9
98.4%49.6%0.8%0%0%49.6%0%10
99.2%49.8%0.4%0%0%49.8%0%11
99.6%49.9%0.2%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.0s (22.5%)

Memory
50.6MiB live, 1 380.7MiB allocated
Samples
778.0ms8 256×0valid
1.0ms11×0invalid
Precisions
Click to see histograms. Total time spent on operations: 599.0ms
ival-add: 237.0ms (39.6% of total)
ival-mult: 101.0ms (16.9% of total)
ival-atan: 78.0ms (13% of total)
ival-sqrt: 61.0ms (10.2% of total)
ival-div: 54.0ms (9% of total)
ival-sub: 54.0ms (9% of total)
exact: 7.0ms (1.2% of total)
ival-true: 6.0ms (1% of total)
ival-assert: 3.0ms (0.5% of total)
Bogosity

explain105.0ms (2.3%)

Memory
-47.3MiB live, 268.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
00-0-(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
00-0-#s(literal 2 binary64)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
39.0ms512×0valid
Compiler

Compiled 104 to 31 computations (70.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-atan: 6.0ms (23.4% of total)
ival-add: 5.0ms (19.5% of total)
ival-sqrt: 4.0ms (15.6% of total)
ival-div: 3.0ms (11.7% of total)
ival-mult: 3.0ms (11.7% of total)
ival-sub: 3.0ms (11.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess34.0ms (0.8%)

Memory
-3.9MiB live, 75.5MiB allocated
Algorithm
egg-herbie
Rules
208×lower-fma.f64
208×lower-fma.f32
132×lower-*.f32
130×lower-*.f64
84×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
13122
25922
310822
418022
535022
662022
764722
0911
01511
12411
23011
34111
46411
59811
613511
720811
833011
949811
1052911
052911
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
2.4MiB live, 2.4MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 12 to 9 computations (25% saved)

simplify15.0ms (0.3%)

Memory
-12.4MiB live, 26.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
cost-diff0
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
cost-diff0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Rules
208×lower-fma.f64
208×lower-fma.f32
132×lower-*.f32
130×lower-*.f64
74×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0944
01544
12444
23044
34144
46444
59844
613544
720844
833044
949844
1052944
052944
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))

localize28.0ms (0.6%)

Memory
22.4MiB live, 61.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
accuracy0.00390625
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy0.00390625
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy0.03515625
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Samples
17.0ms256×0valid
Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-div: 2.0ms (18.8% of total)
ival-mult: 2.0ms (18.8% of total)
ival-atan: 2.0ms (18.8% of total)
ival-sub: 2.0ms (18.8% of total)
ival-sqrt: 2.0ms (18.8% of total)
ival-add: 1.0ms (9.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
9.7MiB live, 9.7MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
Outputs
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 x)) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 2 x) 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) 1) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) 1) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
Calls

3 calls:

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

simplify122.0ms (2.7%)

Memory
-7.1MiB live, 186.2MiB allocated
Algorithm
egg-herbie
Rules
10 954×lower-fma.f64
10 954×lower-fma.f32
2 906×lower-*.f64
2 906×lower-*.f32
1 802×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107541
1276480
2764466
32111454
46112448
08073437
Stop Event
iter limit
node limit
Counts
48 → 48
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* 2 x) 2)))
(fma.f64 (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x))))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x))

rewrite121.0ms (2.7%)

Memory
-14.7MiB live, 225.3MiB allocated
Rules
2 152×lower-fma.f64
2 152×lower-fma.f32
2 042×lower-*.f32
2 040×lower-*.f64
1 870×lower-/.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01536
15236
233936
345898
098248
Stop Event
iter limit
node limit
iter limit
Counts
4 → 7
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(neg.f64 (atan.f64 (/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(neg.f64 (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)

eval5.0ms (0.1%)

Memory
16.1MiB live, 16.1MiB allocated
Compiler

Compiled 650 to 106 computations (83.7% saved)

prune6.0ms (0.1%)

Memory
15.2MiB live, 15.2MiB allocated
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New51455
Fresh000
Picked011
Done000
Total51556
Accuracy
100.0%
Counts
56 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
96.9%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 52 to 40 computations (23.1% saved)

simplify107.0ms (2.4%)

Memory
-14.8MiB live, 104.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(atan.f64 #s(literal 1 binary64))
cost-diff0
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
cost-diff0
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Rules
2 920×lower-fma.f32
2 910×lower-fma.f64
856×lower-*.f32
848×lower-*.f64
496×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027210
046210
168210
292210
3181210
4345210
5613210
61149210
72060210
82506210
92667210
102740210
112839210
122885210
132885210
02885210
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)

localize76.0ms (1.7%)

Memory
-12.1MiB live, 144.4MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy0
(atan.f64 #s(literal 1 binary64))
accuracy0
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
accuracy0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy0.00390625
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy0.8050551918217591
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy0.00390625
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
accuracy0.00390625
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy0.9262799219726098
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy0
(-.f64 #s(literal 1 binary64) x)
accuracy0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
accuracy0.00390625
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy1.1913648588803425
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
Samples
42.0ms256×0valid
Compiler

Compiled 152 to 26 computations (82.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-mult: 10.0ms (36.5% of total)
ival-add: 8.0ms (29.2% of total)
ival-atan: 4.0ms (14.6% of total)
ival-div: 2.0ms (7.3% of total)
ival-sub: 2.0ms (7.3% of total)
ival-sqrt: 2.0ms (7.3% of total)
exact: 1.0ms (3.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory
13.7MiB live, 13.7MiB allocated
Counts
15 → 156
Calls
Call 1
Inputs
#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (atan.f64 #s(literal 1 binary64)) (patch (atan.f64 #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
Calls

3 calls:

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

simplify171.0ms (3.8%)

Memory
11.3MiB live, 201.8MiB allocated
Algorithm
egg-herbie
Rules
16 094×lower-fma.f64
16 094×lower-fma.f32
3 382×lower-*.f64
3 382×lower-*.f32
2 562×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01201615
13281428
210841406
336851378
478211378
081941314
Stop Event
iter limit
node limit
Counts
156 → 156
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1/2
(+ 1/2 (* -1/2 x))
(+ 1/2 (* -1/2 x))
(+ 1/2 (* -1/2 x))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1/2 x)
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)) (sqrt.f64 #s(literal -1 binary64))))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)) (sqrt.f64 #s(literal -1 binary64))))
(* -1/2 (pow x 3))
(*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) x)
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) x)
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1/2 (pow x 3))
(*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) x)
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))

rewrite170.0ms (3.8%)

Memory
9.9MiB live, 203.7MiB allocated
Rules
4 902×lower-fma.f32
4 892×lower-fma.f64
4 440×lower-/.f64
4 440×lower-/.f32
4 296×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027183
046183
1151183
21041183
08475183
Stop Event
iter limit
node limit
iter limit
Counts
15 → 208
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
Outputs
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))) (*.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x))) (pow.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x #s(literal 1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x)))
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(fma.f64 (*.f64 x (fma.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))
(fma.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 x (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x))) (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(+.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(atan.f64 #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x #s(literal 1/4 binary64)) x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))) (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x #s(literal 1/4 binary64)) x #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) #s(literal 1/16 binary64)))) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/64 binary64)))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x #s(literal 1/4 binary64)) x (*.f64 x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x #s(literal 1/4 binary64)) x (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x #s(literal 1/4 binary64)) x (*.f64 x #s(literal 1/4 binary64)))) (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))

eval47.0ms (1%)

Memory
-6.7MiB live, 75.6MiB allocated
Compiler

Compiled 8 717 to 1 099 computations (87.4% saved)

prune35.0ms (0.8%)

Memory
-13.6MiB live, 63.1MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New3631364
Fresh000
Picked044
Done011
Total3636369
Accuracy
100.0%
Counts
369 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
96.9%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 66 to 50 computations (24.2% saved)

simplify165.0ms (3.7%)

Memory
48.9MiB live, 196.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
cost-diff128
(-.f64 (neg.f64 x) #s(literal 1 binary64))
cost-diff1088
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
Rules
18 220×lower-fma.f32
18 218×lower-fma.f64
2 462×lower-*.f32
2 460×lower-*.f64
2 258×lower--.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01581
02281
13881
25276
39276
417556
541656
6149456
7515756
8709656
0804256
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(neg.f64 x)
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) x)
(neg.f64 x)
#s(literal 1 binary64)

localize63.0ms (1.4%)

Memory
-3.9MiB live, 80.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(neg.f64 x)
accuracy0.00390625
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
accuracy0.02734375
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
accuracy1.1913648588803425
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
Samples
50.0ms255×0valid
0.0ms1valid
Compiler

Compiled 55 to 17 computations (69.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-sub: 19.0ms (48.2% of total)
ival-add: 8.0ms (20.3% of total)
ival-div: 3.0ms (7.6% of total)
ival-mult: 3.0ms (7.6% of total)
ival-atan: 2.0ms (5.1% of total)
ival-sqrt: 2.0ms (5.1% of total)
ival-neg: 1.0ms (2.5% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory
-29.0MiB live, 8.2MiB allocated
Counts
6 → 72
Calls
Call 1
Inputs
#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1) (taylor 0 x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1) (taylor 0 x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1) (taylor 0 x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 (neg.f64 x) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
6.0ms
x
@0
((/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))
1.0ms
x
@inf
((/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))
1.0ms
x
@-inf
((/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))

simplify143.0ms (3.2%)

Memory
21.4MiB live, 185.7MiB allocated
Algorithm
egg-herbie
Rules
9 614×lower-fma.f64
9 614×lower-fma.f32
2 626×lower-*.f64
2 626×lower-*.f32
1 910×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
087542
1223481
2647466
31707458
44805448
08068444
Stop Event
iter limit
node limit
Counts
72 → 72
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
-1
(- (* -1 x) 1)
(- (* -1 x) 1)
(- (* -1 x) 1)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 x)
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite121.0ms (2.7%)

Memory
12.1MiB live, 167.8MiB allocated
Rules
5 578×lower-fma.f32
5 576×lower-fma.f64
2 638×lower-/.f32
2 636×lower-/.f64
2 632×lower-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01573
02273
19549
272326
01088426
Stop Event
iter limit
node limit
iter limit
Counts
6 → 647
Calls
Call 1
Inputs
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(neg.f64 x)
Outputs
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))) (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (fma.f64 x x x)))) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64))))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) x (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (*.f64 (*.f64 x x) x) x)))))
(*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64)))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64))) (*.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 #s(literal -1 binary64) x)) (sqrt.f64 (-.f64 #s(literal -1 binary64) x)))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64)))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (*.f64 (*.f64 x x) x))))
(/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))
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(fma.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) x #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal -1 binary64))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(-.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(-.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal -1 binary64) x)
(-.f64 x #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))))
(+.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) x))
(+.f64 #s(literal -1 binary64) x)
(+.f64 x #s(literal -1 binary64))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(pow.f64 x #s(literal 1 binary64))
(/.f64 (*.f64 (*.f64 x x) x) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 x x) x) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 x x) x)
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (*.f64 x x) x)))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) x) x)
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) x)
(-.f64 #s(literal 0 binary64) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal 0 binary64) x)
x

eval253.0ms (5.6%)

Memory
-13.4MiB live, 180.8MiB allocated
Compiler

Compiled 20 169 to 2 685 computations (86.7% saved)

prune106.0ms (2.4%)

Memory
-10.0MiB live, 187.9MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New7181719
Fresh000
Picked101
Done055
Total7196725
Accuracy
100.0%
Counts
725 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
96.9%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify303.0ms (6.7%)

Memory
-33.6MiB live, 158.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
cost-diff1088
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
Rules
17 570×lower-fma.f32
17 568×lower-fma.f64
2 396×lower-*.f32
2 394×lower-*.f64
1 960×lower-+.f64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01473
02073
13473
24573
37973
413873
531153
6111753
7376353
8542653
9666853
10737753
11793753
0800753
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 #s(literal -1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 #s(literal -1 binary64) x)

localize65.0ms (1.4%)

Memory
22.5MiB live, 71.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
accuracy0.00390625
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
accuracy0.02734375
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
accuracy1.1913648588803425
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
Samples
53.0ms255×0valid
0.0ms1valid
Compiler

Compiled 50 to 16 computations (68% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-add: 29.0ms (62.8% of total)
ival-div: 7.0ms (15.1% of total)
ival-mult: 3.0ms (6.5% of total)
ival-sub: 3.0ms (6.5% of total)
ival-atan: 2.0ms (4.3% of total)
ival-sqrt: 2.0ms (4.3% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory
-32.1MiB live, 5.8MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) (patch (*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
Calls

3 calls:

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

simplify210.0ms (4.7%)

Memory
31.2MiB live, 144.4MiB allocated
Algorithm
egg-herbie
Rules
11 462×lower-fma.f64
11 462×lower-fma.f32
3 104×lower-*.f64
3 104×lower-*.f32
1 454×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083477
1208416
2618410
31613402
45509392
08187388
Stop Event
iter limit
node limit
Counts
48 → 48
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))

rewrite180.0ms (4%)

Memory
16.8MiB live, 206.0MiB allocated
Rules
7 108×lower-fma.f32
7 106×lower-fma.f64
4 160×lower-*.f32
4 158×lower-*.f64
4 022×lower-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01463
02063
18843
266943
0852343
Stop Event
iter limit
node limit
iter limit
Counts
4 → 351
Calls
Call 1
Inputs
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
Outputs
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (-.f64 (*.f64 (*.f64 x x) x) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x)) (*.f64 x x) (*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) x (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (*.f64 (*.f64 x x) x) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) (fma.f64 x x x) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) x))) (/.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (*.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))))
(*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 x #s(literal -1 binary64)))
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(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(fma.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (neg.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(+.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (*.f64 (neg.f64 x) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(+.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(+.f64 (*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (neg.f64 x)))
(+.f64 (*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) x)) (*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))) (neg.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal -1 binary64) x)) (-.f64 x #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal -1 binary64) x))))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))

eval64.0ms (1.4%)

Memory
-16.8MiB live, 110.6MiB allocated
Compiler

Compiled 10 167 to 1 427 computations (86% saved)

prune68.0ms (1.5%)

Memory
14.3MiB live, 128.2MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New3990399
Fresh000
Picked011
Done055
Total3996405
Accuracy
100.0%
Counts
405 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
96.9%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 138 to 83 computations (39.9% saved)

regimes17.0ms (0.4%)

Memory
-10.8MiB live, 33.6MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Calls

5 calls:

7.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
3.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
100.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
100.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes13.0ms (0.3%)

Memory
-0.6MiB live, 36.6MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
Calls

5 calls:

4.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
98.8%1x
98.8%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.8%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.8%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.8%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes10.0ms (0.2%)

Memory
-12.1MiB live, 24.8MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
Calls

5 calls:

4.0ms
x
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
Results
AccuracySegmentsBranch
98.6%1x
98.6%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.6%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes7.0ms (0.1%)

Memory
20.0MiB live, 20.0MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Calls

5 calls:

1.0ms
x
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
98.2%1x
98.2%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.2%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.2%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.2%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes7.0ms (0.2%)

Memory
-21.2MiB live, 17.5MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Calls

5 calls:

3.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
96.9%1x
96.9%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
96.9%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
96.9%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
96.9%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

simplify6.0ms (0.1%)

Memory
17.5MiB live, 17.5MiB allocated
Algorithm
egg-herbie
Rules
12×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
1-exp_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03271
14371
24671
34871
44971
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

soundness452.0ms (10%)

Memory
19.7MiB live, 259.3MiB allocated
Rules
10 954×lower-fma.f64
10 954×lower-fma.f32
2 906×lower-*.f64
2 906×lower-*.f32
2 152×lower-fma.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01536
15236
233936
345898
098248
0107541
1276480
2764466
32111454
46112448
08073437
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 80 to 51 computations (36.3% saved)

preprocess69.0ms (1.5%)

Memory
-12.6MiB live, 63.7MiB allocated
Compiler

Compiled 120 to 68 computations (43.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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