bug333 (missed optimization)

Time bar (total: 8.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50%50%0%0%0%0
100%50%0%50%0%0%0%1
Compiler

Compiled 17 to 12 computations (29.4% saved)

sample2.2s (27%)

Memory
28.2MiB live, 2 555.6MiB allocated
Samples
797.0ms3 117×2valid
726.0ms4 812×1valid
21.0ms327×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.3s
adjust: 415.0ms (32.2% of total)
ival-sqrt: 371.0ms (28.8% of total)
ival-sub: 256.0ms (19.8% of total)
ival-add: 179.0ms (13.9% of total)
ival-<=: 43.0ms (3.3% of total)
ival-and: 12.0ms (0.9% of total)
exact: 11.0ms (0.9% of total)
ival-assert: 4.0ms (0.3% of total)
Bogosity

explain812.0ms (10.2%)

Memory
-5.5MiB live, 191.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2550-0-(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
00-0-(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))cancellation2550
Confusion
Predicted +Predicted -
+2550
-01
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25500
-001
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
01
1255
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
696.0ms310×1valid
32.0ms180×2valid
1.0ms22×0valid
Compiler

Compiled 63 to 25 computations (60.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 706.0ms
ival-sqrt: 675.0ms (95.6% of total)
adjust: 12.0ms (1.7% of total)
ival-sub: 11.0ms (1.6% of total)
ival-add: 6.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess506.0ms (6.3%)

Memory
-8.2MiB live, 30.0MiB allocated
Algorithm
egg-herbie
Rules
92×lower-fma.f64
92×lower-fma.f32
64×lower-+.f32
62×lower-+.f64
56×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
12219
25218
310118
416318
523718
626418
727218
079
0129
1199
2269
3379
4519
5749
61149
71499
81969
92119
102199
02199
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Symmetry

(negabs x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify8.0ms (0.1%)

Memory
14.3MiB live, 14.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Rules
92×lower-fma.f64
92×lower-fma.f32
64×lower-+.f32
62×lower-+.f64
56×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0725
01225
11925
22625
33725
45125
57425
611425
714925
819625
921125
1021925
021925
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

localize64.0ms (0.8%)

Memory
2.7MiB live, 47.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 #s(literal 1 binary64) x)
accuracy0.00390625
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy0.0078125
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy58.741880517172625
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Samples
39.0ms155×1valid
15.0ms90×2valid
1.0ms11×0valid
Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-sqrt: 8.0ms (32.5% of total)
adjust: 6.0ms (24.4% of total)
ival-sub: 6.0ms (24.4% of total)
ival-add: 3.0ms (12.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series27.0ms (0.3%)

Memory
-35.0MiB live, 4.1MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.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 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.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 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 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 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
23.0ms
x
@-inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)))
2.0ms
x
@inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)))
1.0ms
x
@0
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)))

simplify259.0ms (3.2%)

Memory
30.3MiB live, 102.0MiB allocated
Algorithm
egg-herbie
Rules
21 484×lower-fma.f64
21 484×lower-fma.f32
4 942×lower-+.f64
4 942×lower-+.f32
4 596×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0161971
1493856
21730798
37227798
08089746
Stop Event
iter limit
node limit
Counts
48 → 45
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (neg.f64 x) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (neg.f64 x) (-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))

rewrite214.0ms (2.7%)

Memory
-14.1MiB live, 74.9MiB allocated
Rules
3 412×lower-fma.f64
3 412×lower-fma.f32
2 124×lower-*.f64
2 124×lower-*.f32
1 648×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
01220
15120
236820
3566420
0932120
Stop Event
iter limit
node limit
iter limit
Counts
4 → 331
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)))) (-.f64 (+.f64 (expm1.f64 (log1p.f64 x)) x) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (fma.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (+.f64 (+.f64 (expm1.f64 (log1p.f64 x)) x) (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(*.f64 (/.f64 (+.f64 (expm1.f64 (log1p.f64 x)) x) (+.f64 (expm1.f64 (log1p.f64 x)) x)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (+.f64 (expm1.f64 (log1p.f64 x)) x) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (+.f64 (+.f64 (expm1.f64 (log1p.f64 x)) x) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (+.f64 (expm1.f64 (log1p.f64 x)) x))
(*.f64 (pow.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(*.f64 (+.f64 (expm1.f64 (log1p.f64 x)) x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(*.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (pow.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (pow.f64 (neg.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (pow.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(pow.f64 (/.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (expm1.f64 (log1p.f64 x)) x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) (fma.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (pow.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64))) (pow.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))))
(/.f64 (-.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (expm1.f64 (log1p.f64 x)) x)) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 (expm1.f64 (log1p.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 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (*.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) (*.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x)) (*.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x)))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) x))
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(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x)))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (sqrt.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log1p.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))

eval138.0ms (1.7%)

Memory
-8.1MiB live, 65.9MiB allocated
Compiler

Compiled 8 829 to 1 202 computations (86.4% saved)

prune92.0ms (1.2%)

Memory
3.5MiB live, 47.8MiB allocated
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3679376
Fresh000
Picked011
Done000
Total36710377
Accuracy
100.0%
Counts
377 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.8%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
7.3%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
7.9%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.8%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.4%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
6.0%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x))
Compiler

Compiled 217 to 163 computations (24.9% saved)

simplify131.0ms (1.6%)

Memory
10.0MiB live, 86.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
cost-diff2432
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
cost-diff0
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
cost-diff0
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
cost-diff0
(pow.f64 x #s(literal 3 binary64))
cost-diff0
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
Rules
3 032×lower-fma.f32
3 022×lower-fma.f64
1 256×lower-*.f32
1 252×lower-*.f64
600×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033210
058196
194196
2169196
3278196
4333196
5407196
6509196
7777196
81146196
91533196
101925196
112318196
122577196
132678196
142696196
152700196
162700196
172726196
182734196
192734196
202738196
02738196
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 7/128 binary64)
(*.f64 x x)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
x
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
#s(literal 7/128 binary64)
(*.f64 x x)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
x
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

localize137.0ms (1.7%)

Memory
9.7MiB live, 283.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy0.01953125
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy0.03125
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
accuracy58.741880517172625
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
accuracy0
(+.f64 #s(literal 1 binary64) x)
accuracy0.0078125
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy0.24191319617623644
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy58.741880517172625
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
accuracy0
(+.f64 #s(literal 1 binary64) x)
accuracy0.0078125
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy0.5178972547042376
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
accuracy58.741880517172625
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
accuracy0
(-.f64 #s(literal 1 binary64) x)
accuracy0.00390625
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy1.3053698987463491
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy0
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy0
(pow.f64 x #s(literal 3 binary64))
accuracy0
(*.f64 x x)
accuracy0.16159128368447132
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
Samples
57.0ms155×1valid
44.0ms90×2valid
4.0ms11×0valid
Compiler

Compiled 177 to 29 computations (83.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 68.0ms
adjust: 19.0ms (27.8% of total)
ival-sqrt: 13.0ms (19% of total)
ival-mult: 12.0ms (17.6% of total)
ival-add: 11.0ms (16.1% of total)
ival-sub: 9.0ms (13.2% of total)
ival-pow: 3.0ms (4.4% of total)
exact: 1.0ms (1.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series17.0ms (0.2%)

Memory
-0.4MiB live, 38.3MiB allocated
Counts
18 → 216
Calls
Call 1
Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.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 #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#s(alt (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.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 x (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.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 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 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 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow (* -1 x) 1/4) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (pow (* -1 x) 1/4)) (* -7/128 (pow (/ -1 (pow x 3)) 1/4))) x)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4)) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (* x x) (sqrt (sqrt (- 1 x))))
2.0ms
x
@inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (* x x) (sqrt (sqrt (- 1 x))))
2.0ms
x
@0
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (* x x) (sqrt (sqrt (- 1 x))))

simplify209.0ms (2.6%)

Memory
-33.7MiB live, 309.5MiB allocated
Algorithm
egg-herbie
Rules
23 126×lower-fma.f64
23 126×lower-fma.f32
5 620×lower-*.f64
5 620×lower-*.f32
4 704×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02404403
16903898
221693595
081113390
Stop Event
iter limit
node limit
Counts
216 → 208
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -1/4 x))
(+ 1 (* x (- (* -3/32 x) 1/4)))
(+ 1 (* x (- (* x (- (* -7/128 x) 3/32)) 1/4)))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (* -1/4 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (+ (* -1/4 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) x)) (* -3/32 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (pow x 2)))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (+ (* -1/4 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) x)) (+ (* -3/32 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (pow x 2))) (* -7/128 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (pow x 3))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow (* -1 x) 1/4)
(+ (* -1/4 (pow (/ -1 (pow x 3)) 1/4)) (pow (* -1 x) 1/4))
(+ (* -1 (/ (+ (* 3/32 (pow (/ -1 (pow x 3)) 1/4)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (pow (* -1 x) 1/4)) (* -7/128 (pow (/ -1 (pow x 3)) 1/4))) x)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 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)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* -1/4 x))
(fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -3/32 x) 1/4)))
(fma.f64 (fma.f64 #s(literal -3/32 binary64) x #s(literal -1/4 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -7/128 x) 3/32)) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -7/128 binary64) x #s(literal -3/32 binary64)) x #s(literal -1/4 binary64)) x #s(literal 1 binary64))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 7/128 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 7/128 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 7/128 binary64))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 7/128 binary64))) (pow.f64 x #s(literal 5 binary64)))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 7/128 (pow x 2))
(*.f64 #s(literal 7/128 binary64) (*.f64 x x))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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x
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(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow (* -1 x) 1/4)
(pow.f64 (neg.f64 x) #s(literal 1/4 binary64))
(+ (* -1/4 (pow (/ -1 (pow x 3)) 1/4)) (pow (* -1 x) 1/4))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* 3/32 (pow (/ -1 (pow x 3)) 1/4)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
(-.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 3/32 binary64) (*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) x))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (pow (* -1 x) 1/4)) (* -7/128 (pow (/ -1 (pow x 3)) 1/4))) x)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
(-.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) #s(literal 1/4 binary64) (/.f64 (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 7/128 binary64) (*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) #s(literal 3/32 binary64))) x)) x))

rewrite180.0ms (2.3%)

Memory
9.7MiB live, 326.2MiB allocated
Rules
5 880×lower-*.f32
5 876×lower-*.f64
4 740×lower-/.f64
4 740×lower-/.f32
4 336×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033159
058145
1222145
21607145
09327145
Stop Event
iter limit
node limit
iter limit
Counts
18 → 523
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(*.f64 x x)
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64)) x))
(*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (-.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) x)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (-.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 (pow.f64 (+.f64 x (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))) #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/512 binary64))) (fma.f64 (+.f64 x (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))) (+.f64 x (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))) (-.f64 (pow.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (*.f64 (+.f64 x (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(/.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 3 binary64)) #s(literal 343/2097152 binary64) (pow.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (-.f64 x (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (-.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (-.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) x))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (-.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) x))))
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(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fabs.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))))
(fabs.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 (neg.f64 x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 (neg.f64 x))))

eval211.0ms (2.6%)

Memory
9.4MiB live, 396.2MiB allocated
Compiler

Compiled 29 716 to 2 972 computations (90% saved)

prune33.0ms (0.4%)

Memory
14.6MiB live, 93.1MiB allocated
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1 22861 234
Fresh404
Picked505
Done011
Total1 23771 244
Accuracy
100.0%
Counts
1 244 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
8.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.4%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
7.8%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
6.0%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
5.1%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Compiler

Compiled 147 to 105 computations (28.6% saved)

simplify147.0ms (1.8%)

Memory
-13.3MiB live, 68.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
cost-diff0
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
cost-diff0
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
cost-diff0
(*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Rules
3 120×lower-fma.f32
3 108×lower-fma.f64
1 296×lower-*.f32
1 292×lower-*.f64
604×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030234
048234
183234
2129232
3253232
4426232
5594232
6732232
7933232
81368232
91756232
102165232
112554232
122782232
132887232
142914232
152932232
162938232
172984232
183000232
193000232
203004232
03004230
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
(*.f64 x x)
x
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)))
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 (*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(*.f64 x x)
x
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)

localize165.0ms (2.1%)

Memory
-5.7MiB live, 282.7MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
accuracy0.24191319617623644
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy0.4918162562075553
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
accuracy0
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
accuracy0.4918162562075553
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy0.5178972547042376
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
accuracy0
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
accuracy0.5178972547042376
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
accuracy1.3053698987463491
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
accuracy1.3053698987463491
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy1.3611759654161286
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
accuracy0
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
accuracy0
(*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
accuracy0
(*.f64 x x)
accuracy0.16159128368447132
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Samples
74.0ms90×2valid
66.0ms155×1valid
2.0ms11×0valid
Compiler

Compiled 165 to 28 computations (83% saved)

Precisions
Click to see histograms. Total time spent on operations: 108.0ms
adjust: 41.0ms (38.1% of total)
ival-add: 34.0ms (31.6% of total)
ival-sqrt: 15.0ms (13.9% of total)
ival-mult: 11.0ms (10.2% of total)
ival-sub: 5.0ms (4.6% of total)
exact: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series17.0ms (0.2%)

Memory
-12.4MiB live, 28.0MiB allocated
Counts
16 → 192
Calls
Call 1
Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/8 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/8 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/8 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (* -1/8 x) -1/2))
1.0ms
x
@inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (* -1/8 x) -1/2))
1.0ms
x
@0
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (* -1/8 x) -1/2))

simplify210.0ms (2.6%)

Memory
27.9MiB live, 255.4MiB allocated
Algorithm
egg-herbie
Rules
21 420×lower-fma.f64
21 420×lower-fma.f32
5 016×lower-+.f64
5 016×lower-+.f32
4 948×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01763924
15473481
218873220
375833220
085293002
Stop Event
iter limit
node limit
Counts
192 → 187
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
-1/2
(- (* -1/8 x) 1/2)
(- (* -1/8 x) 1/2)
(- (* -1/8 x) 1/2)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1/8 x)
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1/8 x)
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* 1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 x) 1/2)
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
(- (* -1/8 x) 1/2)
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
(- (* -1/8 x) 1/2)
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
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(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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(* 7/128 (pow x 4))
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(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
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(* 7/128 (pow x 2))
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(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
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(pow x 2)
(*.f64 x x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
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(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
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(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
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(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
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(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
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(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
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(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
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(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
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(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (/ 1 x) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
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(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
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(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
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(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
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(sqrt x)
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(* 1/2 x)
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(* x (+ 1/2 (/ 1 x)))
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(*.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (neg.f64 x) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (neg.f64 x) (-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal -1/2 binary64) x)))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal -1/2 binary64) x)))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (neg.f64 x) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (neg.f64 x) (-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
(* -1 (* x (+ 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))

rewrite167.0ms (2.1%)

Memory
5.3MiB live, 152.2MiB allocated
Rules
5 458×lower-*.f32
5 454×lower-*.f64
4 584×lower-/.f64
4 584×lower-/.f32
3 740×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030166
048166
1224165
21704165
09236164
Stop Event
iter limit
node limit
iter limit
Counts
16 → 306
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
(*.f64 x x)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(*.f64 (*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 (*.f64 x x) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)))
(*.f64 x (*.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x)) (-.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (*.f64 (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x))) (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x))) (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 #s(literal 7/128 binary64) (*.f64 x x)))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 x x))) (neg.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 343/2097152 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (*.f64 x x))) (neg.f64 (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)))) (neg.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal 343/2097152 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)))) (neg.f64 (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 7/1024 binary64))))))
(/.f64 (*.f64 (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 x x)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal 343/2097152 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (*.f64 x x)) (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 7/1024 binary64)))))
(/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64))) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal 343/2097152 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64))) (fma.f64 #s(literal 49/16384 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 7/1024 binary64)))))
(fma.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x x)) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
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(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64))) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64))) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64))) (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 3 binary64)))))
(fma.f64 #s(literal -1 binary64) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))))) (/.f64 (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))))))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (pow.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(+.f64 (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))))
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))) (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 4 binary64)) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/262144 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 4 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/262144 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/134217728 binary64) (pow.f64 x #s(literal 9 binary64)) #s(literal -1/512 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/262144 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 1/64 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4096 binary64)))) (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 x x))) (-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))) (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))) (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64))))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
(fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) x))) (/.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x x)) (-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(+.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) x))

eval121.0ms (1.5%)

Memory
-21.7MiB live, 154.8MiB allocated
Compiler

Compiled 15 940 to 1 552 computations (90.3% saved)

prune13.0ms (0.2%)

Memory
32.5MiB live, 32.5MiB allocated
Pruning

9 alts after pruning (4 fresh and 5 done)

PrunedKeptTotal
New6533656
Fresh011
Picked145
Done011
Total6549663
Accuracy
100.0%
Counts
663 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
8.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.8%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
6.0%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
6.0%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
5.4%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
5.1%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Compiler

Compiled 91 to 68 computations (25.3% saved)

simplify123.0ms (1.5%)

Memory
-26.6MiB live, 57.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
(+.f64 x #s(literal 1 binary64))
cost-diff0
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff256
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
cost-diff0
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
cost-diff0
#s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))
cost-diff0
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))
cost-diff0
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
cost-diff0
(*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Rules
11 050×lower-fma.f32
11 046×lower-fma.f64
2 726×lower-*.f32
2 720×lower-*.f64
2 316×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038231
055231
195227
2149221
3240221
4881221
52904221
64818221
77105221
08060209
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))
#s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x))
(fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x)
(*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x) x)
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 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(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))
#s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal -1 binary64))
x
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))

localize111.0ms (1.4%)

Memory
21.7MiB live, 96.1MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy0.0078125
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy0.0078125
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy58.67734121199447
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
accuracy0.4918162562075553
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy0.5178972547042376
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))
accuracy1.360379922847554
#s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
accuracy0.5178972547042376
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))
accuracy1.3053698987463491
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy58.741880517172625
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
accuracy62.57855099877415
#s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))
accuracy0
(*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
accuracy0
(*.f64 x x)
accuracy0.16159128368447132
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
accuracy0.5352360814677357
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
Samples
46.0ms155×1valid
43.0ms90×2valid
2.0ms11×0valid
Compiler

Compiled 156 to 28 computations (82.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 63.0ms
adjust: 18.0ms (28.8% of total)
ival-sqrt: 12.0ms (19.2% of total)
ival-add: 12.0ms (19.2% of total)
ival-sub: 9.0ms (14.4% of total)
ival-mult: 8.0ms (12.8% of total)
ival-div: 3.0ms (4.8% of total)
exact: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series17.0ms (0.2%)

Memory
7.8MiB live, 7.8MiB allocated
Counts
20 → 240
Calls
Call 1
Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) (patch (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 2 x) (taylor -inf x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt x (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (sqrt (- 1 x)) (- (+ x 1) (- 1 x)) (/ (- (+ x 1) (- 1 x)) (+ (sqrt (+ x 1)) (sqrt (- 1 x)))) (+ x 1) (- 1 x) (+ (* -1/2 x) 1) (sqrt (+ x 1)) (+ (sqrt (+ x 1)) (sqrt (- 1 x))) (sqrt (- 1 x)))
3.0ms
x
@-inf
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (sqrt (- 1 x)) (- (+ x 1) (- 1 x)) (/ (- (+ x 1) (- 1 x)) (+ (sqrt (+ x 1)) (sqrt (- 1 x)))) (+ x 1) (- 1 x) (+ (* -1/2 x) 1) (sqrt (+ x 1)) (+ (sqrt (+ x 1)) (sqrt (- 1 x))) (sqrt (- 1 x)))
1.0ms
x
@0
((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (sqrt (- 1 x)) (- (+ x 1) (- 1 x)) (/ (- (+ x 1) (- 1 x)) (+ (sqrt (+ x 1)) (sqrt (- 1 x)))) (+ x 1) (- 1 x) (+ (* -1/2 x) 1) (sqrt (+ x 1)) (+ (sqrt (+ x 1)) (sqrt (- 1 x))) (sqrt (- 1 x)))

simplify198.0ms (2.5%)

Memory
-13.6MiB live, 103.7MiB allocated
Algorithm
egg-herbie
Rules
10 600×lower-fma.f64
10 600×lower-fma.f32
6 004×lower-*.f64
6 004×lower-*.f32
3 544×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03454801
110714134
241273907
082003668
Stop Event
iter limit
node limit
Counts
240 → 234
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
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x
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(/.f64 #s(literal -2 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(fma.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (/.f64 (sqrt.f64 x) (*.f64 x x)) (/.f64 #s(literal -2 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(-.f64 (fma.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (/.f64 (sqrt.f64 x) (*.f64 x x)) (/.f64 #s(literal -2 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 (fma.f64 (/.f64 (pow.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (pow.f64 x #s(literal 4 binary64))))
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(-.f64 (/.f64 (+.f64 (fma.f64 (/.f64 (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (pow.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (/.f64 (*.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64)))) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 5 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal -2 binary64) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 x x))) (fma.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* 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)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))

rewrite188.0ms (2.3%)

Memory
8.4MiB live, 167.7MiB allocated
Rules
5 410×lower-*.f32
5 404×lower-*.f64
4 572×lower-/.f32
4 570×lower-/.f64
4 100×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038202
055202
1239191
21920191
09132181
Stop Event
iter limit
node limit
iter limit
Counts
20 → 687
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
(*.f64 x x)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64)))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(+.f64 x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x))
(*.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x) x)
(*.f64 (*.f64 x x) #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)))
(*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 x (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x))
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) #s(literal 2 binary64))) (pow.f64 (+.f64 #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) (pow.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64)))
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(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (neg.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 1 binary64) (neg.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 x)) #s(literal 1/2 binary64)))

eval160.0ms (2%)

Memory
-23.4MiB live, 218.8MiB allocated
Compiler

Compiled 33 214 to 3 406 computations (89.7% saved)

prune32.0ms (0.4%)

Memory
16.9MiB live, 63.5MiB allocated
Pruning

9 alts after pruning (0 fresh and 9 done)

PrunedKeptTotal
New1 06401 064
Fresh000
Picked044
Done055
Total1 06491 073
Accuracy
100.0%
Counts
1 073 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
8.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.8%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
6.0%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
6.0%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
5.4%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
5.1%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
99.7%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Compiler

Compiled 300 to 138 computations (54% saved)

regimes13.0ms (0.2%)

Memory
-21.8MiB live, 15.9MiB allocated
Counts
19 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Calls

2 calls:

8.0ms
x
4.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 10 to 8 computations (20% saved)

regimes7.0ms (0.1%)

Memory
10.1MiB live, 10.1MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
Calls

2 calls:

3.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0.1%)

Memory
7.2MiB live, 7.2MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
7.8%1x
7.8%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0%)

Memory
6.6MiB live, 6.6MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
6.0%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
6.0%1x
Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0%)

Memory
6.0MiB live, 6.0MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
Calls

2 calls:

2.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
6.0%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
6.0%1x
Compiler

Compiled 10 to 8 computations (20% saved)

regimes6.0ms (0.1%)

Memory
-32.0MiB live, 5.3MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
Calls

2 calls:

5.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
5.4%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
5.4%1x
Compiler

Compiled 10 to 8 computations (20% saved)

regimes2.0ms (0%)

Memory
4.6MiB live, 4.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Calls

2 calls:

1.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
5.1%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
5.1%1x
Compiler

Compiled 10 to 8 computations (20% saved)

simplify24.0ms (0.3%)

Memory
-1.3MiB live, 36.3MiB allocated
Algorithm
egg-herbie
Rules
18×+-commutative-binary64-+.f64
18×sub-neg-binary64-neg.f64-+.f64--.f64
14×*-commutative-binary64-*.f64
neg-sub0-binary64--.f64-neg.f64
neg-mul-1-binary64-*.f64-neg.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041140
156140
270140
378140
482140
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))

soundness1.0s (12.7%)

Memory
23.2MiB live, 545.4MiB allocated
Rules
23 126×lower-fma.f64
23 126×lower-fma.f32
21 484×lower-fma.f64
21 484×lower-fma.f32
21 420×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0161971
1493856
21730798
37227798
08089746
033159
058145
1222145
21607145
09327145
02404403
16903898
221693595
081113390
01763924
15473481
218873220
375833220
085293002
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 202 to 140 computations (30.7% saved)

preprocess51.0ms (0.6%)

Memory
-11.3MiB live, 65.1MiB allocated
Remove

(negabs x)

Compiler

Compiled 202 to 112 computations (44.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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