bug333 (missed optimization)

Time bar (total: 15.5s)

analyze0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×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)

sample1.9s (12.1%)

Memory
-25.8MiB live, 2 855.2MiB allocated
Samples
740.0ms3 191×2valid
691.0ms4 787×1valid
14.0ms278×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-sqrt: 373.0ms (32.7% of total)
adjust: 295.0ms (25.9% of total)
ival-sub: 268.0ms (23.5% of total)
ival-add: 135.0ms (11.8% of total)
ival-<=: 43.0ms (3.8% of total)
ival-and: 11.0ms (1% of total)
exact: 10.0ms (0.9% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

preprocess28.0ms (0.2%)

Memory
24.6MiB live, 61.3MiB allocated
Algorithm
1×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
1×iter limit
1×saturated
1×iter limit
1×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)))
Symmetry

(negabs x)

explain218.0ms (1.4%)

Memory
-23.7MiB live, 258.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2540-1(0.03663590245616997)(-.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)))cancellation2530
Confusion
Predicted +Predicted -
+2531
-02
Precision
1.0
Recall
0.9960629921259843
Confusion?
Predicted +Predicted MaybePredicted -
+25301
-002
Precision?
1.0
Recall?
0.9960629921259843
Freqs
test
numberfreq
03
1253
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
79.0ms300×1valid
46.0ms198×2valid
1.0ms14×0valid
Compiler

Compiled 74 to 32 computations (56.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 105.0ms
ival-sqrt: 35.0ms (33.2% of total)
ival-add: 33.0ms (31.3% of total)
ival-sub: 23.0ms (21.8% of total)
adjust: 13.0ms (12.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.1MiB live, 1.1MiB 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 10 to 7 computations (30% saved)

simplify10.0ms (0.1%)

Memory
14.8MiB live, 14.8MiB allocated
Algorithm
1×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
1×iter limit
1×saturated
1×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)))
(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)

localize138.0ms (0.9%)

Memory
-3.3MiB live, 72.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓accuracy8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Samples
61.0ms99×2valid
17.0ms150×1valid
0.0ms7×0valid
Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 68.0ms
adjust: 50.0ms (73.4% of total)
ival-sqrt: 9.0ms (13.2% of total)
ival-sub: 5.0ms (7.3% of total)
ival-add: 3.0ms (4.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory
9.1MiB live, 9.1MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#<alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x))>
#<alt (+.f64 #s(literal 1 binary64) x)>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<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)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
#<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))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<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))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<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))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
Calls

12 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
1.0ms
x
@-inf
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms
x
@0
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms
x
@-inf
(sqrt (+ 1 x))
0.0ms
x
@-inf
(sqrt (- 1 x))

rewrite4.0s (26.1%)

Memory
23.3MiB live, 356.7MiB allocated
Algorithm
1×batch-egg-rewrite
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
1×iter limit
1×node limit
1×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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(+.f64 (neg.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) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.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)))) (neg.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))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 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(literal 0 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) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.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))))))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.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))))))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))))))
(fma.f64 (sqrt.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) x)) (/.f64 (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)))) (neg.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))))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))))))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.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))))))
(fma.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.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))))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
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(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (+.f64 x #s(literal -1 binary64))))
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(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
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(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 #s(literal -1 binary64) (+.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
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(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (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 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log1p.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 x)) #s(literal 2 binary64)))
(fabs.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (*.f64 x 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) (*.f64 x x)))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
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(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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)))
(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))
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #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 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 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 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (+.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 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))

simplify953.0ms (6.2%)

Memory
-109.3MiB live, 792.4MiB allocated
Algorithm
1×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
21729798
37219798
08083746
Stop Event
1×iter limit
1×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))))))))
(* 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)))))))
(* -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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(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 (* (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
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (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 (* (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 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #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 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (*.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.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))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* 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 x (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))
(* 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 x (+.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/16 binary64) (/.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))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -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)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.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))))) (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 x (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (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 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (-.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (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 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (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))))))
(neg.f64 (*.f64 x (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (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 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
(* 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 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(* 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 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (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))))))
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (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)))))))
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))

eval167.0ms (1.1%)

Memory
-11.3MiB live, 65.7MiB allocated
Compiler

Compiled 9 828 to 1 184 computations (88% saved)

prune101.0ms (0.7%)

Memory
27.9MiB live, 67.1MiB allocated
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3724376
Fresh000
Picked011
Done000
Total3725377
Accuracy
100.0%
Counts
377 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
▶99.4%
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
▶8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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))))
✓8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶8.2%
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 74 to 43 computations (41.9% saved)

simplify759.0ms (4.9%)

Memory
-14.6MiB live, 657.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
✓cost-diff0
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
✓cost-diff0
(*.f64 x #s(literal 1/8 binary64))
✓cost-diff0
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
✓cost-diff0
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 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)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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))))
✓cost-diff13184
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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)))
✓cost-diff0
(fma.f64 x x #s(literal -1 binary64))
✓cost-diff0
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
✓cost-diff0
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓cost-diff1408
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
Rules
28 178×lower-fma.f32
28 170×lower-fma.f64
3 258×lower-*.f32
3 246×lower-*.f64
2 162×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030195
057209
1102187
2194168
3374158
4770158
51961158
66185158
08058156
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))
#s(literal 1 binary64)
(+.f64 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)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
x
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(*.f64 x x)
x
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(*.f64 x #s(literal 7/128 binary64))
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
Outputs
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (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 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(+.f64 x #s(literal 1 binary64))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))
#s(literal 1 binary64)
(+.f64 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)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 x #s(literal 1 binary64))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 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
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 (+.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) x)
x
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(fma.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(*.f64 x x)
x
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(*.f64 x #s(literal 7/128 binary64))
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)

localize365.0ms (2.4%)

Memory
32.5MiB live, 551.5MiB allocated
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 x #s(literal 7/128 binary64))
✓accuracy100.0%
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
✓accuracy100.0%
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
✓accuracy100.0%
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
✓accuracy100.0%
(*.f64 x #s(literal 1/8 binary64))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
✓accuracy100.0%
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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)))
✓accuracy8.3%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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))))
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
✓accuracy100.0%
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
✓accuracy8.3%
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Samples
195.0ms99×2valid
119.0ms150×1valid
1.0ms6×0valid
1.0ms1×5exit
Compiler

Compiled 206 to 35 computations (83% saved)

Precisions
Click to see histograms. Total time spent on operations: 273.0ms
ival-pow: 159.0ms (58.3% of total)
ival-sqrt: 37.0ms (13.6% of total)
adjust: 23.0ms (8.4% of total)
ival-mult: 16.0ms (5.9% of total)
ival-div: 13.0ms (4.8% of total)
ival-add: 12.0ms (4.4% of total)
ival-sub: 11.0ms (4% of total)
exact: 1.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series22.0ms (0.1%)

Memory
-38.4MiB live, 42.0MiB allocated
Counts
18 → 216
Calls
Call 1
Inputs
#<alt (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))>
#<alt (-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))>
#<alt (fma.f64 x x #s(literal -1 binary64))>
#<alt (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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)))>
#<alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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))))>
#<alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x))>
#<alt (+.f64 #s(literal 1 binary64) x)>
#<alt (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)>
#<alt (*.f64 x (*.f64 x #s(literal 1/8 binary64)))>
#<alt (*.f64 x #s(literal 1/8 binary64))>
#<alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)>
#<alt (*.f64 x x)>
#<alt (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x))>
#<alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))>
#<alt (*.f64 x #s(literal 7/128 binary64))>
Outputs
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<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)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (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)))))))>
#<alt (* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* (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))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<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))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt -1>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<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)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
#<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))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<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))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<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))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* 7/128 (pow x 3))>
#<alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 3))>
#<alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt 1/8>
#<alt (+ 1/8 (* 7/128 (pow x 2)))>
#<alt (+ 1/8 (* 7/128 (pow x 2)))>
#<alt (+ 1/8 (* 7/128 (pow x 2)))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1/4 x))>
#<alt (+ 1 (* x (- (* -11/32 x) 1/4)))>
#<alt (+ 1 (* x (- (* x (- (* 1/128 x) 11/32)) 1/4)))>
#<alt (* (pow (* 1 (pow x 3)) 1/4) (sqrt -1))>
#<alt (* x (+ (* -1/4 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt -1))) (* (pow (/ 1 x) 1/4) (sqrt -1))))>
#<alt (* x (+ (* -1/4 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt -1))) (+ (* 5/32 (* (pow (/ 1 (pow x 9)) 1/4) (sqrt -1))) (+ (* 1/2 (* (pow (/ 1 (pow x 9)) 1/4) (/ 1 (sqrt -1)))) (* (pow (/ 1 x) 1/4) (sqrt -1))))))>
#<alt (* x (+ (* -1/4 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt -1))) (+ (* -1/8 (* (pow (/ 1 (pow x 13)) 1/4) (/ 1 (sqrt -1)))) (+ (* -15/128 (* (pow (/ 1 (pow x 13)) 1/4) (sqrt -1))) (+ (* 5/32 (* (pow (/ 1 (pow x 9)) 1/4) (sqrt -1))) (+ (* 1/2 (* (pow (/ 1 (pow x 9)) 1/4) (/ 1 (sqrt -1)))) (* (pow (/ 1 x) 1/4) (sqrt -1))))))))>
#<alt (* -1 (* x (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* 5/32 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* 1/4 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 15/128 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/8 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (+ (* 5/32 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))) x)) (* 1/4 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
#<alt (* 7/128 x)>
Calls

54 calls:

TimeVariablePointExpression
1.0ms
x
@0
(+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x)
1.0ms
x
@-inf
(/ (sqrt (- 1 (* x x))) (pow (+ 1 x) 1/4))
1.0ms
x
@-inf
(- (sqrt (* (+ (* x x) -1) (/ 1 (+ x -1)))) (sqrt (- 1 x)))
1.0ms
x
@inf
(/ (sqrt (- 1 (* x x))) (pow (+ 1 x) 1/4))
1.0ms
x
@0
(/ (sqrt (- 1 (* x x))) (pow (+ 1 x) 1/4))

rewrite348.0ms (2.2%)

Memory
-32.7MiB live, 698.8MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 824×lower-fma.f32
5 816×lower-fma.f64
4 162×lower-/.f32
4 156×lower-/.f64
3 890×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030154
057163
1239103
21914103
08643101
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 1 199
Calls
Call 1
Inputs
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 x x #s(literal -1 binary64))
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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) x)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(*.f64 x #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(*.f64 x x)
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 x #s(literal 7/128 binary64))
Outputs
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 x x)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 x x)) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))))
(exp.f64 (log1p.f64 x))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fabs.f64 (+.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (neg.f64 x))
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 #s(literal 1 binary64) (neg.f64 x))))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 #s(literal 1 binary64) (neg.f64 x))))))
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (/.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x x (+.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (/.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 x x) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64)))))
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(*.f64 x #s(literal 7/128 binary64))
(*.f64 #s(literal 7/128 binary64) x)

simplify474.0ms (3.1%)

Memory
12.5MiB live, 882.4MiB allocated
Algorithm
1×egg-herbie
Rules
17 072×lower-fma.f64
17 072×lower-fma.f32
5 572×lower-+.f64
5 572×lower-+.f32
4 184×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03103014
19502694
232872549
080762399
Stop Event
1×iter limit
1×node limit
Counts
216 → 208
Calls
Call 1
Inputs
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* 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))))))))
(* 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)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (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 (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* (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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(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 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (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)))
(* (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 (* (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)))))))
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 (- (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)))))))
(* -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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(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 (* (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
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 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 (* 7/128 (pow x 2))))))
(* 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)))))
(* 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 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/8 x)
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* 7/128 (pow x 3))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 3))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (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)))
(* 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)))))
(* 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
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (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 (* (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
(+ 1 (* -1/4 x))
(+ 1 (* x (- (* -11/32 x) 1/4)))
(+ 1 (* x (- (* x (- (* 1/128 x) 11/32)) 1/4)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt -1))
(* x (+ (* -1/4 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt -1))) (* (pow (/ 1 x) 1/4) (sqrt -1))))
(* x (+ (* -1/4 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt -1))) (+ (* 5/32 (* (pow (/ 1 (pow x 9)) 1/4) (sqrt -1))) (+ (* 1/2 (* (pow (/ 1 (pow x 9)) 1/4) (/ 1 (sqrt -1)))) (* (pow (/ 1 x) 1/4) (sqrt -1))))))
(* x (+ (* -1/4 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt -1))) (+ (* -1/8 (* (pow (/ 1 (pow x 13)) 1/4) (/ 1 (sqrt -1)))) (+ (* -15/128 (* (pow (/ 1 (pow x 13)) 1/4) (sqrt -1))) (+ (* 5/32 (* (pow (/ 1 (pow x 9)) 1/4) (sqrt -1))) (+ (* 1/2 (* (pow (/ 1 (pow x 9)) 1/4) (/ 1 (sqrt -1)))) (* (pow (/ 1 x) 1/4) (sqrt -1))))))))
(* -1 (* x (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))
(* -1 (* x (+ (* -1/4 (/ (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* 5/32 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* 1/4 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 15/128 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/8 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (+ (* 5/32 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))) x)) (* 1/4 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
Outputs
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)
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)
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)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (*.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))))
(* 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 x (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))))))))
(* 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 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/16 binary64) (/.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))) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (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)))))))
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(neg.f64 (*.f64 x (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))) (/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5/32 binary64)))) x)) x))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 15/128 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/8 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (+ (* 5/32 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))) x)) (* 1/4 (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)) (* (exp (* 1/4 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))))
(neg.f64 (*.f64 x (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5/32 binary64)))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 15/128 binary64)))) x)) (neg.f64 x))) x))))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))

eval433.0ms (2.8%)

Memory
4.4MiB live, 386.0MiB allocated
Compiler

Compiled 56 224 to 4 353 computations (92.3% saved)

prune286.0ms (1.8%)

Memory
25.1MiB live, 380.0MiB allocated
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New1 83031 833
Fresh000
Picked134
Done011
Total1 83171 838
Accuracy
100.0%
Counts
1 838 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶8.2%
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓99.5%
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
✓99.4%
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
▶8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
✓8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓8.2%
(-.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶6.3%
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Compiler

Compiled 104 to 63 computations (39.4% saved)

simplify520.0ms (3.4%)

Memory
-13.4MiB live, 593.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
✓cost-diff0
(+.f64 x #s(literal 1 binary64))
✓cost-diff0
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64))
✓cost-diff0
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓cost-diff0
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x 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)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓cost-diff0
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Rules
23 590×lower-fma.f32
23 586×lower-fma.f64
3 718×lower-*.f32
3 710×lower-*.f64
2 456×lower-+.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026180
049170
188168
2143168
3215168
4288168
5399168
6526168
7818168
81350168
92158168
103844168
115290168
126313168
136645168
146831168
156877168
166906168
177038168
08108168
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
x
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 x (*.f64 x x))
(*.f64 x x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(+.f64 #s(literal 1 binary64) (fma.f64 x x x))
(fma.f64 x x x)
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
#s(literal -3/8 binary64)
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
Outputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
x
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
#s(literal 1/8 binary64)
(*.f64 x x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 x (fma.f64 x 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
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 x (*.f64 x x))
(*.f64 x x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(sqrt.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))))
(+.f64 #s(literal 1 binary64) (fma.f64 x x x))
(+.f64 x (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x x)
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
#s(literal -3/8 binary64)
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))

localize484.0ms (3.1%)

Memory
-15.3MiB live, 442.9MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓accuracy100.0%
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓accuracy100.0%
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
✓accuracy8.3%
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
✓accuracy99.9%
(*.f64 x (*.f64 x x))
✓accuracy8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓accuracy99.9%
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Samples
281.0ms99×2valid
151.0ms150×1valid
2.0ms7×0valid
Compiler

Compiled 188 to 29 computations (84.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 406.0ms
ival-pow: 308.0ms (75.8% of total)
ival-sqrt: 24.0ms (5.9% of total)
adjust: 19.0ms (4.7% of total)
ival-neg: 14.0ms (3.4% of total)
ival-add: 13.0ms (3.2% of total)
ival-mult: 10.0ms (2.5% of total)
ival-sub: 9.0ms (2.2% of total)
ival-div: 8.0ms (2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series60.0ms (0.4%)

Memory
-3.6MiB live, 70.5MiB allocated
Counts
14 → 168
Calls
Call 1
Inputs
#<alt (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))>
#<alt (*.f64 #s(literal 1/8 binary64) (*.f64 x x))>
#<alt (*.f64 x x)>
#<alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))>
#<alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x))>
#<alt (+.f64 #s(literal 1 binary64) x)>
#<alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))>
#<alt (fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))>
#<alt (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64))>
#<alt (+.f64 x #s(literal 1 binary64))>
#<alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))>
#<alt (*.f64 x (*.f64 x x))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))>
Outputs
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<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)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
#<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))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<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))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<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))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<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)))))>
#<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))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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))))))>
#<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)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -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))))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (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)))) (+ (* 1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))>
#<alt 1>
#<alt (+ 1 (* -3/8 x))>
#<alt (+ 1 (* x (- (* 33/128 x) 3/8)))>
#<alt (+ 1 (* x (- (* x (+ 33/128 (* -209/1024 x))) 3/8)))>
#<alt (pow (/ 1 (pow x 3)) 1/8)>
#<alt (+ (* -3/8 (pow (/ 1 (pow x 11)) 1/8)) (pow (/ 1 (pow x 3)) 1/8))>
#<alt (+ (* -3/8 (pow (/ 1 (pow x 11)) 1/8)) (+ (* 33/128 (pow (/ 1 (pow x 19)) 1/8)) (pow (/ 1 (pow x 3)) 1/8)))>
#<alt (+ (* -3/8 (pow (/ 1 (pow x 11)) 1/8)) (+ (* -209/1024 (pow (/ 1 (pow x 27)) 1/8)) (+ (* 33/128 (pow (/ 1 (pow x 19)) 1/8)) (pow (/ 1 (pow x 3)) 1/8))))>
#<alt (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x))))))>
#<alt (+ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) (* -3/8 (/ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) x)))>
#<alt (+ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) (* -1 (/ (+ (* -33/128 (/ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) x)) (* 3/8 (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))))) x)))>
#<alt (+ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -209/1024 (/ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) x)) (* 33/128 (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))))) x)) (* 3/8 (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))))) x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt -1>
#<alt (- (* 1/8 x) 1)>
#<alt (- (* x (+ 1/8 (* 55/128 x))) 1)>
#<alt (- (* x (+ 1/8 (* x (+ 55/128 (* -13/1024 x))))) 1)>
#<alt (* -1 (* (pow (* 1 (pow x 7)) 1/8) (sqrt -1)))>
#<alt (* x (+ (* -1 (* (pow (/ 1 x) 1/8) (sqrt -1))) (* 1/8 (* (pow (/ 1 (pow x 9)) 1/8) (sqrt -1)))))>
#<alt (* x (+ (* -1 (* (pow (/ 1 x) 1/8) (sqrt -1))) (+ (* -1 (/ (+ (* 9/128 (* (pow (/ 1 x) 1/8) (sqrt -1))) (* 1/2 (* (pow (/ 1 x) 1/8) (/ 1 (sqrt -1))))) (pow x 2))) (* 1/8 (* (pow (/ 1 (pow x 9)) 1/8) (sqrt -1))))))>
#<alt (* x (+ (* -1 (* (pow (/ 1 x) 1/8) (sqrt -1))) (+ (* -1 (/ (+ (* -1/16 (* (pow (/ 1 x) 1/8) (/ 1 (sqrt -1)))) (* -51/1024 (* (pow (/ 1 x) 1/8) (sqrt -1)))) (pow x 3))) (+ (* -1 (/ (+ (* 9/128 (* (pow (/ 1 x) 1/8) (sqrt -1))) (* 1/2 (* (pow (/ 1 x) 1/8) (/ 1 (sqrt -1))))) (pow x 2))) (* 1/8 (* (pow (/ 1 (pow x 9)) 1/8) (sqrt -1)))))))>
#<alt (* x (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))>
#<alt (* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/8 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)))))>
#<alt (* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* -1 (/ (+ (* -1/8 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (+ (* 9/128 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* 1/2 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (* x (sqrt -1)))))) x)))))>
#<alt (* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* 9/128 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))) (+ (* 51/1024 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* 1/16 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (* x (sqrt -1)))))) x)) (* -1/8 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<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))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<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))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))>
Calls

42 calls:

TimeVariablePointExpression
49.0ms
x
@0
(+ (* (pow (+ x 1) -3/8) (/ (sqrt (- 1 (* x x))) (neg (pow (+ x 1) 1/8)))) (sqrt (+ x 1)))
2.0ms
x
@-inf
(/ (sqrt (- 1 (* x x))) (neg (pow (+ x 1) 1/8)))
1.0ms
x
@inf
(+ (* (pow (+ x 1) -3/8) (/ (sqrt (- 1 (* x x))) (neg (pow (+ x 1) 1/8)))) (sqrt (+ x 1)))
1.0ms
x
@inf
(/ (sqrt (- 1 (* x x))) (neg (pow (+ x 1) 1/8)))
1.0ms
x
@-inf
(+ (* (pow (+ x 1) -3/8) (/ (sqrt (- 1 (* x x))) (neg (pow (+ x 1) 1/8)))) (sqrt (+ x 1)))

rewrite296.0ms (1.9%)

Memory
7.4MiB live, 257.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 670×lower-*.f32
4 662×lower-*.f64
4 154×lower-/.f32
4 150×lower-/.f64
2 842×lower-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026118
049110
120790
2144490
0842990
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
14 → 486
Calls
Call 1
Inputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 x x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64))
(+.f64 x #s(literal 1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(*.f64 x (*.f64 x x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Outputs
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
(*.f64 (*.f64 x x) (*.f64 x #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))
(*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(*.f64 (*.f64 x #s(literal 1/8 binary64)) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(+.f64 (sqrt.f64 (+.f64 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) 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 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))))) (/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(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)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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 (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))))))
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(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64))))
(pow.f64 (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64)))
(*.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (*.f64 x (*.f64 x x)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x x)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))
(fabs.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) 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) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.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)))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 x x))) #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(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 (exp.f64 (log1p.f64 (neg.f64 (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))

simplify312.0ms (2%)

Memory
-13.7MiB live, 300.3MiB allocated
Algorithm
1×egg-herbie
Rules
10 822×lower-fma.f64
10 822×lower-fma.f32
4 028×lower-*.f64
4 028×lower-*.f32
3 928×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03992767
112102537
240182269
081602138
Stop Event
1×iter limit
1×node limit
Counts
168 → 162
Calls
Call 1
Inputs
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(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))))))))
(* 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)))))))
(* -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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(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 (* (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
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (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 (* (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)))))))
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 (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -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))))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (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)))) (+ (* 1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
1
(+ 1 (* -3/8 x))
(+ 1 (* x (- (* 33/128 x) 3/8)))
(+ 1 (* x (- (* x (+ 33/128 (* -209/1024 x))) 3/8)))
(pow (/ 1 (pow x 3)) 1/8)
(+ (* -3/8 (pow (/ 1 (pow x 11)) 1/8)) (pow (/ 1 (pow x 3)) 1/8))
(+ (* -3/8 (pow (/ 1 (pow x 11)) 1/8)) (+ (* 33/128 (pow (/ 1 (pow x 19)) 1/8)) (pow (/ 1 (pow x 3)) 1/8)))
(+ (* -3/8 (pow (/ 1 (pow x 11)) 1/8)) (+ (* -209/1024 (pow (/ 1 (pow x 27)) 1/8)) (+ (* 33/128 (pow (/ 1 (pow x 19)) 1/8)) (pow (/ 1 (pow x 3)) 1/8))))
(exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x))))))
(+ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) (* -3/8 (/ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) x)))
(+ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) (* -1 (/ (+ (* -33/128 (/ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) x)) (* 3/8 (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))))) x)))
(+ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -209/1024 (/ (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))) x)) (* 33/128 (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))))) x)) (* 3/8 (exp (* 1/8 (+ (log -1) (* 3 (log (/ -1 x)))))))) x)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
-1
(- (* 1/8 x) 1)
(- (* x (+ 1/8 (* 55/128 x))) 1)
(- (* x (+ 1/8 (* x (+ 55/128 (* -13/1024 x))))) 1)
(* -1 (* (pow (* 1 (pow x 7)) 1/8) (sqrt -1)))
(* x (+ (* -1 (* (pow (/ 1 x) 1/8) (sqrt -1))) (* 1/8 (* (pow (/ 1 (pow x 9)) 1/8) (sqrt -1)))))
(* x (+ (* -1 (* (pow (/ 1 x) 1/8) (sqrt -1))) (+ (* -1 (/ (+ (* 9/128 (* (pow (/ 1 x) 1/8) (sqrt -1))) (* 1/2 (* (pow (/ 1 x) 1/8) (/ 1 (sqrt -1))))) (pow x 2))) (* 1/8 (* (pow (/ 1 (pow x 9)) 1/8) (sqrt -1))))))
(* x (+ (* -1 (* (pow (/ 1 x) 1/8) (sqrt -1))) (+ (* -1 (/ (+ (* -1/16 (* (pow (/ 1 x) 1/8) (/ 1 (sqrt -1)))) (* -51/1024 (* (pow (/ 1 x) 1/8) (sqrt -1)))) (pow x 3))) (+ (* -1 (/ (+ (* 9/128 (* (pow (/ 1 x) 1/8) (sqrt -1))) (* 1/2 (* (pow (/ 1 x) 1/8) (/ 1 (sqrt -1))))) (pow x 2))) (* 1/8 (* (pow (/ 1 (pow x 9)) 1/8) (sqrt -1)))))))
(* x (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))
(* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/8 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)))))
(* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* -1 (/ (+ (* -1/8 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (+ (* 9/128 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* 1/2 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (* x (sqrt -1)))))) x)))))
(* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* 9/128 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))) (+ (* 51/1024 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* 1/16 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (* x (sqrt -1)))))) x)) (* -1/8 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(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 (* (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
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
Outputs
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 #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)
(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 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 x (*.f64 x (*.f64 #s(literal 1/8 binary64) x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) x) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (*.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (fma.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #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 5 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* 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 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (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))))))
(neg.f64 (*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(* -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 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) (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/16 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (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)) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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)))))
(neg.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (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))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (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)))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.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))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
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(* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* -1 (/ (+ (* -1/8 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (+ (* 9/128 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* 1/2 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (* x (sqrt -1)))))) x)))))
(*.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64))) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 9/128 binary64) x)))) x)))
(* -1 (* x (+ (* -1 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* 9/128 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))) (* 1/2 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1))))) (+ (* 51/1024 (/ (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)) x)) (* 1/16 (/ (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (* x (sqrt -1)))))) x)) (* -1/8 (* (exp (* 1/8 (+ (log -1) (log (/ -1 x))))) (sqrt -1)))) x)))))
(*.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64))) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 #s(literal 51/1024 binary64) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64)))) #s(literal -9/128 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/8 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))) x)) x)))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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)))))
(neg.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (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))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (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)))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.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))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(*.f64 x (+.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* -1 (* x (sqrt -1)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(neg.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(*.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) (neg.f64 x))

eval102.0ms (0.7%)

Memory
2.6MiB live, 115.4MiB allocated
Compiler

Compiled 24 454 to 2 167 computations (91.1% saved)

prune94.0ms (0.6%)

Memory
34.1MiB live, 111.8MiB allocated
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New8006806
Fresh000
Picked213
Done134
Total80310813
Accuracy
100.0%
Counts
813 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
✓99.4%
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
▶8.3%
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
8.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64))))) #s(literal 2 binary64))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64)))))))
▶8.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶8.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))))
▶8.3%
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶8.3%
(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓6.3%
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Compiler

Compiled 399 to 177 computations (55.6% saved)

simplify222.0ms (1.4%)

Memory
-46.5MiB live, 205.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
✓cost-diff0
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
✓cost-diff0
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
✓cost-diff2304
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓cost-diff0
(+.f64 x #s(literal 1 binary64))
✓cost-diff0
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓cost-diff2944
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓cost-diff0
(-.f64 #s(literal 1 binary64) x)
✓cost-diff0
(+.f64 x #s(literal 1 binary64))
✓cost-diff320
(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓cost-diff384
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
✓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 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓cost-diff384
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
✓cost-diff0
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓cost-diff0
(/.f64 (+.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)))
✓cost-diff384
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
✓cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))))
Rules
8 654×lower-fma.f32
8 650×lower-fma.f64
2 132×lower-+.f32
2 126×lower-+.f64
1 988×lower-*.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
030421
059403
1105379
2187363
3402363
41238353
54085350
66335350
08096350
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))))
#s(literal 1 binary64)
(/.f64 (+.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 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
x
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #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 #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 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.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 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.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 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.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 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.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 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
#s(literal 1 binary64)
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(+.f64 #s(literal 1 binary64) (fma.f64 x x x))
(fma.f64 x x x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.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 (+.f64 x x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(literal 1 binary64)
(/.f64 (+.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 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x x))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.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)
x
(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)
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(+.f64 x x)
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (+.f64 x x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(+.f64 x x)
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
x
#s(literal 1 binary64)
(-.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 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 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 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (+.f64 x x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(+.f64 x x)
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
x
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 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))))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.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))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.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 (+.f64 x x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.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 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
x
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.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 x #s(literal 1 binary64)))
(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 x #s(literal 1 binary64)))))
(/.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 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
#s(literal 1 binary64)
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(+.f64 #s(literal 1 binary64) (fma.f64 x x x))
(fma.f64 x x x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x 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) (fma.f64 x x x))))

localize236.0ms (1.5%)

Memory
8.1MiB live, 277.2MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
✓accuracy100.0%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓accuracy99.9%
(*.f64 x (*.f64 x x))
✓accuracy8.3%
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
✓accuracy100.0%
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓accuracy100.0%
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓accuracy100.0%
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓accuracy8.3%
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓accuracy100.0%
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓accuracy100.0%
(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓accuracy100.0%
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓accuracy8.3%
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓accuracy100.0%
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓accuracy8.3%
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓accuracy100.0%
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))))
✓accuracy8.3%
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
Samples
77.0ms150×1valid
74.0ms98×2valid
2.0ms8×0valid
Compiler

Compiled 433 to 33 computations (92.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 113.0ms
ival-sqrt: 27.0ms (23.8% of total)
ival-div: 21.0ms (18.5% of total)
adjust: 20.0ms (17.6% of total)
ival-mult: 16.0ms (14.1% of total)
ival-sub: 15.0ms (13.2% of total)
ival-add: 12.0ms (10.6% of total)
ival-neg: 2.0ms (1.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series35.0ms (0.2%)

Memory
4.4MiB live, 46.0MiB allocated
Counts
20 → 240
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (+.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))))>
#<alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))>
#<alt (/.f64 (+.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)))>
#<alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))>
#<alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))>
#<alt (+.f64 x #s(literal 1 binary64))>
#<alt (-.f64 #s(literal 1 binary64) x)>
#<alt (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))>
#<alt (-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))>
#<alt (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))>
#<alt (/.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))>
#<alt (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))>
#<alt (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x))>
#<alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))>
#<alt (*.f64 x (*.f64 x x))>
#<alt (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -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))))))>
#<alt (- (+ (* -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)))))>
#<alt (- (+ (* -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)))))))>
#<alt (/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (- (* 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))))))>
#<alt (- (* -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)))))))>
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#<alt (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (- (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 3)))>
#<alt (+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2)))>
#<alt (+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 1/8)) 1/2)))>
#<alt (* (sqrt (pow x 3)) (sqrt -1))>
#<alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* (sqrt (pow x 3)) (sqrt -1))>
#<alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 3/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 3/8 (* -3/16 x))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* x (- (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) (* 3/16 (/ 1 (pow x 3)))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- 3/8 (* 3/16 (/ 1 x))) x)) 1/2) x)))))>
Calls

60 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(- (/ (+ x 1) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))) (/ (- 1 x) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))))
2.0ms
x
@-inf
(/ (- 1 x) (+ (sqrt (- 1 x)) (sqrt (+ x 1))))
2.0ms
x
@inf
(/ 1 (/ (+ (sqrt (- 1 x)) (sqrt (+ x 1))) (- (+ x 1) (- 1 x))))
2.0ms
x
@-inf
(- (/ (+ x 1) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))) (/ (- 1 x) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))))
2.0ms
x
@-inf
(/ 1 (/ (+ (sqrt (- 1 x)) (sqrt (+ x 1))) (- (+ x 1) (- 1 x))))

rewrite429.0ms (2.8%)

Memory
35.9MiB live, 496.6MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 590×lower-/.f32
5 576×lower-/.f64
3 688×lower-*.f32
3 678×lower-*.f64
3 436×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030265
059237
1258223
22490217
08901215
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 2 032
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.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 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.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 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.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 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.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 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(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 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 x (*.f64 x x))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
Outputs
(+.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 (neg.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 #s(literal 1 binary64) (/.f64 (neg.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) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.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 (neg.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 1 binary64)))
(+.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(+.f64 (/.f64 (neg.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) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 0 binary64) x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 x #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x))
(+.f64 (*.f64 (+.f64 x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(+.f64 (/.f64 (+.f64 x #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 #s(literal 0 binary64) x)))) #s(literal -1 binary64)))
(-.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 #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 (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 (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 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.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 (+.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)))))) (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) (+.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) #s(literal 1 binary64)) x)) (/.f64 (*.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 (-.f64 #s(literal 1 binary64) x) (*.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 (+.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)))))) (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) (+.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) #s(literal 1 binary64)) x)) (/.f64 (*.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 (*.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 #s(literal 1 binary64) (+.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) #s(literal 1 binary64)) x))) (/.f64 (/.f64 (*.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 #s(literal 1 binary64) (+.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) #s(literal 1 binary64)) x))))
(-.f64 (/.f64 (+.f64 x #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (neg.f64 x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 (+.f64 x (+.f64 #s(literal 0 binary64) x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(-.f64 (/.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.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 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.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 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.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 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.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)))))
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(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (*.f64 x (*.f64 x x)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log1p.f64 (neg.f64 x)) (*.f64 (log1p.f64 (fma.f64 x x x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (fma.f64 x x x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (log1p.f64 (neg.f64 x)))))
(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (*.f64 (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))))
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(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
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(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x))) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (log1p.f64 (fma.f64 x x x)) #s(literal 1/2 binary64)))
(hypot.f64 x (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 x))
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(hypot.f64 (exp.f64 (log.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x x)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x))))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x x x) (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)) (-.f64 (*.f64 x x) (*.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (fma.f64 x x x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (*.f64 x x))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
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(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (fma.f64 x x x))) #s(literal 1/2 binary64))
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(*.f64 (sqrt.f64 (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(*.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))

simplify455.0ms (2.9%)

Memory
3.6MiB live, 589.9MiB allocated
Algorithm
1×egg-herbie
Rules
10 900×lower-fma.f64
10 900×lower-fma.f32
7 376×lower-*.f64
7 376×lower-*.f32
5 496×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07628746
124157191
082206974
Stop Event
1×iter limit
1×node limit
Counts
240 → 231
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))))))))
(/ 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)))))))
(/ -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)))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(/ 1 x)
(/ (+ 1 (* -1/8 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -5/128 (pow x 2)) 1/8))) x)
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(- (* 2 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
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(- (* 2 (/ (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -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))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 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))))) (* 1/16 (* (sqrt (pow x 5)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))))) (pow x 6))) (+ (* -2 (/ (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -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))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
1/2
(+ 1/2 (* 1/2 x))
(+ 1/2 (* x (+ 1/2 (* 1/16 x))))
(+ 1/2 (* x (+ 1/2 (* x (+ 1/16 (* 1/16 x))))))
(/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 2))) (+ (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 3))) (+ (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))
(/ -1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (+ (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* x (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(- (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -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))))))))
(* (sqrt x) (* (sqrt -1) (- (sqrt -1) 1)))
(* x (+ (* (sqrt (/ 1 x)) (* (sqrt -1) (- (sqrt -1) 1))) (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- 1/2 (* 1/2 (/ 1 (sqrt -1))))))))
(* x (+ (* (sqrt (/ 1 x)) (* (sqrt -1) (- (sqrt -1) 1))) (+ (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- 1/2 (* 1/2 (/ 1 (sqrt -1)))))) (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (- 1/8 (* 1/8 (/ 1 (pow (sqrt -1) 3)))))))))
(* x (+ (* (sqrt (/ 1 x)) (* (sqrt -1) (- (sqrt -1) 1))) (+ (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- 1/2 (* 1/2 (/ 1 (sqrt -1)))))) (+ (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (- 1/8 (* 1/8 (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ 9/16 (* 1/2 (/ (- 1 (* 1/8 (/ 1 (pow (sqrt -1) 4)))) (sqrt -1))))))))))
(* -1 (* (sqrt x) (* (sqrt -1) (- (sqrt -1) 1))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- (* 1/2 (/ 1 (sqrt -1))) 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (- (sqrt -1) 1))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- 1/8 (* 1/8 (/ 1 (pow (sqrt -1) 3))))))) (* (sqrt (/ 1 x)) (* (sqrt -1) (- (* 1/2 (/ 1 (sqrt -1))) 1/2)))) x)) (* (sqrt (/ 1 x)) (* (sqrt -1) (- (sqrt -1) 1))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- (* 1/2 (/ (- (* 1/8 (/ 1 (pow (sqrt -1) 4))) 1) (sqrt -1))) 9/16)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (- 1/8 (* 1/8 (/ 1 (pow (sqrt -1) 3))))))) x)) (* (sqrt (/ 1 x)) (* (sqrt -1) (- (* 1/2 (/ 1 (sqrt -1))) 1/2)))) x)) (* (sqrt (/ 1 x)) (* (sqrt -1) (- (sqrt -1) 1))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* -1/2 x)))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* x (- (* 7/128 x) 1/2))))))
(* (pow x 2) (- (sqrt -1) 1))
(* (pow x 2) (- (+ (sqrt -1) (* 1/2 (/ 1 x))) (+ 1 (/ 1/2 (* x (sqrt -1))))))
(* (pow x 2) (- (+ (sqrt -1) (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (+ 1 (+ (/ 1/2 (* x (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))))
(* (pow x 2) (- (+ (sqrt -1) (+ (* 1/2 (/ (- 1 (* 1/8 (/ 1 (pow (sqrt -1) 4)))) (* (pow x 3) (sqrt -1)))) (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 9/16 (/ 1 (pow x 3))))))) (+ 1 (+ (/ 1/2 (* x (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))))
(* (pow x 2) (- (sqrt -1) 1))
(* (pow x 2) (- (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) 1/2) x))) 1))
(* (pow x 2) (- (+ (sqrt -1) (* -1 (/ (- (+ (* -1 (/ (- 1/8 (* 1/8 (/ 1 (pow (sqrt -1) 3)))) x)) (* 1/2 (/ 1 (sqrt -1)))) 1/2) x))) 1))
(* (pow x 2) (- (+ (sqrt -1) (* -1 (/ (- (+ (* -1 (/ (- (+ 1/8 (* -1 (/ (- (* 1/2 (/ (- (* 1/8 (/ 1 (pow (sqrt -1) 4))) 1) (sqrt -1))) 9/16) x))) (* 1/8 (/ 1 (pow (sqrt -1) 3)))) x)) (* 1/2 (/ 1 (sqrt -1)))) 1/2) x))) 1))
-1
(- (* 1/2 (pow x 3)) 1)
(- (* (pow x 3) (+ 1/2 (* 1/8 (pow x 3)))) 1)
(- (* (pow x 3) (+ 1/2 (* (pow x 3) (+ 1/8 (* 1/16 (pow x 3)))))) 1)
(* -1 (* (sqrt (pow x 3)) (sqrt -1)))
(* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt (pow x 3)) (sqrt -1)))
(* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow x 19))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
1
(+ 1 (* -1/2 (pow x 3)))
(+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2)))
(+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 1/8)) 1/2)))
(* (sqrt (pow x 3)) (sqrt -1))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt (pow x 3)) (sqrt -1))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(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 (* (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
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (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 (* (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
(+ 1/2 (* -1/2 x))
(+ 1/2 (* x (- (* 1/16 x) 1/2)))
(+ 1/2 (* x (- (* x (+ 1/16 (* -1/16 x))) 1/2)))
(/ -1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(- (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(- (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 3))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -1 (/ (+ (* 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 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1
(+ 1 (* -1/2 (pow x 3)))
(+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2)))
(+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 1/8)) 1/2)))
(* (sqrt (pow x 3)) (sqrt -1))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt (pow x 3)) (sqrt -1))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 3/8 x))))
(+ 1 (* x (+ 1/2 (* x (+ 3/8 (* -3/16 x))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))))
(* x (- (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) (* 3/16 (/ 1 (pow x 3)))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x))))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- 3/8 (* 3/16 (/ 1 x))) x)) 1/2) x)))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
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(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) x))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))))))) x)) x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 3)))
(fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2)))
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 1/8)) 1/2)))
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt (pow x 3)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (*.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 19 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))
(* (sqrt (pow x 3)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 19 binary64)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 3/8 x))))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (+ 3/8 (* -3/16 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -3/16 binary64) #s(literal 3/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))))
(+.f64 x (fma.f64 x (/.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(* x (- (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) (* 3/16 (/ 1 (pow x 3)))))
(+.f64 (+.f64 x (fma.f64 x (/.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x (/.f64 #s(literal -3/16 binary64) (*.f64 x (*.f64 x x)))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(+.f64 (neg.f64 x) #s(literal -1/2 binary64))
(* -1 (* x (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x))))))
(neg.f64 (+.f64 x (fma.f64 x (/.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- 3/8 (* 3/16 (/ 1 x))) x)) 1/2) x)))))
(neg.f64 (fma.f64 x (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 #s(literal -3/16 binary64) x)) (neg.f64 x)) #s(literal -1/2 binary64)) (neg.f64 x)) x))

eval622.0ms (4%)

Memory
48.9MiB live, 892.2MiB allocated
Compiler

Compiled 190 438 to 8 389 computations (95.6% saved)

prune382.0ms (2.5%)

Memory
-29.3MiB live, 625.1MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New4 58014 581
Fresh101
Picked505
Done044
Total4 58654 591
Accuracy
100.0%
Counts
4 591 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
✓99.4%
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
100.0%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓8.2%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓6.3%
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Compiler

Compiled 362 to 111 computations (69.3% saved)

regimes9.0ms (0.1%)

Memory
9.1MiB live, 9.1MiB allocated
Counts
15 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.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 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 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 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.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 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (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 (-.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64))))) #s(literal 2 binary64))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/8 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/8 binary64)))))))
Outputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Calls

2 calls:

4.0ms
x
4.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0%)

Memory
4.7MiB live, 4.7MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
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
99.5%1x
99.5%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes3.0ms (0%)

Memory
3.8MiB live, 3.8MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
Outputs
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
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
99.4%1x
99.4%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes2.0ms (0%)

Memory
3.5MiB live, 3.5MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Outputs
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
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
6.3%1x
6.3%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0%)

Memory
6.7MiB live, 6.7MiB allocated
Algorithm
1×egg-herbie
Rules
16×*-commutative_binary64
8×+-commutative_binary64
4×sub-neg_binary64
2×1-exp_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02241
13641
24041
34241
44341
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Outputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))

soundness911.0ms (5.9%)

Memory
5.3MiB live, 401.0MiB allocated
Rules
21 484×lower-fma.f64
21 484×lower-fma.f32
17 072×lower-fma.f64
17 072×lower-fma.f32
10 900×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03103014
19502694
232872549
080762399
0161971
1493856
21729798
37219798
08083746
07628746
124157191
082206974
0720
01220
15120
236820
3566420
0932120
026118
049110
120790
2144490
0842990
030154
057163
1239103
21914103
08643101
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 97 to 56 computations (42.3% saved)

preprocess69.0ms (0.4%)

Memory
-17.9MiB live, 98.1MiB allocated
Remove

(negabs x)

Compiler

Compiled 188 to 118 computations (37.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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