bug333 (missed optimization)

Time bar (total: 7.6s)

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB 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)

sample1.8s (23.6%)

Memory
57.7MiB live, 2 737.1MiB allocated
Samples
745.0ms4 820×1valid
602.0ms3 164×2valid
15.0ms272×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-sqrt: 351.0ms (32.2% of total)
adjust: 272.0ms (24.9% of total)
ival-sub: 219.0ms (20.1% of total)
ival-add: 143.0ms (13.1% of total)
ival-<=: 82.0ms (7.5% 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

preprocess70.0ms (0.9%)

Memory
-43.0MiB live, 8.6MiB 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)

explain174.0ms (2.3%)

Memory
21.6MiB live, 61.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2560-0-(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
00-0-(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))cancellation2560
Confusion
Predicted +Predicted -
+2560
-00
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25600
-000
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
1256
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
37.0ms310×1valid
33.0ms188×2valid
1.0ms14×0valid
Compiler

Compiled 74 to 32 computations (56.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-sqrt: 18.0ms (36.8% of total)
adjust: 13.0ms (26.5% of total)
ival-sub: 11.0ms (22.5% of total)
ival-add: 6.0ms (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
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶7.6%
(-.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
2.4MiB live, 2.4MiB 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)

localize90.0ms (1.2%)

Memory
-19.5MiB live, 19.4MiB 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))
✓accuracy7.6%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Samples
61.0ms94×2valid
18.0ms155×1valid
0.0ms7×0valid
Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-sqrt: 9.0ms (36.4% of total)
adjust: 6.0ms (24.2% of total)
ival-sub: 6.0ms (24.2% of total)
ival-add: 4.0ms (16.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
7.0MiB live, 7.0MiB 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
1.0ms
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))

simplify2.0s (26.5%)

Memory
24.6MiB live, 742.2MiB 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))))))))

rewrite290.0ms (3.8%)

Memory
1.7MiB live, 355.9MiB 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))))
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(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 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))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -3 binary64)) (pow.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))) (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (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 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (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 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.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 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.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)))
(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))))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(*.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(*.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)))
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(*.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))))
(/.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 (-.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))))

eval52.0ms (0.7%)

Memory
-25.1MiB live, 91.0MiB allocated
Compiler

Compiled 9 873 to 1 184 computations (88% saved)

prune41.0ms (0.5%)

Memory
9.1MiB live, 127.0MiB allocated
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New3742376
Fresh000
Picked101
Done000
Total3752377
Accuracy
100.0%
Counts
377 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
▶99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Compiler

Compiled 25 to 13 computations (48% saved)

simplify117.0ms (1.5%)

Memory
10.7MiB live, 132.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓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
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Rules
2 336×lower-fma.f32
2 330×lower-fma.f64
1 008×lower-*.f32
998×lower-*.f64
536×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01995
03095
15995
211691
319091
423191
526491
638191
750291
876591
9111791
10148991
11181491
12196691
13201691
14203991
15204391
16204391
17204391
18204791
0204787
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(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)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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 (*.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
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(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)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #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)
(fma.f64 x (*.f64 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)

localize104.0ms (1.4%)

Memory
-11.3MiB live, 172.7MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 x #s(literal 7/128 binary64))
✓accuracy100.0%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓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))
✓accuracy99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Samples
41.0ms155×1valid
40.0ms94×2valid
1.0ms7×0valid
Compiler

Compiled 79 to 22 computations (72.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 66.0ms
adjust: 21.0ms (31.6% of total)
ival-sub: 16.0ms (24.1% of total)
ival-sqrt: 11.0ms (16.5% of total)
ival-mult: 11.0ms (16.5% of total)
ival-add: 7.0ms (10.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory
-22.4MiB live, 16.1MiB allocated
Counts
9 → 108
Calls
Call 1
Inputs
#<alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 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 #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))>
#<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 (*.f64 x #s(literal 7/128 binary64))>
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 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 (* (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 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 (* 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

27 calls:

TimeVariablePointExpression
2.0ms
x
@0
(* x (* x 1/8))
1.0ms
x
@0
(+ (* x (* x (* x 1/8))) x)
0.0ms
x
@-inf
(+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x)
0.0ms
x
@inf
(+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x)
0.0ms
x
@inf
(+ (* x (* x (* x 1/8))) x)

simplify361.0ms (4.8%)

Memory
33.6MiB live, 662.3MiB allocated
Algorithm
1×egg-herbie
Rules
16 226×lower-fma.f64
16 226×lower-fma.f32
4 188×lower-*.f64
4 188×lower-*.f32
3 918×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01331434
13841284
212851192
357661176
085811119
Stop Event
1×iter limit
1×node limit
Counts
108 → 104
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))))))))
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 (* (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))))))))
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)))))
(* 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
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 x (*.f64 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 (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 (+.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 (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))))) (*.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))))))
(* 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 -1/8 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))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.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 #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))) (*.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 (*.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))))))
(*.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) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (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)))))))
(neg.f64 (*.f64 x (fma.f64 (neg.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))) (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 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 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))))) (+ (* -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 #s(literal 1/8 binary64) (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 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))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
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 x (*.f64 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 (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 (+.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 (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))))) (*.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))))))
(* 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 -1/8 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))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.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 #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))) (*.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 (*.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))))))
(*.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) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (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)))))))
(neg.f64 (*.f64 x (fma.f64 (neg.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))) (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 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 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))))) (+ (* -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 #s(literal 1/8 binary64) (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 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))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
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 (* 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)
(* 7/128 (pow x 5))
(*.f64 x (*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x) (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))))
(* 7/128 (pow x 5))
(*.f64 x (*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x) (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x) (+.f64 #s(literal 7/128 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x) (+.f64 #s(literal 7/128 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.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)
(pow x 2)
(*.f64 x x)
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* 7/128 (pow x 3))
(*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* 7/128 (pow x 3))
(*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 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))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))

rewrite314.0ms (4.1%)

Memory
-28.2MiB live, 526.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 344×lower-fma.f32
6 338×lower-fma.f64
4 820×lower-*.f32
4 810×lower-*.f64
3 756×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01984
03084
112680
289880
0858976
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
9 → 161
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 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))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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 (*.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)))
(*.f64 x #s(literal 7/128 binary64))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(+.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(+.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)
(+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x x) x)
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x x)
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/8 binary64)) x)
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) x)
(fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))))))
(neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64) (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (fma.f64 x x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 x x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64) (neg.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))) (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x) (*.f64 x x))) (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) #s(literal 9 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (fma.f64 (*.f64 x x) (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x)))) (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64) (neg.f64 (neg.f64 x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))))) (neg.f64 (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (fma.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x))) (*.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))) (+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
(*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))))))
(*.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64) (neg.f64 (neg.f64 x)))))
(*.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal 1/8 binary64)) x)
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(*.f64 x #s(literal 1/8 binary64))
(*.f64 #s(literal 1/8 binary64) x)
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(/.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal -7/1024 binary64))))
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(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64)) x) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal -7/1024 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal -1/64 binary64)) x) (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal -1/8 binary64)))
(/.f64 (neg.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64)))) (*.f64 x #s(literal 1/8 binary64)))))))
(/.f64 (neg.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 #s(literal -1/8 binary64) x)))) (neg.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 #s(literal -1/8 binary64) x))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64)))) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal -7/1024 binary64)))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal -1/64 binary64)))) (fma.f64 (*.f64 x x) #s(literal -7/128 binary64) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64)) x)) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal -7/1024 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal -1/64 binary64)) x)) (fma.f64 (*.f64 x x) #s(literal -7/128 binary64) #s(literal 1/8 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64))))) (-.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64))))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) x)
(*.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 #s(literal -1/8 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 #s(literal -1/8 binary64) x))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 7/128 binary64)))) (*.f64 x #s(literal 1/8 binary64)))))))
(*.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal -7/1024 binary64)))))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal -1/8 binary64))))
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 343/2097152 binary64) #s(literal 1/512 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal -7/1024 binary64)))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 49/16384 binary64)) #s(literal -1/64 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal -1/8 binary64))))
(*.f64 x #s(literal 7/128 binary64))
(*.f64 #s(literal 7/128 binary64) x)

eval31.0ms (0.4%)

Memory
12.4MiB live, 88.1MiB allocated
Compiler

Compiled 8 485 to 558 computations (93.4% saved)

prune25.0ms (0.3%)

Memory
27.7MiB live, 70.0MiB allocated
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2632265
Fresh000
Picked022
Done000
Total2634267
Accuracy
100.0%
Counts
267 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
▶99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
▶6.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
Compiler

Compiled 45 to 24 computations (46.7% saved)

simplify40.0ms (0.5%)

Memory
-3.0MiB live, 73.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x #s(literal 1/8 binary64))
✓cost-diff0
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
✓cost-diff0
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
✓cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
✓cost-diff0
(*.f64 x (*.f64 x x))
✓cost-diff0
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
✓cost-diff0
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
✓cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
Rules
536×lower-fma.f32
534×lower-fma.f64
344×lower-*.f32
334×lower-*.f64
144×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02199
02892
14985
26785
37885
412285
514985
619385
725685
836385
946585
1055885
1161185
1267285
1371885
1473985
1574185
074181
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
#s(literal 1/8 binary64)
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
x
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
#s(literal 1 binary64)
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
#s(literal 1/8 binary64)
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) x))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) x)
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
x
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
#s(literal 1 binary64)

localize90.0ms (1.2%)

Memory
8.2MiB live, 159.1MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
✓accuracy100.0%
(*.f64 x #s(literal 1/8 binary64))
✓accuracy100.0%
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
✓accuracy99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
✓accuracy100.0%
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
✓accuracy99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
✓accuracy99.9%
(*.f64 x (*.f64 x x))
✓accuracy6.2%
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
Samples
40.0ms155×1valid
27.0ms94×2valid
1.0ms7×0valid
Compiler

Compiled 68 to 19 computations (72.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-sub: 12.0ms (24.9% of total)
adjust: 10.0ms (20.7% of total)
ival-sqrt: 10.0ms (20.7% of total)
ival-mult: 10.0ms (20.7% of total)
ival-add: 6.0ms (12.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
9.0MiB live, 9.0MiB allocated
Counts
8 → 96
Calls
Call 1
Inputs
#<alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))>
#<alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))>
#<alt (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))>
#<alt (*.f64 x (*.f64 x x))>
#<alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))>
#<alt (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)>
#<alt (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))>
#<alt (*.f64 x #s(literal 1/8 binary64))>
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 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 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 (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 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 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>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (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)>
Calls

24 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(* x (* x x))
0.0ms
x
@inf
(* (+ (* x (* x 1/8)) 1) x)
0.0ms
x
@0
(* (+ (* x (* x 1/8)) 1) x)
0.0ms
x
@-inf
(* 1/8 (* x (* x x)))
0.0ms
x
@inf
(* 1/8 (* x (* x x)))

simplify354.0ms (4.7%)

Memory
-13.9MiB live, 545.7MiB allocated
Algorithm
1×egg-herbie
Rules
14 210×lower-fma.f64
14 210×lower-fma.f32
4 634×lower-*.f64
4 634×lower-*.f32
3 906×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01161326
13271164
211221074
368711060
08138999
Stop Event
1×iter limit
1×node limit
Counts
96 → 92
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))))))))
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 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))
(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)
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))))))))
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
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (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)
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 (*.f64 x 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 (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 (+.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 (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))))) (*.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))))))
(* 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 (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))))) (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))) (*.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)) (neg.f64 (*.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 x (-.f64 (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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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)))))))
(neg.f64 (*.f64 x (-.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))) (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))))) (*.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))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(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))
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 (*.f64 x 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 (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 (+.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 (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))))) (*.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))))))
(* 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 (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))))) (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))) (*.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)) (neg.f64 (*.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 x (-.f64 (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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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)))))))
(neg.f64 (*.f64 x (-.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))) (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))))) (*.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))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))

rewrite341.0ms (4.5%)

Memory
-20.5MiB live, 332.2MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
8 888×lower-fma.f32
8 886×lower-fma.f64
5 332×lower-*.f32
5 322×lower-*.f64
3 890×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02191
02884
110077
266477
0851373
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
8 → 235
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
(*.f64 x (*.f64 x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/8 binary64))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
(*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))
(*.f64 (*.f64 x x) (*.f64 x #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))
(*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)))
(*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 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 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(+.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) x)
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (+.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64))))))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 x (/.f64 (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) x)
(fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64) x)
(fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/8 binary64)) x)
(fma.f64 (*.f64 x x) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) x)
(fma.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x x) x)
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x x)
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) x)
(fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 x x)) (/.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (/.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(fma.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64))))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))) (neg.f64 (*.f64 x (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) (*.f64 x x))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(neg.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (*.f64 x (*.f64 x x))) (neg.f64 (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (+.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))))))))
(neg.f64 (/.f64 (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)))) (neg.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (+.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64))))))))
(neg.f64 (/.f64 (neg.f64 (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64))))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 1/8 binary64))))) (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (*.f64 x (-.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)) (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)))))
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(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1/262144 binary64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64)))) (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4096 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4096 binary64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64)))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 1/8 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1/262144 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))))) (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4096 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) #s(literal -1 binary64))) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/8 binary64)))))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/8 binary64)))
(*.f64 x #s(literal 1/8 binary64))
(*.f64 #s(literal 1/8 binary64) x)
(*.f64 (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))

eval36.0ms (0.5%)

Memory
-25.5MiB live, 49.7MiB allocated
Compiler

Compiled 10 005 to 710 computations (92.9% saved)

prune27.0ms (0.4%)

Memory
9.2MiB live, 48.7MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3261327
Fresh000
Picked112
Done022
Total3274331
Accuracy
100.0%
Counts
331 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
✓99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
▶99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
Compiler

Compiled 41 to 22 computations (46.3% saved)

simplify11.0ms (0.1%)

Memory
10.9MiB live, 10.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))
✓cost-diff0
(*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)
✓cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
Rules
118×lower-fma.f64
118×lower-fma.f32
88×lower-+.f64
88×lower-+.f32
74×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01443
01543
12843
23643
34743
46243
58543
612543
717543
823143
924743
1025543
025540
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
(*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))))
(*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)
(*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)))
#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x

localize57.0ms (0.8%)

Memory
-17.8MiB live, 64.4MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)
✓accuracy99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
✓accuracy99.5%
#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))
Samples
22.0ms155×1valid
19.0ms94×2valid
1.0ms7×0valid
Compiler

Compiled 29 to 14 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
adjust: 10.0ms (31.1% of total)
ival-sqrt: 8.0ms (24.8% of total)
ival-sub: 5.0ms (15.5% of total)
ival-add: 4.0ms (12.4% of total)
ival-mult: 4.0ms (12.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#<alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))>
#<alt (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)>
#<alt #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))>
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 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>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
Calls

9 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms
x
@-inf
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms
x
@0
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms
x
@inf
(* (+ (* x (* x 1/8)) 1) x)
0.0ms
x
@-inf
(* (+ (* x (* x 1/8)) 1) x)

simplify321.0ms (4.2%)

Memory
7.1MiB live, 322.7MiB allocated
Algorithm
1×egg-herbie
Rules
12 812×lower-fma.f64
12 812×lower-fma.f32
4 894×lower-*.f64
4 894×lower-*.f32
4 050×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115634
1325553
21124508
36910507
08046471
Stop Event
1×iter limit
1×node limit
Counts
36 → 34
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))))))))
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
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
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)
(* 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) x)) (sqrt.f64 #s(literal -1 binary64)) (*.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))))))))
(* 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 -1/8 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))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (-.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 #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))) (*.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 (*.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))))))
(*.f64 x (neg.f64 (-.f64 (-.f64 (*.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)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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)))))))
(neg.f64 (*.f64 x (-.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 (*.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 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.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))))) (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))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* 1/8 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))

rewrite275.0ms (3.6%)

Memory
11.2MiB live, 214.6MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 870×lower-fma.f64
6 870×lower-fma.f32
4 016×lower-*.f32
4 014×lower-*.f64
3 072×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01441
01541
16941
250841
3698241
0873738
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 8
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
(*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))))
(*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)))
(*.f64 x (*.f64 #s(literal 1 binary64) #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))))
(*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x)
(*.f64 (*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) #s(literal 1 binary64)) x)
#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))

eval4.0ms (0.1%)

Memory
6.5MiB live, 6.5MiB allocated
Compiler

Compiled 679 to 108 computations (84.1% saved)

prune6.0ms (0.1%)

Memory
-30.8MiB live, 7.8MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New42042
Fresh000
Picked011
Done033
Total42446
Accuracy
100.0%
Counts
46 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
✓99.9%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
✓99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
Compiler

Compiled 97 to 44 computations (54.6% saved)

regimes4.0ms (0.1%)

Memory
6.6MiB live, 6.6MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 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
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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
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
5.2MiB live, 5.2MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #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
99.9%1x
99.9%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
4.3MiB live, 4.3MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
Calls

2 calls:

2.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.9%1x
99.9%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
5.2MiB live, 5.2MiB allocated
Accuracy

Total -59.7b remaining (-18519.8%)

Threshold costs -59.7b (-18519.8%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 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
99.5%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)

simplify6.0ms (0.1%)

Memory
9.3MiB live, 9.3MiB allocated
Algorithm
1×egg-herbie
Rules
12×*-commutative_binary64
2×1-exp_binary64
2×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02880
13780
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 x #s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))))

soundness441.0ms (5.8%)

Memory
-34.5MiB live, 246.9MiB allocated
Rules
21 484×lower-fma.f64
21 484×lower-fma.f32
14 210×lower-fma.f64
14 210×lower-fma.f32
6 344×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0161971
1493856
21729798
37219798
08083746
01161326
13271164
211221074
368711060
08138999
01984
03084
112680
289880
0858976
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 104 to 51 computations (51% saved)

preprocess56.0ms (0.7%)

Memory
14.1MiB live, 52.5MiB allocated
Remove

(negabs x)

Compiler

Compiled 214 to 112 computations (47.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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