bug333 (missed optimization)

Time bar (total: 11.3s)

analyze0.0ms (0%)

Memory
0.2MiB live, 0.2MiB 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)

sample2.2s (19.5%)

Memory
8.1MiB live, 2 544.6MiB allocated
Samples
926.0ms3 125×2valid
852.0ms4 864×1valid
14.0ms267×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.4s
ival-sub: 404.0ms (28.6% of total)
ival-sqrt: 339.0ms (24% of total)
ival-add: 293.0ms (20.7% of total)
adjust: 255.0ms (18% of total)
ival-<=: 97.0ms (6.9% of total)
ival-and: 11.0ms (0.8% of total)
exact: 11.0ms (0.8% of total)
ival-assert: 4.0ms (0.3% of total)
Bogosity

preprocess46.0ms (0.4%)

Memory
5.0MiB live, 43.5MiB 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)

explain158.0ms (1.4%)

Memory
8.4MiB live, 253.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2540-0-(-.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)))cancellation2540
Confusion
Predicted +Predicted -
+2540
-02
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25400
-002
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
02
1254
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
40.0ms176×2valid
37.0ms312×1valid
1.0ms24×0valid
Compiler

Compiled 74 to 32 computations (56.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 50.0ms
ival-sqrt: 17.0ms (33.8% of total)
adjust: 13.0ms (25.9% of total)
ival-sub: 13.0ms (25.9% of total)
ival-add: 6.0ms (11.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶9.1%
(-.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)

simplify12.0ms (0.1%)

Memory
-16.3MiB live, 22.9MiB 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)

localize62.0ms (0.5%)

Memory
19.6MiB live, 97.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓accuracy9.1%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Samples
31.0ms88×2valid
18.0ms156×1valid
1.0ms12×0valid
Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
adjust: 22.0ms (55.6% of total)
ival-sqrt: 8.0ms (20.2% of total)
ival-sub: 5.0ms (12.6% of total)
ival-add: 3.0ms (7.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory
8.2MiB live, 8.2MiB 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))

simplify538.0ms (4.8%)

Memory
13.6MiB live, 919.3MiB 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))))))))

rewrite237.0ms (2.1%)

Memory
-43.9MiB live, 366.2MiB 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 (-.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))
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(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (+.f64 x #s(literal -1 binary64))))
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(/.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))))

eval46.0ms (0.4%)

Memory
25.4MiB live, 101.6MiB allocated
Compiler

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

prune74.0ms (0.7%)

Memory
-18.2MiB live, 102.3MiB allocated
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3715376
Fresh000
Picked011
Done000
Total3716377
Accuracy
100.0%
Counts
377 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓9.1%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶8.0%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶7.5%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
▶99.4%
#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))
▶99.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Compiler

Compiled 150 to 85 computations (43.3% saved)

simplify2.3s (20%)

Memory
27.5MiB live, 819.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓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
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 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))
✓cost-diff0
(*.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)))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(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)
✓cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
Rules
35 216×lower-fma.f32
35 198×lower-fma.f64
3 864×lower-+.f64
3 864×lower-+.f32
2 884×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037274
066274
1132274
2270268
3505268
4832268
51184268
61497268
71806268
82533268
93219268
103855268
115174268
125911268
136481268
146530268
156539268
166613268
176651268
186663268
196677268
206681268
216681268
226681268
08133262
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
(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)
(*.f64 x 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)))
(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 (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))
#s(literal 33/1024 binary64)
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
#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)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 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))
(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)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.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))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 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))
(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)
(fma.f64 x (*.f64 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)
(*.f64 x 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)))
(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 (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))
#s(literal 33/1024 binary64)
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
#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 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) x))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) x)
x
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 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))
#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)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

localize214.0ms (1.9%)

Memory
-17.2MiB live, 424.9MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(-.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy99.0%
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 x #s(literal 7/128 binary64))
✓accuracy100.0%
(*.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
✓accuracy99.4%
#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 #s(literal 1 binary64) x)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓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))
✓accuracy99.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
✓accuracy100.0%
(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)
✓accuracy100.0%
(*.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)))
✓accuracy99.9%
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
✓accuracy99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
Samples
81.0ms153×1valid
69.0ms83×2valid
6.0ms8×3valid
3.0ms12×0valid
Compiler

Compiled 226 to 39 computations (82.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 109.0ms
adjust: 39.0ms (35.7% of total)
ival-mult: 31.0ms (28.4% of total)
ival-add: 23.0ms (21.1% of total)
ival-sqrt: 9.0ms (8.2% of total)
ival-sub: 5.0ms (4.6% of total)
exact: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series16.0ms (0.1%)

Memory
3.8MiB live, 43.0MiB allocated
Counts
22 → 264
Calls
Call 1
Inputs
#<alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))>
#<alt (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)>
#<alt (*.f64 x x)>
#<alt (*.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)))>
#<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 (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x))>
#<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 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))>
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))>
#<alt (*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))>
#<alt (-.f64 #s(literal 1 binary64) x)>
#<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 (* (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 (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* x (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* 33/1024 (pow x 5))>
#<alt (* (pow x 5) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* 33/1024 (pow x 5))>
#<alt (* (pow x 5) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<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 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (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 (* 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 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 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (* -1/8 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* -1/8 x)>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* 7/128 x)>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 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)>
#<alt (* 7/128 x)>
Calls

66 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x)
1.0ms
x
@0
(+ (* (* x x) (* x (+ (* x (* x (+ (* (* x x) 33/1024) 7/128))) 1/8))) x)
0.0ms
x
@-inf
(+ (* (* x x) (* x (+ (* x (* x (+ (* (* x x) 33/1024) 7/128))) 1/8))) x)
0.0ms
x
@inf
(+ (* (* x x) (* x (+ (* x (* x (+ (* (* x x) 33/1024) 7/128))) 1/8))) x)
0.0ms
x
@inf
(* x (* x 1/8))

simplify444.0ms (3.9%)

Memory
6.7MiB live, 735.1MiB allocated
Algorithm
1×egg-herbie
Rules
13 004×lower-fma.f64
13 004×lower-fma.f32
5 764×lower-+.f64
5 764×lower-+.f32
3 448×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02354200
17443766
224213502
375803502
083503299
Stop Event
1×iter limit
1×node limit
Counts
264 → 256
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 (* (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))))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/8 x)
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* x (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* 33/1024 (pow x 5))
(* (pow x 5) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 5))
(* (pow x 5) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
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))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (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)))
(* 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)))))
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 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* 7/128 x)
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 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 (*.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))))
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(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* 33/1024 (pow x 3))
(*.f64 #s(literal 33/1024 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* 33/1024 (pow x 3))
(*.f64 #s(literal 33/1024 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* 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))

rewrite601.0ms (5.3%)

Memory
-20.7MiB live, 616.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 064×lower-fma.f32
6 046×lower-fma.f64
4 090×lower-*.f32
4 076×lower-*.f64
3 372×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037225
066225
1285219
22140219
08231213
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 417
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
(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)
(*.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)))
#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))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(sqrt.f64 (-.f64 #s(literal 1 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))
(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 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(-.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 7/128 binary64))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
(+.f64 x (*.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))))
(+.f64 (*.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)
(-.f64 (/.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.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))))) (/.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (-.f64 x (*.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))))))
(fma.f64 #s(literal 1 binary64) x (*.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))))
(fma.f64 x #s(literal 1 binary64) (*.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))))
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(fma.f64 x (*.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 x)) x)
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(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)
(fma.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 x x) x)
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) x)
(fma.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (*.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)))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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)))))) (fma.f64 (*.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))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x)) (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x)))))
(/.f64 (fma.f64 (*.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))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 x (*.f64 x x))) (fma.f64 x (-.f64 x (*.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)))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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)))))))
(/.f64 (fma.f64 (*.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))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 x (*.f64 x x))) (fma.f64 x x (-.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))))))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x)))
(/.f64 (neg.f64 (fma.f64 (*.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))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 x (-.f64 x (*.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)))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))))))
(/.f64 (neg.f64 (fma.f64 (*.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))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 x x (-.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x)))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (*.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)))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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)))))) (fma.f64 (*.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))) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.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))))) (*.f64 x (*.f64 x x))))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (*.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (*.f64 x (*.f64 x x)))) (*.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(/.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal 1 binary64)))))
(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 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x 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 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (-.f64 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 x x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal 1 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 binary64)) (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 x #s(literal 7/128 binary64))
(*.f64 #s(literal 7/128 binary64) x)

eval162.0ms (1.4%)

Memory
13.9MiB live, 300.3MiB allocated
Compiler

Compiled 22 456 to 1 705 computations (92.4% saved)

prune82.0ms (0.7%)

Memory
5.8MiB live, 205.9MiB allocated
Pruning

10 alts after pruning (5 fresh and 5 done)

PrunedKeptTotal
New8095814
Fresh000
Picked145
Done011
Total81010820
Accuracy
100.0%
Counts
820 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓9.1%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓7.5%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶7.6%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
▶7.5%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶7.9%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶6.2%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
✓99.4%
#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))
✓99.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
▶6.3%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
Compiler

Compiled 194 to 111 computations (42.8% saved)

simplify185.0ms (1.6%)

Memory
2.2MiB live, 157.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
#s(approx (sqrt (- 1 x)) (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)))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
✓cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓cost-diff0
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
✓cost-diff0
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
✓cost-diff0
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
✓cost-diff0
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
✓cost-diff0
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
Rules
3 288×lower-fma.f32
3 274×lower-fma.f64
1 032×lower-*.f32
1 026×lower-*.f64
680×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037291
058291
1109291
2176281
3254281
4323281
5394281
6595281
7760281
81116281
91266281
101418281
111707281
122328281
132606281
142637281
152653281
162659281
172659281
182719281
192743281
202743281
02743279
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(*.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(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (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)))
(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))
(fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
#s(literal -1/16 binary64)
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(*.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(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (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)))
(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))
(fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
#s(literal -1/16 binary64)
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)

localize265.0ms (2.3%)

Memory
-26.6MiB live, 222.6MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
✓accuracy99.2%
#s(approx (sqrt (- 1 x)) (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)))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
✓accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
✓accuracy98.9%
#s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓accuracy100.0%
(*.f64 x #s(literal 1/8 binary64))
✓accuracy99.8%
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
✓accuracy99.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
✓accuracy6.3%
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
✓accuracy100.0%
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓accuracy97.2%
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓accuracy100.0%
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓accuracy98.5%
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
Samples
87.0ms156×1valid
41.0ms88×2valid
2.0ms12×0valid
Compiler

Compiled 189 to 32 computations (83.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 99.0ms
adjust: 41.0ms (41.6% of total)
ival-add: 29.0ms (29.4% of total)
ival-mult: 14.0ms (14.2% of total)
ival-sqrt: 9.0ms (9.1% of total)
ival-sub: 5.0ms (5.1% of total)
exact: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory
11.2MiB live, 11.2MiB allocated
Counts
18 → 216
Calls
Call 1
Inputs
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))>
#<alt #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))>
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))>
#<alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))>
#<alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))>
#<alt #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))>
#<alt (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))>
#<alt (*.f64 x (*.f64 x #s(literal 1/8 binary64)))>
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))>
#<alt #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))>
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))>
#<alt #s(approx (sqrt (- 1 x)) (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)))>
#<alt (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))>
#<alt (*.f64 x #s(literal 1/8 binary64))>
#<alt (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 x #s(literal -1/16 binary64) #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 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (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 (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt 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 (* 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 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 (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 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 (* 1/8 x)>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) (+ 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) (+ 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))>
#<alt (* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))>
#<alt -1/8>
#<alt (- (* -1/16 x) 1/8)>
#<alt (- (* -1/16 x) 1/8)>
#<alt (- (* -1/16 x) 1/8)>
#<alt (* -1/16 x)>
#<alt (* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))>
#<alt (* -1/16 x)>
#<alt (* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))>
Calls

54 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(+ (* x (+ (* x -1/8) -1/2)) 1)
0.0ms
x
@inf
(* x (* x (* x 1/8)))
0.0ms
x
@0
(* x (* x (* x 1/8)))
0.0ms
x
@-inf
(* x (* x (* x 1/8)))
0.0ms
x
@inf
(+ (* x -1/16) -1/8)

simplify520.0ms (4.6%)

Memory
34.5MiB live, 575.2MiB allocated
Algorithm
1×egg-herbie
Rules
22 818×lower-fma.f64
22 818×lower-fma.f32
5 620×lower-*.f64
5 620×lower-*.f32
3 960×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01854081
15763624
219933350
379483350
085613117
Stop Event
1×iter limit
1×node limit
Counts
216 → 210
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 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (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 (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
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))
(* 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))
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 (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 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)
(* 1/8 x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (/ 1 (pow x 2)) (+ 1/8 (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (/ 1 (pow x 2)) (+ 1/8 (* 1/2 (/ 1 x)))))
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))
-1/8
(- (* -1/16 x) 1/8)
(- (* -1/16 x) 1/8)
(- (* -1/16 x) 1/8)
(* -1/16 x)
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(* -1/16 x)
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)) x)
(* 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 (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 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (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)))))))))
(* -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 (-.f64 (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)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (fma.f64 (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 (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))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.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 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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 1/16 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))
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 1/16 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)))) (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 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #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) (*.f64 x (*.f64 x x)))) (/.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)))))
(* 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 (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 (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 #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))) (fma.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))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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 x (*.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)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 x (neg.f64 (*.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)))))))
(*.f64 x (neg.f64 (*.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)))) (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
(* 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))))))
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(*.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 x (*.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)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 x (neg.f64 (*.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)))))))
(*.f64 x (neg.f64 (*.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)))) (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
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 x #s(literal -1/2 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))
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 (- (* -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))
(* -1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/8 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) (+ 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) (+ 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1/8 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/8 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
-1/8
#s(literal -1/8 binary64)
(- (* -1/16 x) 1/8)
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(- (* -1/16 x) 1/8)
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(- (* -1/16 x) 1/8)
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(* -1 (* x (+ 1/16 (* 1/8 (/ 1 x)))))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))

rewrite431.0ms (3.8%)

Memory
-24.7MiB live, 613.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 012×lower-fma.f32
5 998×lower-fma.f64
4 110×lower-*.f32
4 104×lower-*.f64
3 610×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037211
058211
1268201
22063201
09156199
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 289
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
#s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
#s(approx (sqrt (- 1 x)) (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)))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x #s(literal 1/8 binary64))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))
Outputs
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(+.f64 (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))) (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))))
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))))
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))) (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))))
(fma.f64 #s(literal -1 binary64) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (-.f64 (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (*.f64 (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))) (fma.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))) (fma.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 (*.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (*.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))))))
(/.f64 (*.f64 (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))) (+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) (fma.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64)))))))
(pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/256 binary64) (-.f64 #s(literal 1/64 binary64) (*.f64 x #s(literal 1/128 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/4096 binary64) #s(literal -1/512 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/256 binary64) #s(literal -1/64 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/4096 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/256 binary64) (-.f64 #s(literal 1/64 binary64) (*.f64 x #s(literal 1/128 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/256 binary64) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64))))

eval97.0ms (0.9%)

Memory
10.3MiB live, 165.9MiB allocated
Compiler

Compiled 21 805 to 1 104 computations (94.9% saved)

prune251.0ms (2.2%)

Memory
-13.1MiB live, 111.7MiB allocated
Pruning

12 alts after pruning (3 fresh and 9 done)

PrunedKeptTotal
New6733676
Fresh000
Picked145
Done055
Total67412686
Accuracy
100.0%
Counts
686 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓9.1%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓7.5%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓7.6%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
✓7.5%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓7.9%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶5.6%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
✓6.2%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
▶6.2%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶5.2%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
✓99.4%
#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))
✓99.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Compiler

Compiled 149 to 84 computations (43.6% saved)

simplify20.0ms (0.2%)

Memory
26.0MiB live, 26.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
#s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64))))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
✓cost-diff0
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓cost-diff0
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
✓cost-diff0
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
✓cost-diff0
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
✓cost-diff0
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Rules
252×lower-fma.f32
248×lower-fma.f64
144×lower-+.f64
144×lower-*.f32
144×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025160
031160
146160
259160
381160
4107160
5153160
6239160
7310160
8445160
9492160
10516160
0516160
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
x
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64))))
#s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
x
#s(literal -1/2 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64))))
#s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

localize89.0ms (0.8%)

Memory
7.9MiB live, 124.4MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓accuracy98.5%
#s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64))))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
✓accuracy2.2%
#s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
✓accuracy98.5%
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓accuracy97.3%
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓accuracy98.5%
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
✓accuracy97.3%
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
✓accuracy97.2%
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
✓accuracy9.1%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Samples
34.0ms156×1valid
25.0ms88×2valid
1.0ms12×0valid
Compiler

Compiled 89 to 15 computations (83.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
adjust: 10.0ms (28% of total)
ival-sqrt: 9.0ms (25.2% of total)
ival-add: 6.0ms (16.8% of total)
ival-mult: 5.0ms (14% of total)
ival-sub: 5.0ms (14% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory
5.5MiB live, 5.5MiB allocated
Counts
11 → 132
Calls
Call 1
Inputs
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))>
#<alt #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))>
#<alt #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))>
#<alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))>
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))>
#<alt #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))>
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))>
#<alt #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64))))>
#<alt #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 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 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (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 (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
Calls

33 calls:

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

simplify695.0ms (6.1%)

Memory
-173.1MiB live, 679.7MiB allocated
Algorithm
1×egg-herbie
Rules
21 400×lower-fma.f64
21 400×lower-fma.f32
4 978×lower-+.f64
4 978×lower-+.f32
4 654×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01652764
15052447
217602276
373282276
081982108
Stop Event
1×iter limit
1×node limit
Counts
132 → 129
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 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (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)))))))
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1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 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)))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 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 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x 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 (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 #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 (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (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 (*.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 (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)))))))
(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 (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)))))))
(* -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 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 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) (*.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 1/16 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))
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 -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x 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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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 x (neg.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) x))) (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #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 (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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #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 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -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))))))
(*.f64 (*.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))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #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 1/16 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 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x 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 (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 #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 (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (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 (*.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))))))
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(*.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 (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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #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 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -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))))))
(*.f64 (*.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))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #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 1/16 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))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* x (- (/ 1 x) 1/2))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))

rewrite300.0ms (2.7%)

Memory
4.9MiB live, 442.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 662×lower-fma.f32
5 658×lower-fma.f64
4 386×lower-*.f32
4 384×lower-*.f64
3 444×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025128
031128
1119128
2861128
08292128
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
11 → 336
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))
#s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64))))
#s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))
Outputs
(+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))
(+.f64 (neg.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))))
(+.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))))
(+.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))) (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))))
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))
(-.f64 (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(literal 0 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (/.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))
(fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))))
(fma.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))))
(fma.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))))
(fma.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))
(fma.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64)))) (/.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))))
(fma.f64 #s(literal -1 binary64) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))))
(fma.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (/.f64 (pow.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))))) (neg.f64 (/.f64 (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) (*.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))))))))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))) (fma.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
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(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
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(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
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(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(*.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
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(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/64 binary64)))) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/16 binary64))))
(*.f64 (/.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/16 binary64)) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))))) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal -1/2 binary64))))
#s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal -1/2 binary64)))

eval60.0ms (0.5%)

Memory
-12.2MiB live, 63.0MiB allocated
Compiler

Compiled 21 650 to 1 095 computations (94.9% saved)

prune72.0ms (0.6%)

Memory
-5.9MiB live, 76.7MiB allocated
Pruning

12 alts after pruning (3 fresh and 9 done)

PrunedKeptTotal
New4883491
Fresh000
Picked123
Done279
Total49112503
Accuracy
100.0%
Counts
503 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓9.1%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓7.6%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
✓7.9%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓6.2%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
5.6%
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
98.5%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
✓6.2%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
5.6%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
✓5.2%
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓99.5%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
✓99.4%
#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))
✓99.2%
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
Compiler

Compiled 336 to 129 computations (61.6% saved)

regimes10.0ms (0.1%)

Memory
13.2MiB live, 13.2MiB allocated
Counts
17 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 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 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (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)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (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))
Calls

2 calls:

5.0ms
x
4.0ms
(-.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)

regimes11.0ms (0.1%)

Memory
-25.4MiB live, 12.5MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 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 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (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))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (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)))
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:

6.0ms
x
4.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.4%1x
99.4%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory
12.0MiB live, 12.0MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 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:

4.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.2%1x
99.2%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)

regimes6.0ms (0.1%)

Memory
10.1MiB live, 10.1MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
Calls

2 calls:

3.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
98.5%1x
98.5%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)

regimes4.0ms (0%)

Memory
7.0MiB live, 7.0MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
6.2%1x
6.2%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
6.4MiB live, 6.4MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
Calls

2 calls:

2.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
6.2%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
6.2%1x
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0%)

Memory
-33.8MiB live, 5.9MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
Calls

2 calls:

2.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
5.6%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
5.6%1x
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes3.0ms (0%)

Memory
5.0MiB live, 5.0MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

2 calls:

1.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
5.2%1x
5.2%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)

simplify8.0ms (0.1%)

Memory
10.2MiB live, 10.2MiB allocated
Algorithm
1×egg-herbie
Rules
22×*-commutative_binary64
16×+-commutative_binary64
16×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050182
169182
281182
387182
490182
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 (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #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))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64))) x))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 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))
#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))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(approx (+ (* x -1/2) 1) (*.f64 x #s(literal -1/2 binary64)))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* x 1/2) 1) #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))

soundness1.0s (9%)

Memory
-17.2MiB live, 467.6MiB allocated
Rules
22 818×lower-fma.f64
22 818×lower-fma.f32
21 484×lower-fma.f64
21 484×lower-fma.f32
21 400×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0161971
1493856
21729798
37219798
08083746
01854081
15763624
219933350
379483350
085613117
02354200
17443766
224213502
375803502
083503299
01652764
15052447
217602276
373282276
081982108
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 236 to 125 computations (47% saved)

preprocess82.0ms (0.7%)

Memory
28.8MiB live, 111.2MiB allocated
Remove

(negabs x)

Compiler

Compiled 260 to 112 computations (56.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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