Given's Rotation SVD example, simplified

Time bar (total: 9.9s)

analyze0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.7s (17%)

Memory
52.6MiB live, 3 161.5MiB allocated
Samples
785.0ms2 929×2valid
356.0ms4 167×0valid
216.0ms1 160×1valid
Precisions
Click to see histograms. Total time spent on operations: 1.0s
ival-hypot: 383.0ms (37.1% of total)
ival-sqrt: 152.0ms (14.7% of total)
ival-div: 124.0ms (12% of total)
ival-sub: 103.0ms (10% of total)
ival-mult: 97.0ms (9.4% of total)
ival-add: 77.0ms (7.5% of total)
adjust: 73.0ms (7.1% of total)
exact: 13.0ms (1.3% of total)
ival-true: 6.0ms (0.6% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

preprocess18.0ms (0.2%)

Memory
-2.6MiB live, 34.2MiB allocated
Algorithm
2×egg-herbie
Rules
38×sub-neg
36×+-lowering-+.f64
36×+-lowering-+.f32
22×+-commutative
20×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01739
14232
27032
39432
413032
515232
616432
717032
817132
01215
12513
23213
33713
44313
55113
66113
77213
87513
07512
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
Outputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
Call 2
Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))
Outputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 (neg x))))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))
(+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 (neg x))))) -1)

explain189.0ms (1.9%)

Memory
-0.6MiB live, 346.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
590-0-(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
00-0-(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
00-0-#s(literal 1 binary64)
00-0-(hypot.f64 #s(literal 1 binary64) x)
00-0-(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
00-0-(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
00-0-(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
00-0-#s(literal 1/2 binary64)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))cancellation590
Confusion
Predicted +Predicted -
+590
-0197
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+5900
-00197
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0197
159
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
74.0ms172×2valid
23.0ms280×0valid
9.0ms60×1valid
Compiler

Compiled 128 to 40 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 85.0ms
ival-hypot: 44.0ms (51.7% of total)
ival-mult: 12.0ms (14.1% of total)
ival-div: 7.0ms (8.2% of total)
ival-sqrt: 7.0ms (8.2% of total)
ival-sub: 5.0ms (5.9% of total)
adjust: 4.0ms (4.7% of total)
ival-add: 4.0ms (4.7% of total)
exact: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 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
▶78.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify6.0ms (0.1%)

Memory
11.5MiB live, 11.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
✓cost-diff320
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓cost-diff5440
(hypot.f64 #s(literal 1 binary64) x)
Rules
36×+-lowering-+.f64
36×+-lowering-+.f32
18×*-lowering-*.f32
18×--lowering--.f32
18×*-lowering-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01267
12561
23261
33761
44361
55161
66161
77261
87561
07555
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
1
(sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))
(* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))
1/2
(+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))
(/ 1 (sqrt (+ (* 1 1) (* x x))))
(sqrt (+ (* 1 1) (* x x)))
x
Outputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
1
#s(literal 1 binary64)
(sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/ 1 (sqrt (+ (* 1 1) (* x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt (+ (* 1 1) (* x x)))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
x

localize64.0ms (0.7%)

Memory
-12.1MiB live, 106.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓accuracy100.0%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓accuracy78.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
Samples
30.0ms86×2valid
13.0ms140×0valid
5.0ms30×1valid
Compiler

Compiled 51 to 11 computations (78.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-hypot: 18.0ms (52.4% of total)
ival-div: 3.0ms (8.7% of total)
ival-sqrt: 3.0ms (8.7% of total)
ival-mult: 3.0ms (8.7% of total)
adjust: 2.0ms (5.8% of total)
ival-sub: 2.0ms (5.8% of total)
ival-add: 2.0ms (5.8% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
10.8MiB live, 10.8MiB allocated
Counts
5 → 60
Calls
Call 1
Inputs
#<alt (sqrt (+ (* 1 1) (* x x)))>
#<alt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))>
#<alt (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))>
#<alt (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))>
#<alt (/ 1 (sqrt (+ (* 1 1) (* x x))))>
Outputs
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (- 1 (* (sqrt 1/2) (sqrt 2)))>
#<alt (- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))>
Calls

15 calls:

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

rewrite314.0ms (3.2%)

Memory
-9.9MiB live, 479.1MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 098×accelerator-lowering-fma.f32
4 098×accelerator-lowering-fma.f64
3 010×*-lowering-*.f32
3 010×*-lowering-*.f64
1 830×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01254
17247
255647
3519947
0881642
Stop Event
1×iter limit
1×node limit
Counts
5 → 375
Calls
Call 1
Inputs
(sqrt (+ (* 1 1) (* x x)))
(* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
(sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))
(/ 1 (sqrt (+ (* 1 1) (* x x))))
Outputs
(+.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x))))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 (*.f64 x x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
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(fabs.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1/8 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (*.f64 x x))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (log1p.f64 (*.f64 x x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 (*.f64 x x))) #s(literal -2 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (neg.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

simplify347.0ms (3.5%)

Memory
37.1MiB live, 541.6MiB allocated
Algorithm
1×egg-herbie
Rules
12 168×accelerator-lowering-fma.f32
12 168×accelerator-lowering-fma.f64
5 188×*-lowering-*.f32
5 188×*-lowering-*.f64
2 706×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219881
1640809
21804769
35719712
08156670
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- 1 (sqrt 1/2))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(/ 1 x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(/ -1 x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) x)))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x (*.f64 x x))))))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(fma.f64 x (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(+.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) x) (*.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 3/16 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -5/32 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -3/16 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64))) x))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(-.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 11/32 binary64) #s(literal 1/4 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 69/256 binary64) #s(literal -11/64 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) #s(literal 1 binary64))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal -3/16 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)))) x) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(fma.f64 (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 11/32 binary64) #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
(fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 69/256 binary64) #s(literal 11/64 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal -3/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal -3/16 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)))) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 3/8 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -5/16 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x)
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) x)
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal -5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))) x)

eval72.0ms (0.7%)

Memory
-54.6MiB live, 110.0MiB allocated
Compiler

Compiled 11 977 to 1 786 computations (85.1% saved)

prune64.0ms (0.6%)

Memory
-0.6MiB live, 159.1MiB allocated
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New42114435
Fresh000
Picked101
Done000
Total42214436
Accuracy
79.6%
Counts
436 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.2%
(/.f64 (-.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal -3 binary64)) (pow.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))))
79.3%
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
▶55.8%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
▶56.3%
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
79.3%
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
54.9%
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))))))
24.6%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))
55.0%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))))
78.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
53.7%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
▶54.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
25.8%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
▶55.0%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶79.3%
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
Compiler

Compiled 970 to 334 computations (65.6% saved)

simplify305.0ms (3.1%)

Memory
18.8MiB live, 329.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x x #s(literal 1 binary64))
✓cost-diff0
(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓cost-diff0
(+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
✓cost-diff0
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓cost-diff0
(/.f64 #s(literal -1/2 binary64) x)
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓cost-diff0
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
✓cost-diff128
(+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓cost-diff320
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
Rules
5 152×accelerator-lowering-fma.f32
5 152×accelerator-lowering-fma.f64
2 152×*-lowering-*.f32
2 152×*-lowering-*.f64
1 364×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029366
157364
2109364
3188364
4309364
5550364
6966364
71835364
83015364
94522364
105591364
115969364
126179364
136502364
147004364
157561364
167874364
08035332
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)
(/ 1/2 (sqrt (+ (* x x) 1)))
1/2
(sqrt (+ (* x x) 1))
(+ (* x x) 1)
x
1
-1/2
(/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))))
(+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
-1
(neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
(- 1 (sqrt 1/2))
1
(sqrt 1/2)
1/2
(- 1 (sqrt (+ 1/2 (/ -1/2 x))))
1
(sqrt (+ 1/2 (/ -1/2 x)))
(+ 1/2 (/ -1/2 x))
1/2
(/ -1/2 x)
-1/2
x
(/ (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
1/2
(/ 1/2 (sqrt (+ (* x x) 1)))
(sqrt (+ (* x x) 1))
(+ (* x x) 1)
x
1
(+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(+ 1/4 (/ 1/4 (+ (* x x) 1)))
1/4
(/ 1/4 (+ (* x x) 1))
(+ (* x x) 1)
x
1
(* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
1/2
(/ 1/2 (sqrt (+ (* x x) 1)))
(sqrt (+ (* x x) 1))
Outputs
(* (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))))
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
(/ 1/2 (sqrt (+ (* x x) 1)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
1/2
#s(literal 1/2 binary64)
(sqrt (+ (* x x) 1))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(+ (* x x) 1)
(fma.f64 x x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
-1/2
#s(literal -1/2 binary64)
(/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
-1
#s(literal -1 binary64)
(neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(- 1 (sqrt (+ 1/2 (/ -1/2 x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ -1/2 x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(+ 1/2 (/ -1/2 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
x
(/ (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
1/2
#s(literal 1/2 binary64)
(/ 1/2 (sqrt (+ (* x x) 1)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt (+ (* x x) 1))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(+ (* x x) 1)
(fma.f64 x x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
(+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(+ 1/4 (/ 1/4 (+ (* x x) 1)))
(+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
1/4
#s(literal 1/4 binary64)
(/ 1/4 (+ (* x x) 1))
(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
(+ (* x x) 1)
(fma.f64 x x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
(* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
1/2
#s(literal 1/2 binary64)
(/ 1/2 (sqrt (+ (* x x) 1)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt (+ (* x x) 1))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

localize162.0ms (1.6%)

Memory
12.7MiB live, 320.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓accuracy100.0%
(*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
✓accuracy99.2%
(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓accuracy73.5%
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓accuracy73.5%
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓accuracy100.0%
(/.f64 #s(literal -1/2 binary64) x)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
✓accuracy99.2%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy98.8%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓accuracy100.0%
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
✓accuracy89.6%
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
✓accuracy73.5%
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
Samples
35.0ms141×0valid
25.0ms41×2valid
18.0ms57×0invalid
7.0ms16×1valid
1.0ms1×3valid
Compiler

Compiled 339 to 31 computations (90.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 62.0ms
ival-div: 20.0ms (32.4% of total)
ival-sqrt: 17.0ms (27.5% of total)
ival-add: 10.0ms (16.2% of total)
ival-mult: 6.0ms (9.7% of total)
adjust: 3.0ms (4.9% of total)
ival-sub: 3.0ms (4.9% of total)
exact: 1.0ms (1.6% of total)
ival-neg: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series30.0ms (0.3%)

Memory
-17.5MiB live, 59.3MiB allocated
Counts
19 → 204
Calls
Call 1
Inputs
#<alt (* (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))))>
#<alt (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))>
#<alt (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)>
#<alt (/ 1/2 (sqrt (+ (* x x) 1)))>
#<alt (- 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (- 1 (sqrt (+ 1/2 (/ -1/2 x))))>
#<alt (sqrt (+ 1/2 (/ -1/2 x)))>
#<alt (+ 1/2 (/ -1/2 x))>
#<alt (/ -1/2 x)>
#<alt (/ (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))>
#<alt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))>
#<alt (sqrt (+ (* x x) 1))>
#<alt (/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))>
#<alt (+ 1/4 (/ 1/4 (+ (* x x) 1)))>
#<alt (/ 1/4 (+ (* x x) 1))>
#<alt (+ (* x x) 1)>
#<alt (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))>
#<alt (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))>
Outputs
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt -2>
#<alt (- (* 1/8 (pow x 2)) 2)>
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#<alt (sqrt 1/2)>
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#<alt (sqrt 1/2)>
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#<alt 2>
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#<alt (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 1/8 (* x (sqrt 1/2)))))>
#<alt (- (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (- (+ (* -1/4 (/ (+ 1 (sqrt 1/2)) (pow x 3))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))))) (+ (/ 1/64 (* (pow x 3) (pow (sqrt 1/2) 3))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<alt (* 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (+ 1 (sqrt 1/2))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (+ 1 (sqrt 1/2))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))>
Calls

51 calls:

TimeVariablePointExpression
7.0ms
x
@inf
(* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
3.0ms
x
@-inf
(* (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))))
2.0ms
x
@inf
(/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
2.0ms
x
@inf
(* (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))))
1.0ms
x
@inf
(/ (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))

rewrite467.0ms (4.7%)

Memory
40.7MiB live, 891.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 342×/-lowering-/.f32
5 342×/-lowering-/.f64
4 150×*-lowering-*.f32
4 150×*-lowering-*.f64
2 530×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029213
1210211
21908211
08547193
Stop Event
1×iter limit
1×node limit
Counts
19 → 1 019
Calls
Call 1
Inputs
(* (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (/ 1 (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))))
(+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)
(/ 1/2 (sqrt (+ (* x x) 1)))
(- 1 (sqrt 1/2))
(sqrt 1/2)
(- 1 (sqrt (+ 1/2 (/ -1/2 x))))
(sqrt (+ 1/2 (/ -1/2 x)))
(+ 1/2 (/ -1/2 x))
(/ -1/2 x)
(/ (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
(sqrt (+ (* x x) 1))
(/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(+ 1/4 (/ 1/4 (+ (* x x) 1)))
(/ 1/4 (+ (* x x) 1))
(+ (* x x) 1)
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
Outputs
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal -1/2 binary64)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal -1/2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal -1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))))
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64))) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
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(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))

simplify495.0ms (5%)

Memory
0.6MiB live, 779.2MiB allocated
Algorithm
1×egg-herbie
Rules
7 960×accelerator-lowering-fma.f32
7 960×accelerator-lowering-fma.f64
4 932×+-lowering-+.f64
4 932×+-lowering-+.f32
4 392×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06254321
119433981
265653964
080763805
Stop Event
1×iter limit
1×node limit
Counts
204 → 204
Calls
Call 1
Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
-2
(- (* 1/8 (pow x 2)) 2)
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(* -1 (+ 1 (sqrt 1/2)))
(* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))
(- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(* -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
-1/2
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))
(- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))
-1/2
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))
(* -1 (* (sqrt (/ 1 x)) (sqrt -1/2)))
(/ (- x (* (sqrt x) (sqrt -1/2))) x)
(/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/2)))))) (* (sqrt x) (sqrt -1/2))) x)
(/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2)))))))) (* (sqrt x) (sqrt -1/2))) x)
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/4 (* x (sqrt 1/2))) (+ (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5))))))) (sqrt 1/2))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 x)) (sqrt -1/2))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt -1/2)))) (* (sqrt x) (sqrt -1/2))) x)
(/ (+ (* (sqrt x) (sqrt -1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2))))))) x)
(/ (+ (* (sqrt x) (sqrt -1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1/2) 5))))))))) x)
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(- (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) (pow x 2)))) (/ 1/4 (* x (sqrt 1/2))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (/ 1/128 (* (pow x 2) (pow (sqrt 1/2) 5))) (+ (/ 1/32 (* x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))) x)))
(/ -1/2 x)
(/ (- (* 1/2 x) 1/2) x)
(/ (- (* 1/2 x) 1/2) x)
(/ (- (* 1/2 x) 1/2) x)
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- 1/2 (* 1/2 (/ 1 x)))
(- 1/2 (* 1/2 (/ 1 x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
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(- 1/2 (* 1/2 (/ 1 x)))
(/ -1/2 x)
(/ -1/2 x)
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(/ -1/2 x)
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(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
1/2
(+ 1/2 (* -3/32 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 17/256 (pow x 2)) 3/32)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 17/256 (* -435/8192 (pow x 2)))) 3/32)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(- (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
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(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
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1
(+ 1 (* -1/4 (pow x 2)))
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1/2
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(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
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(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
1/4
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(/ 1/2 (+ 1 (sqrt 1/2)))
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(- (+ (/ 1/64 (* (pow x 3) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/2 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 2 (/ (* (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3))))) (+ 1 (sqrt 1/2)))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 2 (/ (* (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))
1/4
(+ 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (* 1/4 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))
(- (+ 1/4 (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))
1/4
(+ 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (* 1/4 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))
(- (+ 1/4 (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))
1/4
(+ 1/4 (* -1/4 (pow x 2)))
(+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))
(/ 1/4 (pow x 2))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/ 1/4 (pow x 2))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
2
(+ 2 (* -5/8 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 63/128 (pow x 2)) 5/8)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 63/128 (* -435/1024 (pow x 2)))) 5/8)))
(* 1/2 (+ 1 (sqrt 1/2)))
(+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 1/8 (* x (sqrt 1/2)))))
(- (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(- (+ (* -1/4 (/ (+ 1 (sqrt 1/2)) (pow x 3))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))))) (+ (/ 1/64 (* (pow x 3) (pow (sqrt 1/2) 3))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (+ 1 (sqrt 1/2))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
Outputs
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))
(+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))))))
(+.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x)))))) (fma.f64 #s(literal -1/32 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (*.f64 x x) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (/.f64 #s(literal 3/64 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) x)) x))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (/.f64 (+.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))) x)) x)) x))
-2
#s(literal -2 binary64)
(- (* 1/8 (pow x 2)) 2)
(fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
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(/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (*.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (*.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 11/128 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -69/1024 binary64) #s(literal 11/128 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/32 binary64) (*.f64 x (*.f64 x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) x))
2
#s(literal 2 binary64)
(+ 2 (* -5/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -5/8 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 63/128 (pow x 2)) 5/8)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 63/128 binary64)) #s(literal -5/8 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 63/128 (* -435/1024 (pow x 2)))) 5/8)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -435/1024 binary64) #s(literal 63/128 binary64)) #s(literal -5/8 binary64)) #s(literal 2 binary64))
(* 1/2 (+ 1 (sqrt 1/2)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 1/8 (* x (sqrt 1/2)))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) (/.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (+.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x))))
(- (+ (* -1/4 (/ (+ 1 (sqrt 1/2)) (pow x 3))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))))) (+ (/ 1/64 (* (pow x 3) (pow (sqrt 1/2) 3))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(+.f64 (+.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) (/.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -3/64 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64) #s(literal -1/4 binary64)) (*.f64 x (*.f64 x x))) (-.f64 (/.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))))))
(* 1/2 (+ 1 (sqrt 1/2)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+ (* -1 (/ (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) x))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))) x))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (+ 1 (sqrt 1/2))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (/.f64 #s(literal -3/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))) x))

eval419.0ms (4.2%)

Memory
-3.9MiB live, 695.8MiB allocated
Compiler

Compiled 93 225 to 6 378 computations (93.2% saved)

prune423.0ms (4.3%)

Memory
-12.2MiB live, 633.1MiB allocated
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2 19072 197
Fresh729
Picked325
Done000
Total2 200112 211
Accuracy
100.0%
Counts
2 211 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
55.0%
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
55.8%
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
▶78.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
▶53.7%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓54.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓55.0%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶79.3%
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
▶45.7%
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
47.1%
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
47.2%
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
▶14.3%
#s(literal 1/4 binary64)
Compiler

Compiled 226 to 147 computations (35% saved)

simplify78.0ms (0.8%)

Memory
29.6MiB live, 110.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓cost-diff0
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓cost-diff0
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
✓cost-diff0
(-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓cost-diff320
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
Rules
894×accelerator-lowering-fma.f32
894×accelerator-lowering-fma.f64
596×*-lowering-*.f32
596×*-lowering-*.f64
260×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028215
163213
2122213
3183213
4213213
5281213
6509213
7890213
81381213
91766213
101844213
111881213
121920213
131940213
141945213
151947213
01947195
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2))
(/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
1
(- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
-1
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
1/2
(/ 1/2 (sqrt (+ (* x x) 1)))
(sqrt (+ (* x x) 1))
(+ (* x x) 1)
x
(+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)
-1/2
1/4
(* (* x x) (+ (* (* x x) -11/128) 1/8))
(* x x)
x
(+ (* (* x x) -11/128) 1/8)
-11/128
1/8
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
1
(sqrt (+ 1/2 (/ 1/2 x)))
(+ 1/2 (/ 1/2 x))
1/2
(/ 1/2 x)
x
(- 1 (sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)))
1
(sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)
(/ 1/2 (sqrt (+ (* x x) 1)))
1/2
(sqrt (+ (* x x) 1))
(+ (* x x) 1)
x
Outputs
(* (/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2))
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
1
#s(literal 1 binary64)
(- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
-1
#s(literal -1 binary64)
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
1/2
#s(literal 1/2 binary64)
(/ 1/2 (sqrt (+ (* x x) 1)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt (+ (* x x) 1))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(+ (* x x) 1)
(fma.f64 x x #s(literal 1 binary64))
x
(+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
1/4
#s(literal 1/4 binary64)
(* (* x x) (+ (* (* x x) -11/128) 1/8))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))))
(* x x)
(*.f64 x x)
x
(+ (* (* x x) -11/128) 1/8)
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
-11/128
#s(literal -11/128 binary64)
1/8
#s(literal 1/8 binary64)
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ 1/2 x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(+ 1/2 (/ 1/2 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
x
(- 1 (sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
1
#s(literal 1 binary64)
(sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/ 1/2 (sqrt (+ (* x x) 1)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
1/2
#s(literal 1/2 binary64)
(sqrt (+ (* x x) 1))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(+ (* x x) 1)
(fma.f64 x x #s(literal 1 binary64))
x

localize149.0ms (1.5%)

Memory
-17.6MiB live, 248.2MiB allocated
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓accuracy88.9%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓accuracy73.5%
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) x)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓accuracy99.9%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓accuracy99.2%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓accuracy100.0%
(*.f64 x x)
✓accuracy99.9%
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
✓accuracy99.9%
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓accuracy89.7%
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
✓accuracy73.5%
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
Samples
42.0ms140×0valid
23.0ms42×2valid
13.0ms59×0invalid
5.0ms15×1valid
Compiler

Compiled 199 to 30 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-sqrt: 11.0ms (25.6% of total)
ival-add: 9.0ms (21% of total)
ival-div: 7.0ms (16.3% of total)
ival-mult: 7.0ms (16.3% of total)
ival-sub: 5.0ms (11.6% of total)
adjust: 3.0ms (7% of total)
exact: 1.0ms (2.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory
25.5MiB live, 25.5MiB allocated
Counts
17 → 204
Calls
Call 1
Inputs
#<alt (* (/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2))>
#<alt (/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))>
#<alt (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))>
#<alt (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))>
#<alt (* (* x x) (+ (* (* x x) -11/128) 1/8))>
#<alt (* x x)>
#<alt (+ (* (* x x) -11/128) 1/8)>
#<alt (- 1 (sqrt (+ 1/2 (/ 1/2 x))))>
#<alt (sqrt (+ 1/2 (/ 1/2 x)))>
#<alt (+ 1/2 (/ 1/2 x))>
#<alt (/ 1/2 x)>
#<alt (- 1 (sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)))>
#<alt (sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2))>
#<alt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)>
#<alt (/ 1/2 (sqrt (+ (* x x) 1)))>
#<alt (sqrt (+ (* x x) 1))>
#<alt (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)>
Outputs
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt -1/2>
#<alt (- (* -1/32 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (- (* 5/256 (pow x 2)) 1/32)) 1/2)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (+ 5/256 (* -117/8192 (pow x 2)))) 1/32)) 1/2)>
#<alt (/ -1 (+ 1 (sqrt 1/2)))>
#<alt (- (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))>
#<alt (- (+ (* -1 (/ (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (pow x 2))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))>
#<alt (- (+ (/ 1/128 (* (pow x 3) (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/16 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))))))>
#<alt (/ -1 (+ 1 (sqrt 1/2)))>
#<alt (* -1 (+ (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (* -1 (/ (+ (/ 1/32 (* x (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/16 (* x (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) x)) (/ 1 (+ 1 (sqrt 1/2))))>
#<alt (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))))) x)) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (/ 1 (+ 1 (sqrt 1/2))))>
#<alt -2>
#<alt (- (* 1/8 (pow x 2)) 2)>
#<alt (- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)>
#<alt (- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)>
#<alt (* -1 (+ 1 (sqrt 1/2)))>
#<alt (* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))>
#<alt (- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))>
#<alt (* -1 (+ 1 (sqrt 1/2)))>
#<alt (- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))>
#<alt (- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))>
#<alt (- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))>
#<alt (/ (- x (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 x)) (sqrt 1/2))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))>
#<alt -1/2>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))>
#<alt (- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))>
#<alt -1/2>
#<alt (* -1 (+ 1/2 (* 1/2 (/ 1 x))))>
#<alt (- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)>
#<alt (- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)>
Calls

51 calls:

TimeVariablePointExpression
2.0ms
x
@0
(sqrt (+ 1/2 (/ 1/2 x)))
1.0ms
x
@inf
(/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
0.0ms
x
@0
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
0.0ms
x
@-inf
(/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
0.0ms
x
@inf
(* (* x x) (+ (* (* x x) -11/128) 1/8))

rewrite662.0ms (6.7%)

Memory
-139.0MiB live, 745.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 492×/-lowering-/.f32
4 492×/-lowering-/.f64
4 332×*-lowering-*.f32
4 332×*-lowering-*.f64
3 766×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027166
1193164
21531164
08629151
Stop Event
1×iter limit
1×node limit
Counts
17 → 697
Calls
Call 1
Inputs
(* (/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2))
(/ 1 (- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
(- -1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))
(* (* x x) (+ (* (* x x) -11/128) 1/8))
(* x x)
(+ (* (* x x) -11/128) 1/8)
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
(sqrt (+ 1/2 (/ 1/2 x)))
(+ 1/2 (/ 1/2 x))
(/ 1/2 x)
(- 1 (sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)))
(sqrt (+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) 1/2)
(/ 1/2 (sqrt (+ (* x x) 1)))
(sqrt (+ (* x x) 1))
(+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)
Outputs
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(+.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(-.f64 (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(fma.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
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(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (+.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(pow.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))))

simplify590.0ms (6%)

Memory
37.6MiB live, 909.0MiB allocated
Algorithm
1×egg-herbie
Rules
13 610×accelerator-lowering-fma.f32
13 610×accelerator-lowering-fma.f64
5 920×*-lowering-*.f32
5 920×*-lowering-*.f64
4 230×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04703200
114312882
244682855
087272750
Stop Event
1×iter limit
1×node limit
Counts
204 → 204
Calls
Call 1
Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
-1/2
(- (* -1/32 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* 5/256 (pow x 2)) 1/32)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (+ 5/256 (* -117/8192 (pow x 2)))) 1/32)) 1/2)
(/ -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))
(- (+ (* -1 (/ (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (pow x 2))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))
(- (+ (/ 1/128 (* (pow x 3) (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/16 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))))))
(/ -1 (+ 1 (sqrt 1/2)))
(* -1 (+ (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2)))))
(- (* -1 (/ (+ (/ 1/32 (* x (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/16 (* x (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) x)) (/ 1 (+ 1 (sqrt 1/2))))
(- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))))) x)) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (/ 1 (+ 1 (sqrt 1/2))))
-2
(- (* 1/8 (pow x 2)) 2)
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(* -1 (+ 1 (sqrt 1/2)))
(* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))
(- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(* -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))
(/ (- x (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
-1/2
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))
(- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))
-1/2
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
Outputs
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64))) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))
(+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))))))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x) (+.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/32 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (*.f64 x x) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (/.f64 #s(literal 3/64 binary64) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))))) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x)))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) x))) x))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (/.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/64 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))) x)) x)) x))
-1/2
#s(literal -1/2 binary64)
(- (* -1/32 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal -1/32 binary64) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* 5/256 (pow x 2)) 1/32)) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 5/256 binary64)) #s(literal -1/32 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (+ 5/256 (* -117/8192 (pow x 2)))) 1/32)) 1/2)
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -117/8192 binary64) #s(literal 5/256 binary64)) #s(literal -1/32 binary64))) #s(literal -1/2 binary64))
(/ -1 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))
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(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) x)
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) x))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) x) (*.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) x))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) x)))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) x) (*.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(* -1/4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/4 binary64)))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 3/16 binary64)) #s(literal -1/4 binary64))))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -5/32 binary64)) #s(literal 3/16 binary64)) #s(literal -1/4 binary64)))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 35/256 binary64) #s(literal -5/32 binary64))) #s(literal 3/16 binary64)) #s(literal -1/4 binary64)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/2 (/ 1 x)) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) #s(literal -1/2 binary64))
(- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))
(+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) x))

eval173.0ms (1.8%)

Memory
10.9MiB live, 340.8MiB allocated
Compiler

Compiled 34 625 to 3 348 computations (90.3% saved)

prune144.0ms (1.5%)

Memory
-18.0MiB live, 319.0MiB allocated
Pruning

12 alts after pruning (6 fresh and 6 done)

PrunedKeptTotal
New1 04441 048
Fresh224
Picked145
Done022
Total1 047121 059
Accuracy
100.0%
Counts
1 059 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶45.5%
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
55.0%
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
▶55.8%
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓78.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓53.7%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓54.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓55.0%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶25.8%
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓79.3%
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
▶45.7%
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
▶47.2%
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
✓14.3%
#s(literal 1/4 binary64)
Compiler

Compiled 183 to 121 computations (33.9% saved)

simplify6.0ms (0.1%)

Memory
7.6MiB live, 7.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
✓cost-diff0
(*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x)
✓cost-diff640
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
✓cost-diff0
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
✓cost-diff0
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
✓cost-diff192
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
Rules
76×*-lowering-*.f32
76×*-lowering-*.f64
48×accelerator-lowering-fma.f32
48×accelerator-lowering-fma.f64
30×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01993
14193
26791
37991
48291
08287
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ 1/2 (+ 1 (sqrt 1/2)))
1/2
(+ 1 (sqrt 1/2))
1
(sqrt 1/2)
(- 1 1)
1
(* (* x x) 1/8)
(* x x)
x
1/8
(* (* x (+ (* (* x x) -11/128) 1/8)) x)
(* x (+ (* (* x x) -11/128) 1/8))
x
(+ (* (* x x) -11/128) 1/8)
(* x x)
-11/128
1/8
(+ (* (* (* (* x x) -11/128) x) x) (* (* x x) 1/8))
(* (* (* x x) -11/128) x)
(* (* x x) -11/128)
(* x x)
x
-11/128
(* (* x x) 1/8)
1/8
Outputs
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- 1 1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
(* (* x x) 1/8)
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(* x x)
(*.f64 x x)
x
1/8
#s(literal 1/8 binary64)
(* (* x (+ (* (* x x) -11/128) 1/8)) x)
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(* x (+ (* (* x x) -11/128) 1/8))
(*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
x
(+ (* (* x x) -11/128) 1/8)
(fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))
(* x x)
(*.f64 x x)
-11/128
#s(literal -11/128 binary64)
1/8
#s(literal 1/8 binary64)
(+ (* (* (* (* x x) -11/128) x) x) (* (* x x) 1/8))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(* (* (* x x) -11/128) x)
(*.f64 x (*.f64 x (*.f64 x #s(literal -11/128 binary64))))
(* (* x x) -11/128)
(*.f64 x (*.f64 x #s(literal -11/128 binary64)))
(* x x)
(*.f64 x x)
x
-11/128
#s(literal -11/128 binary64)
(* (* x x) 1/8)
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
1/8
#s(literal 1/8 binary64)

localize86.0ms (0.9%)

Memory
-5.8MiB live, 113.0MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x x)
✓accuracy99.9%
(*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x)
✓accuracy99.9%
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
✓accuracy71.4%
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
✓accuracy99.9%
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
✓accuracy99.9%
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
✓accuracy100.0%
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
Samples
63.0ms256×0valid
Compiler

Compiled 97 to 20 computations (79.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 10.0ms (48.1% of total)
ival-add: 5.0ms (24% of total)
ival-div: 2.0ms (9.6% of total)
ival-sqrt: 2.0ms (9.6% of total)
ival-sub: 1.0ms (4.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0%)

Memory
12.2MiB live, 12.2MiB allocated
Counts
12 → 96
Calls
Call 1
Inputs
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (- 1 1)>
#<alt (* (* x x) 1/8)>
#<alt (* x x)>
#<alt (* (* x (+ (* (* x x) -11/128) 1/8)) x)>
#<alt (* x (+ (* (* x x) -11/128) 1/8))>
#<alt (+ (* (* x x) -11/128) 1/8)>
#<alt (+ (* (* (* (* x x) -11/128) x) x) (* (* x x) 1/8))>
#<alt (* (* (* x x) -11/128) x)>
#<alt (* (* x x) -11/128)>
Outputs
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
Calls

24 calls:

TimeVariablePointExpression
0.0ms
x
@0
(* (* (* x x) -11/128) x)
0.0ms
x
@inf
(+ (* (* (* (* x x) -11/128) x) x) (* (* x x) 1/8))
0.0ms
x
@inf
(* (* x x) 1/8)
0.0ms
x
@-inf
(* (* (* x x) -11/128) x)
0.0ms
x
@inf
(* (* (* x x) -11/128) x)

rewrite358.0ms (3.6%)

Memory
6.4MiB live, 710.8MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
7 584×accelerator-lowering-fma.f32
7 584×accelerator-lowering-fma.f64
4 698×*-lowering-*.f32
4 698×*-lowering-*.f64
2 548×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01971
19169
262367
3551667
0859563
Stop Event
1×iter limit
1×node limit
Counts
12 → 620
Calls
Call 1
Inputs
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ 1 (sqrt 1/2))
(sqrt 1/2)
(- 1 1)
(* (* x x) 1/8)
(* x x)
(* (* x (+ (* (* x x) -11/128) 1/8)) x)
(* x (+ (* (* x x) -11/128) 1/8))
(+ (* (* x x) -11/128) 1/8)
(+ (* (* (* (* x x) -11/128) x) x) (* (* x x) 1/8))
(* (* (* x x) -11/128) x)
(* (* x x) -11/128)
Outputs
(+.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+.f64 (*.f64 (*.f64 #s(literal 4/7 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (*.f64 (*.f64 #s(literal 4/7 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (-.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (*.f64 #s(literal 4/7 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (-.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (*.f64 #s(literal 4/7 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
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(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal -1/512 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal -1/512 binary64))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal -1/512 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 14641/268435456 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal 1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal 1/64 binary64))))
(/.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))) x) (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))
(/.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))) (*.f64 x x)) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) x)
(*.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))) (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))))
(*.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))) (/.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -11/1024 binary64)) #s(literal 1/64 binary64))) (*.f64 x x)))
(*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))) (*.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))) (/.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 11/128 binary64) #s(literal 1/8 binary64))) (*.f64 x x)))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (neg.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))))))
(*.f64 (neg.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 11/128 binary64) #s(literal 1/8 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))))
(*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64))))))
(*.f64 (/.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))) x) (/.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (/.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))) (*.f64 x x)) (/.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))
(*.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -11/1024 binary64)) #s(literal 1/64 binary64))))
(*.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 11/128 binary64) #s(literal 1/8 binary64))))
(*.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))))
(*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (fma.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64))))) (*.f64 (*.f64 #s(literal 1771561/4398046511104 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))) (fma.f64 (*.f64 x (*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64)))))) (-.f64 (*.f64 x (*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 11/128 binary64)))))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)))) (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 14641/268435456 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal -1/8 binary64))))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/1024 binary64))))))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/1024 binary64))))))
(*.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal -1/64 binary64))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1331/2097152 binary64)) #s(literal -1/512 binary64)))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 121/16384 binary64)) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -11/1024 binary64))))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(*.f64 (*.f64 x x) (*.f64 x #s(literal -11/128 binary64)))
(*.f64 #s(literal -11/128 binary64) (*.f64 x (*.f64 x x)))
(*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x)
(*.f64 (*.f64 x #s(literal -11/128 binary64)) (*.f64 x x))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal -11/128 binary64))
(exp.f64 (log.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) #s(literal 1 binary64))
(*.f64 x (*.f64 x #s(literal -11/128 binary64)))
(*.f64 x (exp.f64 (log.f64 (*.f64 x #s(literal -11/128 binary64)))))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(*.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal -11/128 binary64))))
(*.f64 #s(literal -11/128 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal -11/128 binary64)) x)
(*.f64 (exp.f64 (log.f64 (*.f64 x #s(literal -11/128 binary64)))) x)
(*.f64 (exp.f64 (log.f64 #s(literal -11/128 binary64))) (*.f64 x x))

simplify206.0ms (2.1%)

Memory
-40.1MiB live, 210.8MiB allocated
Algorithm
1×egg-herbie
Rules
2 840×*-lowering-*.f32
2 840×*-lowering-*.f64
2 464×accelerator-lowering-fma.f32
2 464×accelerator-lowering-fma.f64
1 448×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029612
171612
2169612
3485612
41478612
54108612
65820612
77128612
08020576
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
Calls
Call 1
Inputs
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 3))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
Outputs
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 4))
(*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 4))
(*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* 1/8 x)
(*.f64 #s(literal 1/8 binary64) x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
(* 1/8 (pow x 2))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 4))
(*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 4))
(*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))

eval352.0ms (3.6%)

Memory
-21.7MiB live, 131.5MiB allocated
Compiler

Compiled 21 591 to 1 493 computations (93.1% saved)

prune224.0ms (2.3%)

Memory
12.5MiB live, 129.5MiB allocated
Pruning

12 alts after pruning (2 fresh and 10 done)

PrunedKeptTotal
New7981799
Fresh011
Picked145
Done066
Total79912811
Accuracy
100.0%
Counts
811 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓45.5%
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
55.0%
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
✓55.8%
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓78.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓53.7%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓54.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓55.0%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓79.3%
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
✓45.7%
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
✓47.2%
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
✓14.3%
#s(literal 1/4 binary64)
25.8%
#s(literal 0 binary64)
Compiler

Compiled 715 to 193 computations (73% saved)

regimes53.0ms (0.5%)

Memory
19.9MiB live, 64.0MiB allocated
Counts
27 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal -3 binary64)) (pow.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))))
Outputs
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
Calls

7 calls:

9.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
8.0ms
x
8.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
7.0ms
(hypot.f64 #s(literal 1 binary64) x)
6.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
Results
AccuracySegmentsBranch
100.0%3x
100.0%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
100.0%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
100.0%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
100.0%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
100.0%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
100.0%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes53.0ms (0.5%)

Memory
-6.4MiB live, 32.2MiB allocated
Counts
18 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
Outputs
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
Calls

6 calls:

28.0ms
(hypot.f64 #s(literal 1 binary64) x)
6.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
4.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
4.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
Results
AccuracySegmentsBranch
99.7%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
99.7%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
99.7%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.7%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.7%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.7%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes71.0ms (0.7%)

Memory
-5.2MiB live, 33.4MiB allocated
Counts
16 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -11/128 binary64)) x) x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
Outputs
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

6 calls:

48.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
5.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms
(hypot.f64 #s(literal 1 binary64) x)
4.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
4.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
Results
AccuracySegmentsBranch
99.2%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
99.2%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
99.2%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.2%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.2%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.2%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes29.0ms (0.3%)

Memory
-0.9MiB live, 36.8MiB allocated
Counts
10 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))
Outputs
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Calls

7 calls:

9.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
4.0ms
x
3.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
3.0ms
(hypot.f64 #s(literal 1 binary64) x)
3.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
Results
AccuracySegmentsBranch
98.4%3x
98.4%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
98.4%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
98.4%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.4%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.4%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.4%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes28.0ms (0.3%)

Memory
-17.6MiB live, 25.0MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
Outputs
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Calls

6 calls:

14.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
3.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
3.0ms
(hypot.f64 #s(literal 1 binary64) x)
3.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
2.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
Results
AccuracySegmentsBranch
98.4%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
98.4%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.4%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.4%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.4%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
98.4%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes15.0ms (0.2%)

Memory
21.4MiB live, 21.4MiB allocated
Counts
7 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
Outputs
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Calls

6 calls:

3.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms
(hypot.f64 #s(literal 1 binary64) x)
2.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
2.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
2.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
Results
AccuracySegmentsBranch
98.1%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
98.1%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.1%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.1%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.1%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
98.1%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes19.0ms (0.2%)

Memory
-17.6MiB live, 21.1MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
Outputs
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/4 binary64)
Calls

7 calls:

6.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
2.0ms
x
2.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms
(hypot.f64 #s(literal 1 binary64) x)
2.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
Results
AccuracySegmentsBranch
57.5%3x
57.5%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
57.5%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
57.5%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
57.5%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
57.5%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
57.5%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes12.0ms (0.1%)

Memory
26.4MiB live, 26.4MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
Outputs
#s(literal 1/4 binary64)
#s(literal 0 binary64)
Calls

7 calls:

2.0ms
x
2.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms
(hypot.f64 #s(literal 1 binary64) x)
2.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
2.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
Results
AccuracySegmentsBranch
36.9%3x
36.7%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
36.7%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
36.7%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
36.7%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
36.7%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
36.7%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes12.0ms (0.1%)

Memory
-20.3MiB live, 16.5MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
Outputs
#s(literal 0 binary64)
Calls

7 calls:

5.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
1.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms
x
1.0ms
(hypot.f64 #s(literal 1 binary64) x)
1.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
Results
AccuracySegmentsBranch
25.8%1x
25.8%1(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
25.8%1(hypot.f64 #s(literal 1 binary64) x)
25.8%1(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
25.8%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
25.8%1(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
25.8%1(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
Compiler

Compiled 54 to 37 computations (31.5% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000000015231
406.92497075742114
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
0.0ms
0.9999999999988716
1.0
Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify11.0ms (0.1%)

Memory
22.5MiB live, 22.5MiB allocated
Algorithm
1×egg-herbie
Rules
30×+-commutative_binary64
22×*-commutative_binary64
18×sub-neg_binary64
14×neg-sub0_binary64
14×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048170
167170
279170
394170
4104170
5110170
6112170
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(if (<=.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 2251799813682707/2251799813685248 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
Outputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) #s(literal 1/4 binary64))
(if (<=.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 2251799813682707/2251799813685248 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)

soundness1.4s (14.3%)

Memory
-5.7MiB live, 1 070.4MiB allocated
Rules
13 610×accelerator-lowering-fma.f32
13 610×accelerator-lowering-fma.f64
12 168×accelerator-lowering-fma.f32
12 168×accelerator-lowering-fma.f64
7 960×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219881
1640809
21804769
35719712
08156670
027166
1193164
21531164
08629151
04703200
114312882
244682855
087272750
029213
1210211
21908211
08547193
06254321
119433981
265653964
080763805
01971
19169
262367
3551667
0859563
01254
17247
255647
3519947
0881642
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
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 377 to 189 computations (49.9% saved)

preprocess48.0ms (0.5%)

Memory
-3.0MiB live, 117.1MiB allocated
Compiler

Compiled 368 to 112 computations (69.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...