Given's Rotation SVD example, simplified

Time bar (total: 8.7s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 19 to 11 computations (42.1% saved)

sample1.8s (21.3%)

Memory
101.9MiB live, 2 198.4MiB allocated
Samples
927.0ms2 806×2valid
384.0ms4 167×0valid
209.0ms1 283×1valid
Precisions
Click to see histograms. Total time spent on operations: 1.3s
ival-hypot: 493.0ms (39.1% of total)
ival-sqrt: 152.0ms (12.1% of total)
adjust: 136.0ms (10.8% of total)
ival-div: 130.0ms (10.3% of total)
ival-sub: 112.0ms (8.9% of total)
ival-add: 111.0ms (8.8% of total)
ival-mult: 107.0ms (8.5% of total)
exact: 8.0ms (0.6% of total)
ival-true: 7.0ms (0.6% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain215.0ms (2.5%)

Memory
-56.7MiB live, 308.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
841(-4.814432824490744e-162)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))))))cancellation850
Confusion
Predicted +Predicted -
+840
-1171
Precision
0.9882352941176471
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+8400
-10171
Precision?
0.9882352941176471
Recall?
1.0
Freqs
test
numberfreq
0171
185
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
51.0ms190×2valid
19.0ms236×0valid
14.0ms86×1valid
Compiler

Compiled 174 to 31 computations (82.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 63.0ms
ival-hypot: 23.0ms (36.4% of total)
adjust: 8.0ms (12.7% of total)
ival-div: 8.0ms (12.7% of total)
ival-sqrt: 8.0ms (12.7% of total)
ival-mult: 6.0ms (9.5% of total)
ival-sub: 5.0ms (7.9% of total)
ival-add: 5.0ms (7.9% of total)
ival-true: 1.0ms (1.6% of total)
exact: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)

preprocess15.0ms (0.2%)

Memory
27.0MiB live, 27.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01431
13727
27027
39527
412727
513427
0912
01812
13510
26510
310510
413710
514410
014410
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.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))))))
Outputs
(-.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 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
Symmetry

(abs x)

Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.4%
(-.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 12 to 9 computations (25% saved)

simplify8.0ms (0.1%)

Memory
-37.2MiB live, 9.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
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-diff2
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0949
01849
13543
26543
310543
413743
514443
014443
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.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))))))
#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 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
#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) (hypot.f64 #s(literal 1 binary64) x))
(hypot.f64 #s(literal 1 binary64) x)
x
Outputs
(-.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 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#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)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.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 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
(hypot.f64 #s(literal 1 binary64) x)
x

localize50.0ms (0.6%)

Memory
38.0MiB live, 84.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy0.01171875
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy0.01171875
(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)))))
accuracy19.58972408888815
(-.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
25.0ms95×2valid
9.0ms118×0valid
7.0ms43×1valid
Compiler

Compiled 81 to 11 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-hypot: 11.0ms (36.7% of total)
adjust: 4.0ms (13.4% of total)
ival-div: 4.0ms (13.4% of total)
ival-sqrt: 4.0ms (13.4% of total)
ival-mult: 3.0ms (10% of total)
ival-sub: 2.0ms (6.7% of total)
ival-add: 2.0ms (6.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
8.8MiB live, 8.8MiB allocated
Counts
5 → 54
Calls
Call 1
Inputs
(*.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 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(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) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
Outputs
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 (* (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)))
(* (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))))))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(+ 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)))
1/2
(+ 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 (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)))))
(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)))))
(+ 1 (/ 1 x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(/ 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)
(- 1/2 (* 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 (* 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) (* -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 x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) 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))
Calls

3 calls:

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

simplify160.0ms (1.8%)

Memory
-8.6MiB live, 228.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0206845
1633767
21960714
37820714
08462676
Stop Event
iter limit
node limit
Counts
54 → 54
Calls
Call 1
Inputs
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 (* (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)))
(* (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))))))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(+ 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)))
1/2
(+ 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 (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)))))
(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)))))
(+ 1 (/ 1 x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(/ 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)
(- 1/2 (* 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 (* 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) (* -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 x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) 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 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/32 binary64) (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) (*.f64 x x) #s(literal 1 binary64))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 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)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) #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)))
(-.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (fma.f64 (*.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/16 binary64) (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 2 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/16 binary64) (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(-.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 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) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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)))))
(-.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3/16 binary64) #s(literal 1 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) 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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (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 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (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 #s(literal -3/16 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ 1 (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))))
(/ (- (+ 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 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(- 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 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(+ 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 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64))))))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -3/16 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (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 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (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 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x))
(- 1 (/ 1 x))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64)))))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (neg.f64 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 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 x))

rewrite183.0ms (2.1%)

Memory
-18.6MiB live, 262.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0943
01833
18233
260933
3635833
0824330
Stop Event
iter limit
node limit
iter limit
Counts
5 → 280
Calls
Call 1
Inputs
(*.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 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(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) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
Outputs
(*.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) #s(literal 2 binary64)))) (+.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) (cosh.f64 (atanh.f64 x))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) (-.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)))) (fma.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64))) (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))
(*.f64 (*.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))
(*.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cosh.f64 (atanh.f64 x)))))
(*.f64 (+.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))
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(-.f64 (cosh.f64 (log.f64 (cosh.f64 (atanh.f64 x)))) (sinh.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))
(fabs.f64 (neg.f64 (cosh.f64 (atanh.f64 x))))
(fabs.f64 (cosh.f64 (atanh.f64 x)))
(cos.f64 (asin.f64 (neg.f64 (tanh.f64 (asinh.f64 x)))))
(cos.f64 (asin.f64 (cos.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (atan.f64 x)))))
(cos.f64 (asin.f64 (sin.f64 (neg.f64 (atan.f64 x)))))
(cos.f64 (asin.f64 (fabs.f64 (tanh.f64 (asinh.f64 x)))))
(cos.f64 (asin.f64 (tanh.f64 (asinh.f64 x))))
(cos.f64 (atan.f64 (exp.f64 (log.f64 x))))
(cos.f64 (neg.f64 (atan.f64 x)))
(cos.f64 (atan.f64 x))
(exp.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)))
(exp.f64 (log.f64 (cosh.f64 (atanh.f64 x))))
(+.f64 (cosh.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64))))
(+.f64 (*.f64 (tanh.f64 (asinh.f64 x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cosh.f64 (atanh.f64 x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (cosh.f64 (atanh.f64 x)))) (sinh.f64 (log.f64 (cosh.f64 (atanh.f64 x)))))

eval39.0ms (0.5%)

Memory
37.9MiB live, 83.2MiB allocated
Compiler

Compiled 8 248 to 1 577 computations (80.9% saved)

prune17.0ms (0.2%)

Memory
-19.0MiB live, 34.5MiB allocated
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New32212334
Fresh000
Picked101
Done000
Total32312335
Accuracy
69.9%
Counts
335 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
25.2%
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
69.4%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
2.6%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)))) (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64))))) (*.f64 (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))))))
25.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
44.2%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
25.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
25.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
45.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
25.9%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
45.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
25.1%
(*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
45.4%
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
Compiler

Compiled 606 to 394 computations (35% saved)

simplify209.0ms (2.4%)

Memory
-15.7MiB live, 77.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
cost-diff0
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
cost-diff1
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
cost-diff0
(+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) 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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
cost-diff1
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))
cost-diff0
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
cost-diff0
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
cost-diff0
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 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 -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042294
069294
1106280
2188280
3348280
4544280
5644280
6670280
7694280
8740280
9864280
101117280
111788280
122858280
133847280
144615280
155462280
166668280
177062280
187664280
197784280
207842280
217844280
227844280
237844280
247844280
07844275
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/4 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)
Outputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/4 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))))
(sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))
(fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
(+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)

localize273.0ms (3.1%)

Memory
58.7MiB live, 412.0MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.10546875
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
accuracy0.453125
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
accuracy1.0
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy34.49096680402474
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
accuracy0.01171875
(+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
accuracy0.01171875
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
accuracy28.402820056656445
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
accuracy0.01171875
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
accuracy0.38269311493409647
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
accuracy28.52574729952384
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
accuracy0.01171875
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
accuracy29.33060181232164
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy0.0078125
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy0.01171875
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy0.01171875
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
Samples
136.0ms95×2valid
56.0ms43×1valid
27.0ms118×0valid
Compiler

Compiled 307 to 31 computations (89.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 91.0ms
ival-mult: 24.0ms (26.3% of total)
ival-hypot: 15.0ms (16.4% of total)
adjust: 13.0ms (14.2% of total)
ival-div: 12.0ms (13.2% of total)
ival-sub: 11.0ms (12.1% of total)
ival-sqrt: 10.0ms (11% of total)
ival-add: 6.0ms (6.6% of total)
exact: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory
-9.8MiB live, 35.7MiB allocated
Counts
21 → 93
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))))
(+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Outputs
(* 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
(+ 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)))
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(- 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)))
(* (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))))))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(* 1/8 (/ (sqrt 1/2) (pow x 2)))
(/ (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))) (pow x 2))
(/ (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (- 1 (sqrt 1/2)))))) (pow x 2))
(/ (sqrt 1/2) x)
(+ 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 (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)))))
(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)))))
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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(- (+ 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)))))
(+ (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)))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(+ 1 (/ 1 x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))) (sqrt 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 (* 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))
(- (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)))
(- 1/2 (* 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 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(- (+ 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) (* -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 x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(- (+ 1 (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(/ -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))
Calls

3 calls:

TimeVariablePointExpression
8.0ms
x
@0
((- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (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))))))) (* 1/2 (+ 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))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (* 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 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (+ (* (/ (sqrt 1/2) x) (- (/ 1/8 x) 1/2)) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (/ 1 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt 1/2)))
3.0ms
x
@inf
((- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (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))))))) (* 1/2 (+ 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))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (* 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 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (+ (* (/ (sqrt 1/2) x) (- (/ 1/8 x) 1/2)) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (/ 1 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt 1/2)))
3.0ms
x
@-inf
((- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (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))))))) (* 1/2 (+ 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))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (* 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 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (+ (* (/ (sqrt 1/2) x) (- (/ 1/8 x) 1/2)) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (/ 1 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt 1/2)))

simplify902.0ms (10.4%)

Memory
-142.6MiB live, 282.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03511459
110851344
234161294
084261237
Stop Event
iter limit
node limit
Counts
93 → 93
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
(+ 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)))
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(- 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)))
(* (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))))))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(* 1/8 (/ (sqrt 1/2) (pow x 2)))
(/ (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))) (pow x 2))
(/ (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (- 1 (sqrt 1/2)))))) (pow x 2))
(/ (sqrt 1/2) x)
(+ 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 (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)))))
(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)))))
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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(- (+ 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)))))
(+ (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)))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(+ 1 (/ 1 x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))) (sqrt 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 (* 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))
(- (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)))
(- 1/2 (* 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 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(- (+ 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) (* -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 x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(- (+ 1 (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(/ -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
(* 1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(*.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64) (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64))) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -69/1024 binary64) (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/32 binary64) (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) (*.f64 x x) #s(literal 1 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/16 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 5/32 binary64) (*.f64 x x)) #s(literal 3/16 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 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 #s(literal 1 binary64) (fma.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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)))
(-.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x) (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (fma.f64 (*.f64 x x) (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x) (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/16 binary64) (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 2 binary64))
(* 1/8 (/ (sqrt 1/2) (pow x 2)))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))
(/ (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))) (pow x 2))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (/.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/8 binary64)) x))
(/ (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (- 1 (sqrt 1/2)))))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/8 binary64)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (*.f64 x x))
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/16 binary64) (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(-.f64 (-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(- (+ 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)))))
(-.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 1/32 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))))
(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 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(-.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) (/.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x))
(- (+ (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 (+.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))))) x)
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 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)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3/16 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1/4 (pow x 2))
(*.f64 #s(literal -1/4 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(*.f64 (*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/4 binary64)) x) x)
(+ 1 (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1 (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) x)
(/ (- (+ 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 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(- (+ 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))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/4 binary64)) x) #s(literal 1/2 binary64) #s(literal 1/16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x))) x) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 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 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (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 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/4 binary64) (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 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/4 binary64)) x) #s(literal 1/2 binary64) #s(literal 1/16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x))) x))
(- 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 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) 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) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (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 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (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 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x))
(- 1 (/ 1 x))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) x))
(- (+ 1 (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal -1 binary64) #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) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (neg.f64 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 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 x))

rewrite185.0ms (2.1%)

Memory
1.2MiB live, 334.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042254
069230
1281230
22194230
08741220
Stop Event
iter limit
node limit
iter limit
Counts
21 → 491
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))))
(+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Outputs
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(-.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
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(*.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)))))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64))))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)))) (pow.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64))) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (pow.f64 (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

eval113.0ms (1.3%)

Memory
25.6MiB live, 265.7MiB allocated
Compiler

Compiled 25 633 to 2 569 computations (90% saved)

prune20.0ms (0.2%)

Memory
-30.5MiB live, 62.5MiB allocated
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New58611597
Fresh707
Picked325
Done000
Total59613609
Accuracy
100.0%
Counts
609 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
70.1%
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
70.0%
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
46.2%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
70.0%
(-.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
69.4%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
44.2%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
45.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
45.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
27.1%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
25.9%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
56.7%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
55.4%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
56.6%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
Compiler

Compiled 591 to 380 computations (35.7% saved)

simplify40.0ms (0.5%)

Memory
10.2MiB live, 63.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
cost-diff0
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff0
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
cost-diff0
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
cost-diff0
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
cost-diff0
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
cost-diff0
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
cost-diff0
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
cost-diff0
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
cost-diff0
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))
cost-diff0
(-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
cost-diff2
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043313
070307
1102307
2199307
3429307
4860307
51473307
61566307
71603307
81615307
91619307
101619307
01619307
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
#s(literal 1 binary64)
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
x
#s(literal 3/2 binary64)
(+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
#s(literal 1/2 binary64)
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
#s(literal 69/1024 binary64)
(*.f64 x x)
x
#s(literal 11/128 binary64)
#s(literal 1/8 binary64)
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64))))
(-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
#s(literal 1 binary64)
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
x
#s(literal 3/2 binary64)
(+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64)))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 1 binary64))
#s(literal -1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
#s(literal 1/2 binary64)
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
#s(literal 69/1024 binary64)
(*.f64 x x)
x
#s(literal 11/128 binary64)
#s(literal 1/8 binary64)

localize329.0ms (3.8%)

Memory
6.3MiB live, 576.4MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.04296875
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy0.0546875
(fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
accuracy0.7577189749320747
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
accuracy27.716456382649703
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy0.01171875
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
accuracy0.01171875
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
accuracy33.65545911933585
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
accuracy0.0
(*.f64 x x)
accuracy0.41073984918566164
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
accuracy28.517474798284606
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
accuracy23.298343411480353
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
accuracy0.01171875
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy0.01953125
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))
accuracy0.12109375
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
accuracy19.139650861929702
(-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
Samples
188.0ms95×2valid
29.0ms118×0valid
26.0ms43×1valid
Compiler

Compiled 373 to 31 computations (91.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 212.0ms
ival-pow: 135.0ms (63.8% of total)
ival-div: 15.0ms (7.1% of total)
adjust: 13.0ms (6.1% of total)
ival-hypot: 12.0ms (5.7% of total)
ival-sub: 11.0ms (5.2% of total)
ival-mult: 10.0ms (4.7% of total)
ival-add: 7.0ms (3.3% of total)
ival-sqrt: 6.0ms (2.8% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series36.0ms (0.4%)

Memory
-19.7MiB live, 29.2MiB allocated
Counts
20 → 104
Calls
Call 1
Inputs
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
Outputs
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(* 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))))
(* 3/8 (pow x 2))
(* (pow x 2) (+ 3/8 (* -39/128 (pow x 2))))
(* (pow x 2) (+ 3/8 (* (pow x 2) (- (* 275/1024 (pow x 2)) 39/128))))
(* (pow x 2) (+ 3/8 (* (pow x 2) (- (* (pow x 2) (+ 275/1024 (* -8043/32768 (pow x 2)))) 39/128))))
1
(+ 1 (* -3/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 39/128 (pow x 2)) 3/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 39/128 (* -275/1024 (pow x 2)))) 3/8)))
(+ 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)))
(pow x 2)
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(* 69/1024 (pow x 2))
3/2
(+ 3/2 (* 1/2 (/ 1 x)))
(- (+ 3/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 3/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(/ (- 1 (sqrt 1/8)) (+ 3/2 (sqrt 1/2)))
(- (+ (* -1 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (/ 1 (+ 3/2 (sqrt 1/2)))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (* (pow x 2) (+ 3/2 (sqrt 1/2))))) (+ (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))) (+ (/ 3/16 (* x (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (* x (pow (+ 3/2 (sqrt 1/2)) 2))))))))
(- (+ (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (+ (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (pow x 3) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (/ 1 (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (* (pow x 2) (+ 3/2 (sqrt 1/2))))) (+ (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))) (+ (* 1/32 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 3/2 (sqrt 1/2)))))) (+ (/ 3/16 (* x (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))) (+ (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (* x (pow (+ 3/2 (sqrt 1/2)) 2))) (+ (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))))) (* (pow x 3) (+ 3/2 (sqrt 1/2)))) (/ (* (- 1 (sqrt 1/8)) (- (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) 1/4)) (* (pow x 3) (pow (+ 3/2 (sqrt 1/2)) 2)))))))))))
(- 1 (sqrt 1/8))
(- 1 (+ (sqrt 1/8) (* 3/16 (/ 1 (* x (sqrt 1/8))))))
(- (+ 1 (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8))))) (+ (sqrt 1/8) (/ 3/16 (* x (sqrt 1/8)))))
(- (+ 1 (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (pow x 3) (sqrt 1/8))))) (+ (sqrt 1/8) (+ (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8)))) (/ 3/16 (* x (sqrt 1/8))))))
(sqrt 1/8)
(+ (sqrt 1/8) (* 3/16 (/ 1 (* x (sqrt 1/8)))))
(+ (sqrt 1/8) (+ (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8)))) (/ 3/16 (* x (sqrt 1/8)))))
(+ (sqrt 1/8) (+ (* -1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (pow x 3) (sqrt 1/8)))) (+ (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8)))) (/ 3/16 (* x (sqrt 1/8))))))
(- 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)))))
(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)))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8))
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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 5))
(* (pow x 5) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(- 3/2 (* 1/2 (/ 1 x)))
(+ 3/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 3/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(- (+ (/ 3/16 (* x (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (/ 1 (+ 3/2 (sqrt 1/2))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (* x (pow (+ 3/2 (sqrt 1/2)) 2))))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2)))))) x)) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* 1/32 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) (* (pow (sqrt 1/2) 3) (+ 3/2 (sqrt 1/2))))) (+ (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))))) (+ 3/2 (sqrt 1/2))) (/ (* (- 1 (sqrt 1/8)) (- (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) 1/4)) (pow (+ 3/2 (sqrt 1/2)) 2))))) x)) (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2)))))) x)) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ 1 (* 3/16 (/ 1 (* x (sqrt 1/8))))) (sqrt 1/8))
(- (+ 1 (* -1 (/ (- (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 3/16 (/ 1 (sqrt 1/8)))) x))) (sqrt 1/8))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (sqrt 1/8)))) x)) (* 3/16 (/ 1 (sqrt 1/8)))) x))) (sqrt 1/8))
(- (sqrt 1/8) (* 3/16 (/ 1 (* x (sqrt 1/8)))))
(+ (sqrt 1/8) (* -1 (/ (+ (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 3/16 (/ 1 (sqrt 1/8)))) x)))
(+ (sqrt 1/8) (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (sqrt 1/8)))) x)) (* 3/16 (/ 1 (sqrt 1/8)))) x)))
(- (+ 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))
(- (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)))
(- 1/2 (* 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 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) 69/1024)))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4))))))
Calls

3 calls:

TimeVariablePointExpression
27.0ms
x
@-inf
((+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (* -1/8 (* x x)) 1) (* x x) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (* (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) x) x) (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) x) (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* 69/1024 (* x x)))
5.0ms
x
@inf
((+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (* -1/8 (* x x)) 1) (* x x) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (* (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) x) x) (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) x) (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* 69/1024 (* x x)))
2.0ms
x
@0
((+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (* -1/8 (* x x)) 1) (* x x) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (* (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) x) x) (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) x) (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* 69/1024 (* x x)))

simplify228.0ms (2.6%)

Memory
3.1MiB live, 335.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04292419
113482081
248301968
090911927
Stop Event
iter limit
node limit
Counts
104 → 104
Calls
Call 1
Inputs
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(* 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))))
(* 3/8 (pow x 2))
(* (pow x 2) (+ 3/8 (* -39/128 (pow x 2))))
(* (pow x 2) (+ 3/8 (* (pow x 2) (- (* 275/1024 (pow x 2)) 39/128))))
(* (pow x 2) (+ 3/8 (* (pow x 2) (- (* (pow x 2) (+ 275/1024 (* -8043/32768 (pow x 2)))) 39/128))))
1
(+ 1 (* -3/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 39/128 (pow x 2)) 3/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 39/128 (* -275/1024 (pow x 2)))) 3/8)))
(+ 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)))
(pow x 2)
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(* 69/1024 (pow x 2))
3/2
(+ 3/2 (* 1/2 (/ 1 x)))
(- (+ 3/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 3/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(/ (- 1 (sqrt 1/8)) (+ 3/2 (sqrt 1/2)))
(- (+ (* -1 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (/ 1 (+ 3/2 (sqrt 1/2)))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (* (pow x 2) (+ 3/2 (sqrt 1/2))))) (+ (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))) (+ (/ 3/16 (* x (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (* x (pow (+ 3/2 (sqrt 1/2)) 2))))))))
(- (+ (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (+ (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (pow x 3) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (/ 1 (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (* (pow x 2) (+ 3/2 (sqrt 1/2))))) (+ (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))) (+ (* 1/32 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 3/2 (sqrt 1/2)))))) (+ (/ 3/16 (* x (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))) (+ (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (* x (pow (+ 3/2 (sqrt 1/2)) 2))) (+ (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))))) (* (pow x 3) (+ 3/2 (sqrt 1/2)))) (/ (* (- 1 (sqrt 1/8)) (- (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) 1/4)) (* (pow x 3) (pow (+ 3/2 (sqrt 1/2)) 2)))))))))))
(- 1 (sqrt 1/8))
(- 1 (+ (sqrt 1/8) (* 3/16 (/ 1 (* x (sqrt 1/8))))))
(- (+ 1 (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8))))) (+ (sqrt 1/8) (/ 3/16 (* x (sqrt 1/8)))))
(- (+ 1 (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (pow x 3) (sqrt 1/8))))) (+ (sqrt 1/8) (+ (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8)))) (/ 3/16 (* x (sqrt 1/8))))))
(sqrt 1/8)
(+ (sqrt 1/8) (* 3/16 (/ 1 (* x (sqrt 1/8)))))
(+ (sqrt 1/8) (+ (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8)))) (/ 3/16 (* x (sqrt 1/8)))))
(+ (sqrt 1/8) (+ (* -1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (pow x 3) (sqrt 1/8)))) (+ (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (pow x 2) (sqrt 1/8)))) (/ 3/16 (* x (sqrt 1/8))))))
(- 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)))))
(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)))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8))
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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 5))
(* (pow x 5) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(- 3/2 (* 1/2 (/ 1 x)))
(+ 3/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 3/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(- (+ (/ 3/16 (* x (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (/ 1 (+ 3/2 (sqrt 1/2))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (* x (pow (+ 3/2 (sqrt 1/2)) 2))))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2)))))) x)) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* 1/32 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) (* (pow (sqrt 1/2) 3) (+ 3/2 (sqrt 1/2))))) (+ (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2))))))) (+ 3/2 (sqrt 1/2))) (/ (* (- 1 (sqrt 1/8)) (- (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) 1/4)) (pow (+ 3/2 (sqrt 1/2)) 2))))) x)) (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* (sqrt 1/8) (+ 3/2 (sqrt 1/2)))))) (+ (* -1 (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) (+ 3/2 (sqrt 1/2)))) (* -1/32 (/ (- 1 (sqrt 1/8)) (* (pow (sqrt 1/2) 3) (pow (+ 3/2 (sqrt 1/2)) 2)))))) x)) (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2)))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
(- (+ 1 (* 3/16 (/ 1 (* x (sqrt 1/8))))) (sqrt 1/8))
(- (+ 1 (* -1 (/ (- (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 3/16 (/ 1 (sqrt 1/8)))) x))) (sqrt 1/8))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (sqrt 1/8)))) x)) (* 3/16 (/ 1 (sqrt 1/8)))) x))) (sqrt 1/8))
(- (sqrt 1/8) (* 3/16 (/ 1 (* x (sqrt 1/8)))))
(+ (sqrt 1/8) (* -1 (/ (+ (* -1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 3/16 (/ 1 (sqrt 1/8)))) x)))
(+ (sqrt 1/8) (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (+ 1/16 (* 3/16 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (pow (sqrt 1/8) 2)))) (* x (sqrt 1/8)))) (* 1/2 (/ (- 3/8 (* 9/256 (/ 1 (pow (sqrt 1/8) 2)))) (sqrt 1/8)))) x)) (* 3/16 (/ 1 (sqrt 1/8)))) x)))
(- (+ 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))
(- (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)))
(- 1/2 (* 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 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) 69/1024)))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4))))))
Outputs
2
#s(literal 2 binary64)
(+ 2 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) x) x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 2 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 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
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rewrite161.0ms (1.9%)

Memory
37.9MiB live, 316.5MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
043250
070246
1265228
21947228
08277228
Stop Event
iter limit
node limit
iter limit
Counts
20 → 350
Calls
Call 1
Inputs
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
Outputs
(/.f64 (neg.f64 (-.f64 #s(literal 9/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (neg.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 27/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 9/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 9/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 27/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (+.f64 #s(literal 9/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(fma.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 9/4 binary64) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 27/8 binary64) (+.f64 #s(literal 9/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 #s(literal 9/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(-.f64 (pow.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (-.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
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(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(pow.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (fabs.f64 (sqrt.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.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)))))) (sqrt.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 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 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (sinh.f64 (log.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(*.f64 (fabs.f64 (*.f64 #s(literal 69/1024 binary64) (neg.f64 x))) x)
(*.f64 (fabs.f64 (*.f64 #s(literal 69/1024 binary64) x)) x)
(*.f64 (*.f64 #s(literal 69/1024 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 69/1024 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 69/1024 binary64)))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 69/1024 binary64))
(*.f64 x (fabs.f64 (*.f64 (neg.f64 x) #s(literal 69/1024 binary64))))
(*.f64 x (fabs.f64 (*.f64 #s(literal 69/1024 binary64) x)))
(*.f64 x (*.f64 #s(literal 69/1024 binary64) x))
(sqrt.f64 (*.f64 #s(literal 4761/1048576 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (neg.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(fabs.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)))

eval146.0ms (1.7%)

Memory
-22.8MiB live, 267.2MiB allocated
Compiler

Compiled 22 122 to 2 289 computations (89.7% saved)

prune16.0ms (0.2%)

Memory
13.3MiB live, 60.3MiB allocated
Pruning

12 alts after pruning (6 fresh and 6 done)

PrunedKeptTotal
New4934497
Fresh426
Picked145
Done022
Total49812510
Accuracy
100.0%
Counts
510 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.2%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
70.1%
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
69.4%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
44.2%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
45.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
45.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
27.1%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
25.9%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
55.3%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
55.4%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
56.6%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
56.7%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
Compiler

Compiled 629 to 339 computations (46.1% saved)

simplify284.0ms (3.3%)

Memory
-15.1MiB live, 265.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
cost-diff0
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
cost-diff0
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
cost-diff0
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
cost-diff0
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
cost-diff0
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
cost-diff0
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff0
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
cost-diff0
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
cost-diff0
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
cost-diff0
(hypot.f64 #s(literal 1 binary64) x)
cost-diff0
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
cost-diff0
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
049357
076353
1126341
2222341
3435341
4950341
51667341
61959341
72264341
82701341
93443341
104062341
115155341
125577341
135668341
145726341
155756341
165756341
175756341
186676341
08316341
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal -11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(literal 1/2 binary64)
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
#s(literal 1/4 binary64)
(*.f64 x x)
x
Outputs
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(*.f64 x x)
x
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal -11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(literal 1/2 binary64)
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
#s(literal 1/4 binary64)
(*.f64 x x)
x

localize333.0ms (3.8%)

Memory
1.1MiB live, 866.2MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.04296875
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
accuracy0.6817420073046264
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
accuracy19.58972408888815
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
accuracy35.05599609335983
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
accuracy0.0078125
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
accuracy0.01171875
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy19.18299218598809
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy29.33060181232164
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy0.0390625
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy0.0546875
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
accuracy0.46551042145101407
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy28.560703041227345
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy0.0
(*.f64 x x)
accuracy0.41073984918566164
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy27.797292964725514
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
accuracy0.0078125
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy0.01171875
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy0.01171875
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy19.154144236980066
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
Samples
215.0ms95×2valid
35.0ms43×1valid
33.0ms118×0valid
Compiler

Compiled 413 to 39 computations (90.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 251.0ms
ival-pow: 136.0ms (54.3% of total)
ival-div: 24.0ms (9.6% of total)
adjust: 22.0ms (8.8% of total)
ival-mult: 18.0ms (7.2% of total)
ival-add: 16.0ms (6.4% of total)
ival-sub: 13.0ms (5.2% of total)
ival-hypot: 12.0ms (4.8% of total)
ival-sqrt: 8.0ms (3.2% of total)
exact: 1.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series22.0ms (0.3%)

Memory
9.2MiB live, 55.7MiB allocated
Counts
24 → 124
Calls
Call 1
Inputs
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(hypot.f64 #s(literal 1 binary64) x)
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 x x)
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
Outputs
(* 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))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
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)))))
(pow x 2)
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(* 1/4 (/ (pow x 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))
(* (pow x 2) (+ (* -1 (* (pow x 2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (* (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/4 (/ (* (sqrt 1/2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/8 (/ (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 35/256 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))))) (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(+ 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 (* (sqrt 1/2) (sqrt 2)))
(+ 1 (+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))))
(+ 1 (+ (* (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)))))))
(+ 1 (+ (* (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)))))))))
(+ 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 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))))))))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(/ 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)))))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 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)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 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)))))) (+ (* -1/4 (/ (+ (* 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)))))) (+ (* 1/32 (/ (+ (* 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 (/ (- (* 1/64 (/ 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)))))) (* (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))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))))
(/ -1/2 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
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 (sqrt 1/8)) (+ 3/2 (sqrt 1/2)))
(- (+ (* -1 (/ (+ (* 3/16 (/ 1 (* (sqrt 1/8) (+ 3/2 (sqrt 1/2))))) (/ (* (+ 1/2 (* 1/4 (/ 1 (sqrt 1/2)))) (- 1 (sqrt 1/8))) (pow (+ 3/2 (sqrt 1/2)) 2))) x)) (/ 1 (+ 3/2 (sqrt 1/2)))) (/ (sqrt 1/8) (+ 3/2 (sqrt 1/2))))
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(* -11/128 (pow x 3))
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(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
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(+ 1/2 (* 1/2 (/ 1 x)))
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(+ 1 (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(+ 1 (+ (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))))))
(- 1 (sqrt 1/2))
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(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
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(+ (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)))))
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(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -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)))))
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(- (+ 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))
(- (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)))
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
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(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
Calls

3 calls:

TimeVariablePointExpression
7.0ms
x
@inf
((/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (+ (* 1 1) (* x x))) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (* 1/8 (* x x)) (* x x) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ 1/4 (* x x)) (/ (- (/ 1/4 (* x x)) 1/2) x))
6.0ms
x
@0
((/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (+ (* 1 1) (* x x))) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (* 1/8 (* x x)) (* x x) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ 1/4 (* x x)) (/ (- (/ 1/4 (* x x)) 1/2) x))
6.0ms
x
@-inf
((/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (+ (* 1 1) (* x x))) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (* 1/8 (* x x)) (* x x) (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) 1) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ 1/4 (* x x)) (/ (- (/ 1/4 (* x x)) 1/2) x))

simplify185.0ms (2.1%)

Memory
13.1MiB live, 343.3MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06244201
121213775
084883591
Stop Event
iter limit
node limit
Counts
124 → 123
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))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
1
(+ 1 (* 1/2 (pow x 2)))
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(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1 (+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))))
(- (+ 1 (* 1/4 (/ 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))
(- (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)))
(+ (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 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
Outputs
(* 1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))
(* 1/4 (pow x 2))
(*.f64 #s(literal 1/4 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 5/32 binary64) (*.f64 x x)) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -35/256 binary64) (*.f64 x x) #s(literal 5/32 binary64)) x) x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 5/32 binary64) (*.f64 x x)) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* 1/8 x)
(*.f64 #s(literal 1/8 binary64) x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* 1/4 (/ (pow x 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))
(*.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) x) x)
(* (pow x 2) (+ (* -1 (* (pow x 2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(*.f64 (fma.f64 (*.f64 (neg.f64 x) x) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(*.f64 (fma.f64 (-.f64 (fma.f64 (-.f64 (/.f64 #s(literal 5/32 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 11/256 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 x x) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (* (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/4 (/ (* (sqrt 1/2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/8 (/ (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 35/256 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))))) (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (neg.f64 x) x) (+.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 11/32 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 5/32 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 11/256 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal -69/2048 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -35/256 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (-.f64 (/.f64 #s(literal 5/32 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 11/256 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 x x)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (pow.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 3/16 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x))
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64)) x) x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2))))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* (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 (fma.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* (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 (fma.f64 (/.f64 (fma.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -69/1024 binary64) (*.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (fma.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (fma.f64 (/.f64 (fma.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 3))
(/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
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(+ (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 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 3/16 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/8 binary64))) (neg.f64 x))) x))
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 x))

rewrite190.0ms (2.2%)

Memory
19.7MiB live, 350.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049319
076303
1310247
22303247
09200242
Stop Event
iter limit
node limit
iter limit
Counts
24 → 412
Calls
Call 1
Inputs
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(hypot.f64 #s(literal 1 binary64) x)
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 x x)
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
(+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
Outputs
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (-.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))) (+.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (hypot.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (hypot.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal 1/2 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (hypot.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal -1/2 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (hypot.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal 1/2 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(/.f64 (fma.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal -1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal 1/2 binary64))) (*.f64 (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal -1/2 binary64))) (*.f64 (*.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) #s(literal 1/2 binary64))) (*.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
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(/.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.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) (hypot.f64 #s(literal 1 binary64) x))))
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(-.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(fabs.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) (hypot.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(fabs.f64 (-.f64 (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))))
(fabs.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(fabs.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(fabs.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
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(exp.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(+.f64 (cosh.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sinh.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(*.f64 (neg.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))) (sqrt.f64 (neg.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(pow.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
(fabs.f64 (neg.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(fabs.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))) (sinh.f64 (log.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))))
(/.f64 (fabs.f64 (/.f64 #s(literal 1/4 binary64) (neg.f64 x))) x)
(/.f64 (fabs.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x))) x)
(/.f64 (fabs.f64 (/.f64 #s(literal 1/4 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1/4 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1/4 binary64) x) x)
(/.f64 #s(literal -1/4 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
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(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 x)))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) x) (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/8 binary64)) (*.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(neg.f64 (/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (neg.f64 x)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x))

eval155.0ms (1.8%)

Memory
0.6MiB live, 289.8MiB allocated
Compiler

Compiled 30 472 to 3 011 computations (90.1% saved)

prune39.0ms (0.5%)

Memory
-9.2MiB live, 137.4MiB allocated
Pruning

14 alts after pruning (5 fresh and 9 done)

PrunedKeptTotal
New6544658
Fresh011
Picked235
Done066
Total65614670
Accuracy
100.0%
Counts
670 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
44.8%
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
70.1%
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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)))
69.4%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
44.2%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
45.1%
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
45.5%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
27.1%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
25.9%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
55.3%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
55.4%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
55.4%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
56.6%
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
46.2%
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
56.7%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
Compiler

Compiled 1 432 to 463 computations (67.7% saved)

regimes145.0ms (1.7%)

Memory
-9.4MiB live, 321.8MiB allocated
Counts
32 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.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))))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)))) (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64))))) (*.f64 (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))))))
Outputs
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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)))
Calls

7 calls:

48.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
37.0ms
(hypot.f64 #s(literal 1 binary64) x)
35.0ms
x
7.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
6.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
100.0%2x
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 47 to 37 computations (21.3% saved)

regimes75.0ms (0.9%)

Memory
1.0MiB live, 246.9MiB allocated
Counts
24 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.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))))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
Outputs
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
Calls

7 calls:

26.0ms
x
19.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
8.0ms
(hypot.f64 #s(literal 1 binary64) x)
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))))
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)))))
Results
AccuracySegmentsBranch
99.9%2x
99.9%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))))))
99.9%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)))))
99.9%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.9%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.9%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.9%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes80.0ms (0.9%)

Memory
2.5MiB live, 278.0MiB allocated
Counts
23 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.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))))))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
Calls

7 calls:

26.0ms
x
18.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
9.0ms
(hypot.f64 #s(literal 1 binary64) x)
8.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
8.0ms
(-.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
99.9%2x
99.9%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))))))
99.9%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)))))
99.9%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.9%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.9%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.9%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes71.0ms (0.8%)

Memory
-3.1MiB live, 244.2MiB allocated
Counts
20 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
Calls

7 calls:

23.0ms
x
16.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
11.0ms
(hypot.f64 #s(literal 1 binary64) x)
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))))
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
99.3%2x
99.3%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))))))
99.3%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)))))
99.3%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.3%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.3%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.3%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes101.0ms (1.2%)

Memory
-1.2MiB live, 192.7MiB allocated
Counts
17 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
Calls

7 calls:

35.0ms
x
31.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
15.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
6.0ms
(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))))
Results
AccuracySegmentsBranch
99.0%2x
99.0%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))))))
99.0%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)))))
99.0%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.0%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.0%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.0%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes61.0ms (0.7%)

Memory
-2.4MiB live, 190.1MiB allocated
Counts
15 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #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 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
Outputs
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
Calls

7 calls:

18.0ms
x
14.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
7.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
7.0ms
(-.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))))))
6.0ms
(hypot.f64 #s(literal 1 binary64) x)
Results
AccuracySegmentsBranch
98.9%2x
98.9%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))))))
98.9%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)))))
98.9%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.9%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.9%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.9%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes45.0ms (0.5%)

Memory
10.2MiB live, 153.0MiB allocated
Counts
11 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
Outputs
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
Calls

7 calls:

13.0ms
x
10.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms
(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 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
Results
AccuracySegmentsBranch
98.8%2x
98.8%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))))))
98.8%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)))))
98.8%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.8%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.8%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.8%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes43.0ms (0.5%)

Memory
0.2MiB live, 144.2MiB allocated
Counts
10 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
Calls

7 calls:

12.0ms
x
10.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms
(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
98.8%2x
98.8%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))))))
98.8%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)))))
98.8%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.8%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.8%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.8%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes40.0ms (0.5%)

Memory
-12.0MiB live, 131.5MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
Calls

7 calls:

10.0ms
x
9.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms
(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
98.2%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)))))
98.2%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.2%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.2%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.2%2x
98.2%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))))))
98.2%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes35.0ms (0.4%)

Memory
16.6MiB live, 111.3MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
Calls

7 calls:

9.0ms
x
7.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms
(hypot.f64 #s(literal 1 binary64) x)
4.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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)))))
Results
AccuracySegmentsBranch
97.8%2x
97.8%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))))))
97.8%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)))))
97.8%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
97.8%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
97.8%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
97.8%2(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes19.0ms (0.2%)

Memory
2.8MiB live, 51.4MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
Calls

7 calls:

4.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
3.0ms
x
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
(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
56.6%1x
56.6%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))))))
56.6%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)))))
56.6%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
56.6%1(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
56.6%1(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
56.6%1(hypot.f64 #s(literal 1 binary64) x)
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes16.0ms (0.2%)

Memory
8.0MiB live, 55.3MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

7 calls:

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))))
2.0ms
x
2.0ms
(/.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))))))
2.0ms
(hypot.f64 #s(literal 1 binary64) x)
Results
AccuracySegmentsBranch
25.9%1x
25.9%1(hypot.f64 #s(literal 1 binary64) x)
25.9%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))))))
25.9%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)))))
25.9%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
25.9%1(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
25.9%1(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
Compiler

Compiled 47 to 37 computations (21.3% saved)

bsearch1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.0000001094616768
399.4213280629747
Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify89.0ms (1%)

Memory
-7.1MiB live, 86.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0103750
1154742
2236742
3324742
4406742
5527742
6777742
71135742
81336742
91600742
102070742
114963742
Stop Event
node limit
Calls
Call 1
Inputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x)) #s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
Outputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- 1 (pow (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 3/2)) (+ (+ 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) (*.f64 (fma.f64 (*.f64 #s(literal -11/128 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x)) x)) #s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1/2) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))

derivations1.4s (15.6%)

Memory
-27.3MiB live, 1 573.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06244201
121213775
084883591
042254
069230
1281230
22194230
08741220
049319
076303
1310247
22303247
09200242
03511459
110851344
234161294
084261237
043250
070246
1265228
21947228
08277228
0206845
1633767
21960714
37820714
08462676
04292419
113482081
248301968
090911927
0943
01833
18233
260933
3635833
0824330
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 816 to 106 computations (87% saved)

preprocess76.0ms (0.9%)

Memory
-3.7MiB live, 134.8MiB allocated
Remove

(abs x)

Compiler

Compiled 1 842 to 324 computations (82.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...