Given's Rotation SVD example, simplified

Time bar (total: 8.4s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Algorithm
1×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)

sample2.8s (34.1%)

Memory
-137.9MiB live, 3 120.0MiB allocated; 1.8s collecting garbage
Samples
1.1s4 182×0valid
1.0s2 838×2valid
325.0ms1 236×1valid
Precisions
Click to see histograms. Total time spent on operations: 1.5s
ival-hypot: 553.0ms (37.9% of total)
adjust: 228.0ms (15.6% of total)
ival-div: 188.0ms (12.9% of total)
ival-sqrt: 178.0ms (12.2% of total)
ival-mult: 117.0ms (8% of total)
ival-sub: 103.0ms (7.1% of total)
ival-add: 75.0ms (5.1% of total)
exact: 8.0ms (0.5% of total)
ival-true: 6.0ms (0.4% of total)
ival-assert: 4.0ms (0.3% of total)
Bogosity

explain311.0ms (3.7%)

Memory
-9.9MiB live, 371.9MiB allocated; 77ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
660-0-(-.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))))))cancellation660
Confusion
Predicted +Predicted -
+660
-0190
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+6600
-00190
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0190
166
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
75.0ms206×2valid
24.0ms236×0valid
15.0ms70×1valid
Compiler

Compiled 174 to 31 computations (82.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 90.0ms
ival-hypot: 29.0ms (32.4% of total)
adjust: 18.0ms (20.1% of total)
ival-div: 13.0ms (14.5% of total)
ival-sqrt: 9.0ms (10.1% of total)
ival-mult: 7.0ms (7.8% of total)
ival-sub: 6.0ms (6.7% of total)
ival-add: 6.0ms (6.7% of total)
exact: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess21.0ms (0.3%)

Memory
-5.1MiB live, 37.6MiB allocated; 11ms collecting garbage
Algorithm
1×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
1×iter limit
1×saturated
1×iter limit
1×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
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶76.4%
(-.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)

simplify5.0ms (0.1%)

Memory
11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Algorithm
1×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
1×iter limit
1×saturated
1×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

localize66.0ms (0.8%)

Memory
3.9MiB live, 143.2MiB allocated; 27ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy0.00390625
(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)))))
accuracy0.0078125
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy15.104726448355205
(-.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
41.0ms103×2valid
9.0ms118×0valid
6.0ms35×1valid
Compiler

Compiled 81 to 11 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-hypot: 11.0ms (25.5% of total)
ival-mult: 9.0ms (20.9% of total)
adjust: 7.0ms (16.2% of total)
ival-sqrt: 7.0ms (16.2% of total)
ival-div: 4.0ms (9.3% of total)
ival-sub: 2.0ms (4.6% of total)
ival-add: 2.0ms (4.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
21.9MiB live, 21.9MiB allocated; 0ms collecting garbage
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)))))

simplify189.0ms (2.3%)

Memory
-8.6MiB live, 227.4MiB allocated; 31ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0206845
1633767
21960714
37820714
08462676
Stop Event
1×iter limit
1×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))

rewrite195.0ms (2.3%)

Memory
-1.9MiB live, 237.2MiB allocated; 51ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0943
01833
18233
260933
3635833
0824330
Stop Event
1×iter limit
1×node limit
1×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)))))
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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)))))

eval41.0ms (0.5%)

Memory
-4.4MiB live, 95.6MiB allocated; 9ms collecting garbage
Compiler

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

prune14.0ms (0.2%)

Memory
-10.8MiB live, 36.3MiB allocated; 1ms collecting garbage
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New32311334
Fresh000
Picked101
Done000
Total32411335
Accuracy
76.8%
Counts
335 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
31.3%
(/.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)))
▶76.4%
(-.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)))))
2.4%
(-.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))))))))
31.7%
(-.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 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))))
▶31.7%
(-.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)))))
▶31.2%
(-.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)))))
46.2%
(-.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)))))
32.4%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
▶46.8%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
3.6%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
▶2.3%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
Compiler

Compiled 616 to 402 computations (34.7% saved)

simplify166.0ms (2%)

Memory
-4.9MiB live, 326.5MiB allocated; 30ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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)))))
cost-diff0
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
cost-diff3
(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)))
cost-diff3
(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))))
cost-diff0
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff0
#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)))
cost-diff0
(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))))
cost-diff0
(-.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)))))
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
047396
078396
1131374
2298364
3864364
42845358
56278358
08296350
Stop Event
1×iter limit
1×node limit
1×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 #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)))))
#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))))
#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)))
(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 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
#s(literal 3/16 binary64)
(*.f64 x x)
x
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
#s(literal 1 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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)))))
(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))))
(/.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)))
(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)))
(*.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)
(*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 11/64 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 #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)))))
#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))))
#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)))
(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 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
#s(literal 3/16 binary64)
(*.f64 x x)
x
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (*.f64 #s(literal 11/64 binary64) x) x #s(literal -1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 #s(literal 2 binary64))))))
#s(literal 1 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (*.f64 #s(literal 11/64 binary64) x) x #s(literal -1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 #s(literal 2 binary64)))))
(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))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (*.f64 #s(literal 11/64 binary64) x) x #s(literal -1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 #s(literal 2 binary64))))
(/.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 (*.f64 (fma.f64 (*.f64 #s(literal 11/64 binary64) x) x #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(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)))
(*.f64 (fma.f64 (*.f64 #s(literal 11/64 binary64) x) x #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 11/64 binary64)) x)
(*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 11/64 binary64))
#s(literal 11/64 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))

localize254.0ms (3%)

Memory
-6.3MiB live, 379.8MiB allocated; 72ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy1.0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy1.0
(*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy15.104726448355205
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
accuracy28.229057589396227
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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)))))
accuracy0.0234375
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy0.31814567808979477
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
accuracy15.104726448355205
(-.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)))))
accuracy28.234746159435712
#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)))
accuracy0.0
(*.f64 x x)
accuracy0.00390625
(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))))
accuracy15.104726448355205
(-.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)))))
accuracy29.085351582627318
#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)))
accuracy0.00390625
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy15.104726448355205
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
accuracy28.51058042410447
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy0.00390625
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy0.00390625
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy0.0078125
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy15.104726448355205
(-.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
107.0ms103×2valid
49.0ms35×1valid
48.0ms118×0valid
Compiler

Compiled 368 to 39 computations (89.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 142.0ms
ival-mult: 39.0ms (27.5% of total)
adjust: 24.0ms (16.9% of total)
ival-sub: 23.0ms (16.2% of total)
ival-hypot: 22.0ms (15.5% of total)
ival-sqrt: 14.0ms (9.9% of total)
ival-div: 10.0ms (7.1% of total)
ival-add: 8.0ms (5.6% of total)
exact: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory
22.6MiB live, 22.6MiB allocated; 0ms collecting garbage
Counts
23 → 79
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 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)))))
(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))))
#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)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(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))))
(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)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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)))))
(*.f64 x x)
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 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))))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 11/64 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))))))
(* -1/4 (sqrt 1/2))
(+ (* -1/4 (sqrt 1/2)) (* 11/64 (* (pow x 2) (sqrt 1/2))))
(pow x 2)
(* 3/16 (pow x 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))
(* 3/16 (pow x 4))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(* 11/64 (/ (* (pow x 4) (sqrt 1/2)) (sqrt 2)))
(* (pow x 4) (+ (* -1/4 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 11/64 (/ (sqrt 1/2) (sqrt 2)))))
(* (pow x 4) (+ (* -1/4 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (+ (* 11/64 (/ (sqrt 1/2) (sqrt 2))) (/ (* (sqrt 1/2) (sqrt 2)) (pow x 4)))))
(* 11/64 (* (pow x 2) (sqrt 1/2)))
(* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (pow x 2))) (* 11/64 (sqrt 1/2))))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(- (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)))
Calls

3 calls:

TimeVariablePointExpression
5.0ms
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 (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)))))) (+ (* (- (* 3/16 (* x x)) 1/4) (* x x)) 1) (+ (* (/ (+ (* (* (* 11/64 (sqrt 1/2)) x) x) (* (sqrt 1/2) -1/4)) (sqrt 2)) (* x x)) (* (sqrt 2) (sqrt 1/2))) (+ (* (* (* 11/64 (sqrt 1/2)) x) x) (* (sqrt 1/2) -1/4)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* x x) (* 3/16 (* x x)) (* 11/64 (sqrt 1/2)) (* (sqrt 2) (sqrt 1/2)))
3.0ms
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 (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)))))) (+ (* (- (* 3/16 (* x x)) 1/4) (* x x)) 1) (+ (* (/ (+ (* (* (* 11/64 (sqrt 1/2)) x) x) (* (sqrt 1/2) -1/4)) (sqrt 2)) (* x x)) (* (sqrt 2) (sqrt 1/2))) (+ (* (* (* 11/64 (sqrt 1/2)) x) x) (* (sqrt 1/2) -1/4)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* x x) (* 3/16 (* x x)) (* 11/64 (sqrt 1/2)) (* (sqrt 2) (sqrt 1/2)))
2.0ms
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 (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)))))) (+ (* (- (* 3/16 (* x x)) 1/4) (* x x)) 1) (+ (* (/ (+ (* (* (* 11/64 (sqrt 1/2)) x) x) (* (sqrt 1/2) -1/4)) (sqrt 2)) (* x x)) (* (sqrt 2) (sqrt 1/2))) (+ (* (* (* 11/64 (sqrt 1/2)) x) x) (* (sqrt 1/2) -1/4)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* x x) (* 3/16 (* x x)) (* 11/64 (sqrt 1/2)) (* (sqrt 2) (sqrt 1/2)))

simplify159.0ms (1.9%)

Memory
13.4MiB live, 240.2MiB allocated; 49ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03241312
19991194
232151117
083851069
Stop Event
1×iter limit
1×node limit
Counts
79 → 79
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))))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 11/64 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))))))
(* -1/4 (sqrt 1/2))
(+ (* -1/4 (sqrt 1/2)) (* 11/64 (* (pow x 2) (sqrt 1/2))))
(pow x 2)
(* 3/16 (pow x 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))
(* 3/16 (pow x 4))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(* 11/64 (/ (* (pow x 4) (sqrt 1/2)) (sqrt 2)))
(* (pow x 4) (+ (* -1/4 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 11/64 (/ (sqrt 1/2) (sqrt 2)))))
(* (pow x 4) (+ (* -1/4 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (+ (* 11/64 (/ (sqrt 1/2) (sqrt 2))) (/ (* (sqrt 1/2) (sqrt 2)) (pow x 4)))))
(* 11/64 (* (pow x 2) (sqrt 1/2)))
(* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (pow x 2))) (* 11/64 (sqrt 1/2))))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(- (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)))
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 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #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 (*.f64 #s(literal 11/128 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -69/1024 binary64)) #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 (*.f64 #s(literal 3/16 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/32 binary64)) #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 (*.f64 #s(literal 1/4 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/16 binary64)) #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 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) #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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 11/64 binary64) (*.f64 x x) #s(literal -1/4 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 (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x)) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal 11/64 binary64) (*.f64 x x) #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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 11/64 binary64) (*.f64 x x) #s(literal -1/4 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 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x)) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal 11/64 binary64) (*.f64 x x) #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))) (* 11/64 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))))))
(fma.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 11/64 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1/4 (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64))
(+ (* -1/4 (sqrt 1/2)) (* 11/64 (* (pow x 2) (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal 11/64 binary64) (*.f64 x x) #s(literal -1/4 binary64)))
(pow x 2)
(*.f64 x x)
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(- 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 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (+ (* -1/2 (/ (- (* 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 #s(literal 1 binary64) (-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x) (/.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)))
(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 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) x) (/.f64 (/.f64 #s(literal 1/32 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(-.f64 (+.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 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 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 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 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 (/.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) (* 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 (/.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 (/.f64 #s(literal -1/8 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)
(* 3/16 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3/16 binary64))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 11/64 (/ (* (pow x 4) (sqrt 1/2)) (sqrt 2)))
(*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 11/64 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 4) (+ (* -1/4 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 11/64 (/ (sqrt 1/2) (sqrt 2)))))
(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal -11/64 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* -1/4 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (+ (* 11/64 (/ (sqrt 1/2) (sqrt 2))) (/ (* (sqrt 1/2) (sqrt 2)) (pow x 4)))))
(*.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal -11/64 binary64)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)))
(* 11/64 (* (pow x 2) (sqrt 1/2)))
(*.f64 (*.f64 (*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)
(* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (pow x 2))) (* 11/64 (sqrt 1/2))))
(*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal -11/64 binary64))) x) 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 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) 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 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 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))
(-.f64 #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))))
(- (+ 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))

rewrite204.0ms (2.4%)

Memory
30.6MiB live, 262.4MiB allocated; 40ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047332
078294
1299294
22153288
08731274
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
23 → 403
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 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)))))
(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))))
#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)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(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))))
(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)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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)))))
(*.f64 x x)
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 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)))
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(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (fabs.f64 (*.f64 #s(literal 3/16 binary64) (neg.f64 x))) x)
(*.f64 (fabs.f64 (*.f64 #s(literal 3/16 binary64) x)) x)
(*.f64 (*.f64 #s(literal 3/16 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 3/16 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 3/16 binary64)))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 3/16 binary64))
(*.f64 x (fabs.f64 (*.f64 (neg.f64 x) #s(literal 3/16 binary64))))
(*.f64 x (fabs.f64 (*.f64 #s(literal 3/16 binary64) x)))
(*.f64 x (*.f64 #s(literal 3/16 binary64) x))
(sqrt.f64 (*.f64 #s(literal 9/256 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (neg.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x))))
(fabs.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 11/64 binary64))
(*.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)

eval164.0ms (2%)

Memory
-10.5MiB live, 181.5MiB allocated; 50ms collecting garbage
Compiler

Compiled 22 916 to 2 449 computations (89.3% saved)

prune32.0ms (0.4%)

Memory
7.3MiB live, 52.8MiB allocated; 4ms collecting garbage
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New5399548
Fresh606
Picked415
Done000
Total54910559
Accuracy
100.0%
Counts
559 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
47.5%
(/.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)))
▶77.1%
(-.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))))
▶46.2%
(-.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)))))
✓46.8%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
31.7%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶32.4%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
54.6%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #s(literal 11/128 binary64))) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
▶55.8%
#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))
▶54.5%
#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))
55.9%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
Compiler

Compiled 517 to 341 computations (34% saved)

simplify114.0ms (1.4%)

Memory
-4.4MiB live, 55.9MiB allocated; 7ms collecting garbage
Algorithm
1×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
(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 (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
#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
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
cost-diff0
(+.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))
cost-diff0
(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))
cost-diff0
(-.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))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043314
070314
1101314
2199314
3492314
41138314
52106314
62698314
72857314
83045314
93275314
103332314
113415314
123496314
133507314
143507314
153507314
163580314
173582314
03582314
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.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))))
(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 (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)
#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 (-.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) #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))
#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 (*.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 #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 (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 (/.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)))))) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (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 -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))
(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)
#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 (-.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 #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) #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))
#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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #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 (*.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(*.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
#s(literal -11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 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)))))
#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)

localize147.0ms (1.8%)

Memory
-10.3MiB live, 267.6MiB allocated; 24ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.0390625
(*.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))
accuracy0.34648146173681227
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
accuracy28.296407682845274
#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))
accuracy0.00390625
(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x)))
accuracy0.00390625
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))))
accuracy15.104726448355205
(-.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)))))
accuracy32.94680328185631
#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #s(literal -1/2 binary64) x))
accuracy0.0234375
(*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
accuracy0.03515625
(*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy0.278577220702817
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy29.125265861063642
#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))
accuracy15.104726448355205
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
accuracy23.624657137017966
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))
accuracy0.0078125
(/.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)))
accuracy0.0078125
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy0.0078125
(+.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))
accuracy14.662191050197496
(-.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))))
Samples
68.0ms103×2valid
27.0ms118×0valid
17.0ms35×1valid
Compiler

Compiled 369 to 32 computations (91.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 80.0ms
adjust: 24.0ms (30% of total)
ival-hypot: 12.0ms (15% of total)
ival-mult: 12.0ms (15% of total)
ival-div: 9.0ms (11.3% of total)
ival-sub: 8.0ms (10% of total)
ival-pow: 5.0ms (6.3% of total)
ival-add: 5.0ms (6.3% of total)
ival-sqrt: 4.0ms (5% of total)
exact: 1.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series21.0ms (0.3%)

Memory
-12.4MiB live, 31.5MiB allocated; 10ms collecting garbage
Counts
21 → 106
Calls
Call 1
Inputs
(-.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))))
(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 (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 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))
#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 (*.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 #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))
(/.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))) (+.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 69/1024 binary64) (*.f64 x 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))))
1/2
(+ 1/2 (* 1/32 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/32 (* -5/256 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/32 (* (pow x 2) (- (* 117/8192 (pow x 2)) 5/256)))))
2
(+ 2 (* -1/8 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
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)))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (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)
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/2 (* -3/32 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 17/256 (pow x 2)) 3/32)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 17/256 (* -435/8192 (pow x 2)))) 3/32)))
(* 69/1024 (pow x 2))
(/ 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)))))
(- (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(- (+ (* -1/2 (/ (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))))) (pow x 3))) (+ (* -1/2 (/ (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (pow x 3))) (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(/ 1 (+ 1 (sqrt 1/2)))
(- (/ 1 (+ 1 (sqrt 1/2))) (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))
(- (+ (* 1/16 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
(- (+ (* -1 (/ (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))) (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) (pow x 3))) (+ (* 1/16 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2)))))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* 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 (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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(+ 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)))))
(- (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
(- (+ (/ 1/2 (* x (+ 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 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))
(- (+ (* -1 (/ (+ (* -1/32 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) (pow x 3))) (+ (/ 1/2 (* x (+ 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 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (/ 1/8 (* x (* (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 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3))))))) (* -1/2 (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (/ 1 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/128 (* x (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))))))) x)) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (/ 1 (+ 1 (sqrt 1/2))))
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(/ 1/2 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))))))
(+ (* -1 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/32 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
Calls

3 calls:

TimeVariablePointExpression
10.0ms
x
@-inf
((- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (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 (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 (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) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (* 69/1024 (* x x)))
6.0ms
x
@inf
((- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (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 (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 (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) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (* 69/1024 (* x x)))
2.0ms
x
@0
((- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) (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 (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 (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) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (* 69/1024 (* x x)))

simplify200.0ms (2.4%)

Memory
23.4MiB live, 266.0MiB allocated; 47ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04402750
113922412
253632346
087382284
Stop Event
1×iter limit
1×node limit
Counts
106 → 106
Calls
Call 1
Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
1/2
(+ 1/2 (* 1/32 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/32 (* -5/256 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/32 (* (pow x 2) (- (* 117/8192 (pow x 2)) 5/256)))))
2
(+ 2 (* -1/8 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
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)))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (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)
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/2 (* -3/32 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 17/256 (pow x 2)) 3/32)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 17/256 (* -435/8192 (pow x 2)))) 3/32)))
(* 69/1024 (pow x 2))
(/ 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)))))
(- (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(- (+ (* -1/2 (/ (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))))) (pow x 3))) (+ (* -1/2 (/ (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (pow x 3))) (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(/ 1 (+ 1 (sqrt 1/2)))
(- (/ 1 (+ 1 (sqrt 1/2))) (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))
(- (+ (* 1/16 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
(- (+ (* -1 (/ (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))) (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) (pow x 3))) (+ (* 1/16 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2)))))) (/ 1/4 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* 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 (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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(+ 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)))))
(- (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))
(- (+ (/ 1/2 (* x (+ 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 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))
(- (+ (* -1 (/ (+ (* -1/32 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) (pow x 3))) (+ (/ 1/2 (* x (+ 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 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (/ 1/8 (* x (* (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 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3))))))) (* -1/2 (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* 1/4 (/ 1 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (/ 1 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/128 (* x (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))))))) x)) (* 1/4 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (/ 1 (+ 1 (sqrt 1/2))))
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(/ 1/2 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))))))
(+ (* -1 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/32 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
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))))
(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 (*.f64 x x) #s(literal 1/8 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/32 (pow x 2)))
(fma.f64 #s(literal 1/32 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/32 (* -5/256 (pow x 2)))))
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(/ 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 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) 69/1024)))
(*.f64 (neg.f64 (-.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 69/1024 binary64))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4))))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 69/1024 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))))
(+ (* -1 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 x)) (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) x) #s(literal -1 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) x) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/32 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* 1/4 (/ (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64))) #s(literal -1/32 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal -3/64 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) x))) x) #s(literal -1 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) x) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))

rewrite234.0ms (2.8%)

Memory
8.9MiB live, 240.3MiB allocated; 52ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043271
070271
1243250
21702250
08528249
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
21 → 412
Calls
Call 1
Inputs
(-.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))))
(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 (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 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))
#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 (*.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 #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))
(/.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))) (+.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 69/1024 binary64) (*.f64 x x))
Outputs
(*.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)))) (-.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 #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 (-.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 (+.f64 (pow.f64 (/.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))) #s(literal 3 binary64)) (pow.f64 (/.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))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.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))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.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))) #s(literal 2 binary64)) (*.f64 (/.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 #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 (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 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.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)) (*.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))) (*.f64 #s(literal 1 binary64) (*.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))))))
(/.f64 (+.f64 #s(literal -1/2 binary64) (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 (neg.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 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))))) (neg.f64 (neg.f64 (/.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 (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 (-.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 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 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (/.f64 (+.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 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))) (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 (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))))))))
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(-.f64 (/.f64 #s(literal 1/4 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 1/4 binary64) (fma.f64 x 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 1/8 binary64) (*.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 1/2 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) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (*.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 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (+.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 1/4 binary64) (fma.f64 x 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 (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 1/8 binary64) (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 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (/.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 (/.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 1/2 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 (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)) (+.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 1/4 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 (neg.f64 (/.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 (+.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 (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)))

eval107.0ms (1.3%)

Memory
17.6MiB live, 159.2MiB allocated; 37ms collecting garbage
Compiler

Compiled 30 441 to 2 543 computations (91.6% saved)

prune21.0ms (0.3%)

Memory
-34.9MiB live, 53.4MiB allocated; 13ms collecting garbage
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New6025607
Fresh314
Picked235
Done011
Total60710617
Accuracy
100.0%
Counts
617 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.9%
(-.f64 (pow.f64 (+.f64 (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)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #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 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64))))
✓46.2%
(-.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)))))
✓46.8%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
▶31.7%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓32.4%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
▶54.5%
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
▶47.5%
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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))))
▶55.8%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x x)))
✓54.5%
#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))
▶55.9%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
Compiler

Compiled 617 to 332 computations (46.2% saved)

simplify252.0ms (3%)

Memory
36.4MiB live, 226.5MiB allocated; 27ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.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))
cost-diff0
(pow.f64 x #s(literal 4 binary64))
cost-diff0
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
cost-diff1
(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 (*.f64 x x) #s(literal 1/8 binary64)))
cost-diff0
(-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64))
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
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x x)))
cost-diff1
(*.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)) (*.f64 x x))
cost-diff0
(-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
cost-diff0
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
cost-diff0
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
cost-diff0
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
cost-diff0
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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))))
cost-diff0
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
cost-diff0
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
cost-diff0
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
cost-diff0
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052417
078417
1132417
2317417
3834417
41910417
52804417
63215417
73451417
83674417
93928417
104028417
114213417
124624417
135180417
145840417
156728417
167768417
177837417
187892417
197906417
09528399
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
x
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
#s(literal 1/2 binary64)
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(*.f64 #s(literal 11/128 binary64) (*.f64 x x))
#s(literal 11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 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)) (*.f64 x 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)
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
(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 (*.f64 x x) #s(literal 1/8 binary64)))
(pow.f64 x #s(literal 4 binary64))
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 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x)
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
#s(literal -1843/32768 binary64)
(*.f64 x x)
#s(literal 69/1024 binary64)
#s(literal 11/128 binary64)
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
x
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
#s(literal 1/2 binary64)
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #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 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64))
(*.f64 #s(literal 11/128 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 11/128 binary64))
#s(literal 11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x x)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x #s(literal -11/128 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(*.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)) (*.f64 x x))
(fma.f64 (fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x #s(literal -11/128 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(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)
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x #s(literal -11/128 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(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 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x #s(literal -11/128 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(pow.f64 x #s(literal 4 binary64))
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))
(fma.f64 #s(literal -1843/32768 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) x)
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
#s(literal -1843/32768 binary64)
(*.f64 x x)
#s(literal 69/1024 binary64)
#s(literal 11/128 binary64)
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)

localize230.0ms (2.7%)

Memory
-18.8MiB live, 327.0MiB allocated; 45ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.20520650300678028
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
accuracy0.27300175219884504
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
accuracy13.523326034831134
(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 (*.f64 x x) #s(literal 1/8 binary64)))
accuracy29.04557679855402
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
accuracy0.0390625
(*.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)) (*.f64 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))
accuracy0.34648146173681227
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
accuracy28.296407682845274
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x x)))
accuracy0.03125
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy0.337170970702817
(*.f64 #s(literal 11/128 binary64) (*.f64 x x))
accuracy15.104726448355205
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy28.229057589396227
#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy0.0
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
accuracy0.0
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy0.0
(sqrt.f64 #s(literal 1/2 binary64))
accuracy33.624400814806386
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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))))
accuracy0.0234375
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
accuracy0.03515625
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
accuracy29.125265861063642
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
accuracy29.223117589229947
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
Samples
128.0ms103×2valid
37.0ms118×0valid
25.0ms35×1valid
Compiler

Compiled 356 to 48 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 158.0ms
ival-mult: 43.0ms (27.2% of total)
adjust: 38.0ms (24.1% of total)
ival-sub: 26.0ms (16.5% of total)
ival-div: 12.0ms (7.6% of total)
ival-hypot: 12.0ms (7.6% of total)
ival-add: 12.0ms (7.6% of total)
ival-pow: 8.0ms (5.1% of total)
ival-sqrt: 6.0ms (3.8% of total)
exact: 1.0ms (0.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
14.7MiB live, 14.7MiB allocated; 0ms collecting garbage
Counts
24 → 71
Calls
Call 1
Inputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(*.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)) (*.f64 x x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x 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))
(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 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
(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 11/128 binary64) (*.f64 x x))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
(*.f64 (*.f64 x x) #s(literal 1/8 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))))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
-1/8
(- (* 11/128 (pow x 2)) 1/8)
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
-11/128
(- (* 69/1024 (pow x 2)) 11/128)
(pow x 4)
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(* 11/128 (pow x 2))
(* 69/1024 (pow x 2))
69/1024
(+ 69/1024 (* -1843/32768 (pow x 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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(- (+ (* -1/2 (/ (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))))) (pow x 3))) (+ (* -1/2 (/ (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (pow x 3))) (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (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)))))
(* 11/128 (pow x 4))
(* (pow x 4) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 11/128 (/ 1 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))
(* 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 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)))))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3))))))) (* -1/2 (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (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)))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@inf
((- 1 (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) (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (/ 1/2 (+ (sqrt 1/2) 1)) (+ (sqrt 1/2) 1) (sqrt 1/2) (- 1 (sqrt (- 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)) 1) (- (* 11/128 (* x x)) 1/8) (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (* x x)) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (- (* 69/1024 (* x x)) 11/128) (+ (* (pow x 4) (- (* (* (+ (* -1843/32768 (* x x)) 69/1024) x) x) 11/128)) (* (* x x) 1/8)) (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (pow x 4) (- (* (* (+ (* -1843/32768 (* x x)) 69/1024) x) x) 11/128) (* 11/128 (* x x)) (* 69/1024 (* x x)) (+ (* -1843/32768 (* x x)) 69/1024) (* (* x x) 1/8))
3.0ms
x
@-inf
((- 1 (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) (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (/ 1/2 (+ (sqrt 1/2) 1)) (+ (sqrt 1/2) 1) (sqrt 1/2) (- 1 (sqrt (- 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)) 1) (- (* 11/128 (* x x)) 1/8) (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (* x x)) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (- (* 69/1024 (* x x)) 11/128) (+ (* (pow x 4) (- (* (* (+ (* -1843/32768 (* x x)) 69/1024) x) x) 11/128)) (* (* x x) 1/8)) (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (pow x 4) (- (* (* (+ (* -1843/32768 (* x x)) 69/1024) x) x) 11/128) (* 11/128 (* x x)) (* 69/1024 (* x x)) (+ (* -1843/32768 (* x x)) 69/1024) (* (* x x) 1/8))
2.0ms
x
@0
((- 1 (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) (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (/ 1/2 (+ (sqrt 1/2) 1)) (+ (sqrt 1/2) 1) (sqrt 1/2) (- 1 (sqrt (- 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)) 1) (- (* 11/128 (* x x)) 1/8) (* (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (* x x)) (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ (* (- (* 69/1024 (* x x)) 11/128) (* x x)) 1/8) (- (* 69/1024 (* x x)) 11/128) (+ (* (pow x 4) (- (* (* (+ (* -1843/32768 (* x x)) 69/1024) x) x) 11/128)) (* (* x x) 1/8)) (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (pow x 4) (- (* (* (+ (* -1843/32768 (* x x)) 69/1024) x) x) 11/128) (* 11/128 (* x x)) (* 69/1024 (* x x)) (+ (* -1843/32768 (* x x)) 69/1024) (* (* x x) 1/8))

simplify232.0ms (2.8%)

Memory
-27.6MiB live, 245.3MiB allocated; 40ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02471346
17481247
226181226
084941199
Stop Event
1×iter limit
1×node limit
Counts
71 → 71
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))))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
-1/8
(- (* 11/128 (pow x 2)) 1/8)
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
-11/128
(- (* 69/1024 (pow x 2)) 11/128)
(pow x 4)
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(* 11/128 (pow x 2))
(* 69/1024 (pow x 2))
69/1024
(+ 69/1024 (* -1843/32768 (pow x 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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(- (+ (* -1/2 (/ (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3)))))) (pow x 3))) (+ (* -1/2 (/ (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (pow x 3))) (+ (* 1/2 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (pow x 2))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (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)))))
(* 11/128 (pow x 4))
(* (pow x 4) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 11/128 (/ 1 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (- 11/128 (* 1/8 (/ 1 (pow x 2)))))
(* 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 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)))))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/128 (/ 1 (* (pow (sqrt 1/2) 4) (pow (+ 1 (sqrt 1/2)) 3))))))) (* -1/2 (- (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (+ (* 1/16 (/ 1 (* (pow (sqrt 1/2) 2) (pow (+ 1 (sqrt 1/2)) 3)))) (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (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)))
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 (*.f64 x x) #s(literal -11/128 binary64) #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 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #s(literal 11/128 binary64))) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))
(* 1/8 x)
(*.f64 #s(literal 1/8 binary64) x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
1
#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 (*.f64 #s(literal 11/128 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -69/1024 binary64)) #s(literal 1/8 binary64))) (*.f64 x x) #s(literal 1 binary64))
-1/8
#s(literal -1/8 binary64)
(- (* 11/128 (pow x 2)) 1/8)
(-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(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))
-11/128
#s(literal -11/128 binary64)
(- (* 69/1024 (pow x 2)) 11/128)
(-.f64 (*.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 11/128 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #s(literal 11/128 binary64)))
(* 11/128 (pow x 2))
(*.f64 #s(literal 11/128 binary64) (*.f64 x x))
(* 69/1024 (pow x 2))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
69/1024
#s(literal 69/1024 binary64)
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 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 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(- (+ 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))))
(* -11/128 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -11/128 binary64))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* -11/128 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -11/128 binary64))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -11/128 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -11/128 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) x) x)
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) x))
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(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
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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))
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(+ (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))

rewrite171.0ms (2.1%)

Memory
46.6MiB live, 236.0MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052372
078372
1328296
22441296
08619292
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
24 → 325
Calls
Call 1
Inputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #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 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(*.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)) (*.f64 x x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x 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))
(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 (*.f64 x x) #s(literal 1/8 binary64)))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
(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 11/128 binary64) (*.f64 x x))
(*.f64 #s(literal 69/1024 binary64) (*.f64 x x))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 x x) #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)))
(*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
(*.f64 x (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x))
(*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x)
(*.f64 x #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)))
#s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal -1 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 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 1 binary64) (+.f64 #s(literal 1/2 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 1 binary64) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 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)))
(neg.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (*.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 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 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (fma.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 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #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 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64))
(fma.f64 (fabs.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.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)))) (pow.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(fabs.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(fabs.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)))) (*.f64 (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (*.f64 (fma.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64))) (+.f64 #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 11/128 binary64)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))
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(/.f64 (fma.f64 (*.f64 #s(literal -6260024107/35184372088832 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64)))) (*.f64 (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64)))) #s(literal 328509/1073741824 binary64))) (*.f64 (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64)))) (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64))))))
(/.f64 (-.f64 #s(literal 4761/1048576 binary64) (*.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 69/1024 binary64) (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 4761/1048576 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x)) #s(literal 69/1024 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -6260024107/35184372088832 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 328509/1073741824 binary64))) (neg.f64 (+.f64 #s(literal 4761/1048576 binary64) (-.f64 (*.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -6260024107/35184372088832 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 328509/1073741824 binary64))) (neg.f64 (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 4761/1048576 binary64)) (-.f64 (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x)) #s(literal 69/1024 binary64)))
(/.f64 (fma.f64 #s(literal -6260024107/35184372088832 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 328509/1073741824 binary64)) (+.f64 #s(literal 4761/1048576 binary64) (-.f64 (*.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64)))))
(/.f64 (fma.f64 #s(literal -6260024107/35184372088832 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 328509/1073741824 binary64)) (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64)))))
(fma.f64 (*.f64 #s(literal -1843/32768 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 69/1024 binary64))
(fma.f64 (*.f64 #s(literal -1843/32768 binary64) x) x #s(literal 69/1024 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1843/32768 binary64)) #s(literal 69/1024 binary64))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
(fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64))
(fma.f64 x (*.f64 #s(literal -1843/32768 binary64) x) #s(literal 69/1024 binary64))
(-.f64 (/.f64 (*.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x)) #s(literal 69/1024 binary64))) (/.f64 #s(literal 4761/1048576 binary64) (-.f64 (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x)) #s(literal 69/1024 binary64))))
(-.f64 #s(literal 69/1024 binary64) (*.f64 (neg.f64 (*.f64 #s(literal -1843/32768 binary64) x)) x))
(-.f64 #s(literal 69/1024 binary64) (*.f64 (*.f64 (neg.f64 x) x) #s(literal -1843/32768 binary64)))
(-.f64 #s(literal 69/1024 binary64) (*.f64 #s(literal 1843/32768 binary64) (*.f64 x x)))
(+.f64 (/.f64 (*.f64 #s(literal -6260024107/35184372088832 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64))))) (/.f64 #s(literal 328509/1073741824 binary64) (fma.f64 #s(literal 3396649/1073741824 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4761/1048576 binary64) (*.f64 (*.f64 x x) #s(literal -127167/33554432 binary64))))))
(+.f64 (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x)) #s(literal 69/1024 binary64))
(+.f64 #s(literal 69/1024 binary64) (*.f64 #s(literal -1843/32768 binary64) (*.f64 x x)))
(*.f64 (fabs.f64 (*.f64 #s(literal 1/8 binary64) (neg.f64 x))) x)
(*.f64 (fabs.f64 (*.f64 #s(literal 1/8 binary64) x)) x)
(*.f64 (*.f64 #s(literal 1/8 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1/8 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1/8 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 x (fabs.f64 (*.f64 (neg.f64 x) #s(literal 1/8 binary64))))
(*.f64 x (fabs.f64 (*.f64 #s(literal 1/8 binary64) x)))
(*.f64 x (*.f64 #s(literal 1/8 binary64) x))
(sqrt.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (*.f64 (*.f64 (neg.f64 x) x) #s(literal 1/8 binary64)))
(fabs.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))

eval139.0ms (1.7%)

Memory
-59.7MiB live, 128.7MiB allocated; 46ms collecting garbage
Compiler

Compiled 22 967 to 1 799 computations (92.2% saved)

prune26.0ms (0.3%)

Memory
4.3MiB live, 50.8MiB allocated; 2ms collecting garbage
Pruning

11 alts after pruning (3 fresh and 8 done)

PrunedKeptTotal
New3912393
Fresh011
Picked145
Done044
Total39211403
Accuracy
100.0%
Counts
403 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.9%
(-.f64 (pow.f64 (+.f64 (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)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #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 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64))))
✓46.2%
(-.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)))))
✓46.8%
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
✓31.7%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓32.4%
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
54.5%
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
54.6%
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64)))))
✓47.5%
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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))))
✓55.8%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 x x)))
✓54.5%
#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))
✓55.9%
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
Compiler

Compiled 1 370 to 415 computations (69.7% saved)

regimes51.0ms (0.6%)

Memory
3.6MiB live, 98.0MiB allocated; 9ms collecting garbage
Counts
28 → 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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.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)))
#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))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 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) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #s(literal 11/128 binary64))) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64)))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
(-.f64 (pow.f64 (+.f64 (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)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #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 #s(literal -1/2 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 (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 #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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (pow.f64 (+.f64 (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)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #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 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64))))
Calls

7 calls:

11.0ms
x
9.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
6.0ms
(hypot.f64 #s(literal 1 binary64) x)
6.0ms
(-.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
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
Results
AccuracySegmentsBranch
100.0%2(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(+.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(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 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%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes41.0ms (0.5%)

Memory
-0.7MiB live, 92.4MiB allocated; 3ms collecting garbage
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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.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)))
#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))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 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) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #s(literal 11/128 binary64))) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64)))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (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 (*.f64 x x) #s(literal 1/8 binary64))))
Outputs
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64)))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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:

8.0ms
x
6.0ms
(/.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)))
5.0ms
(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
99.6%2(hypot.f64 #s(literal 1 binary64) x)
99.6%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.6%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.6%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.6%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)))))
99.6%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))))))
99.6%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes41.0ms (0.5%)

Memory
-28.4MiB live, 69.8MiB allocated; 9ms collecting garbage
Counts
22 → 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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.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)))
#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))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 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) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (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))))))
(-.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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 69/1024 binary64) x) x (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64)) #s(literal 11/128 binary64))) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
Outputs
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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:

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))))))
6.0ms
(hypot.f64 #s(literal 1 binary64) x)
6.0ms
x
6.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms
(*.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
99.5%2(hypot.f64 #s(literal 1 binary64) x)
99.5%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.5%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.5%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.5%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
99.5%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
99.5%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes31.0ms (0.4%)

Memory
14.9MiB live, 59.6MiB allocated; 6ms collecting garbage
Counts
16 → 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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.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)))
#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))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* 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)) (*.f64 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) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (*.f64 x x)) #s(literal 1/2 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))
#s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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:

8.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms
x
4.0ms
(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))))
3.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.5%2(hypot.f64 #s(literal 1 binary64) x)
99.5%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.5%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.5%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.5%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
99.5%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
99.5%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes24.0ms (0.3%)

Memory
-0.7MiB live, 44.4MiB allocated; 5ms collecting garbage
Counts
12 → 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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (*.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.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)))
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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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:

5.0ms
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
4.0ms
x
3.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
3.0ms
(hypot.f64 #s(literal 1 binary64) x)
3.0ms
(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
99.4%2(hypot.f64 #s(literal 1 binary64) x)
99.4%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
99.4%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
99.4%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
99.4%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
99.4%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
99.4%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes14.0ms (0.2%)

Memory
24.1MiB live, 24.1MiB allocated; 0ms collecting garbage
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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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))
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:

2.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms
x
2.0ms
(hypot.f64 #s(literal 1 binary64) x)
2.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
2.0ms
(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
98.7%2(hypot.f64 #s(literal 1 binary64) x)
98.7%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.7%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.7%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.7%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
98.7%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
98.7%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes53.0ms (0.6%)

Memory
-24.9MiB live, 25.9MiB allocated; 10ms collecting garbage
Counts
5 → 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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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:

42.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
2.0ms
x
2.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms
(hypot.f64 #s(literal 1 binary64) x)
2.0ms
(-.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
98.5%2(hypot.f64 #s(literal 1 binary64) x)
98.5%2(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
98.5%2(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
98.5%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
98.5%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
98.5%2(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
98.5%2x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes15.0ms (0.2%)

Memory
-5.8MiB live, 35.2MiB allocated; 7ms collecting garbage
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 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
Outputs
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
Calls

7 calls:

6.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms
x
1.0ms
(hypot.f64 #s(literal 1 binary64) x)
1.0ms
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
1.0ms
(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
55.9%1(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
55.9%1(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
55.9%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
55.9%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)))))
55.9%1(hypot.f64 #s(literal 1 binary64) x)
55.9%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))))))
55.9%1x
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes8.0ms (0.1%)

Memory
22.2MiB live, 22.2MiB allocated; 0ms collecting garbage
Counts
2 → 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)))
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:

1.0ms
x
1.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms
(hypot.f64 #s(literal 1 binary64) x)
1.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
1.0ms
(-.f64 #s(literal 1 binary64) (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
55.9%1(hypot.f64 #s(literal 1 binary64) x)
55.9%1x
55.9%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))))))
55.9%1(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
55.9%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
55.9%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)))))
55.9%1(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes7.0ms (0.1%)

Memory
18.9MiB live, 18.8MiB allocated; 0ms collecting garbage
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:

1.0ms
x
1.0ms
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms
(hypot.f64 #s(literal 1 binary64) x)
1.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
1.0ms
(-.f64 #s(literal 1 binary64) (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
32.4%1(hypot.f64 #s(literal 1 binary64) x)
32.4%1x
32.4%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))))))
32.4%1(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
32.4%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
32.4%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)))))
32.4%1(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
Compiler

Compiled 47 to 37 computations (21.3% saved)

bsearch25.0ms (0.3%)

Memory
-22.8MiB live, 68.3MiB allocated; 7ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
23.0ms
0.009407423950070513
108193310.68921037
Samples
14.0ms160×0valid
Compiler

Compiled 1 280 to 543 computations (57.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-hypot: 5.0ms (48% of total)
ival-div: 1.0ms (9.6% of total)
ival-add: 1.0ms (9.6% of total)
ival-mult: 1.0ms (9.6% of total)
ival-sub: 1.0ms (9.6% of total)
ival-sqrt: 1.0ms (9.6% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory
8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
2.0ms
0.009407423950070513
108193310.68921037
Compiler

Compiled 1 230 to 563 computations (54.2% saved)

bsearch2.0ms (0%)

Memory
5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
2.0ms
0.009407423950070513
108193310.68921037
Compiler

Compiled 1 270 to 543 computations (57.2% saved)

bsearch8.0ms (0.1%)

Memory
18.8MiB live, 18.8MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
7.0ms
0.009407423950070513
108193310.68921037
Samples
3.0ms48×0valid
Compiler

Compiled 870 to 473 computations (45.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-hypot: 1.0ms (43.6% of total)
ival-div: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch51.0ms (0.6%)

Memory
-61.2MiB live, 3.3MiB allocated; 16ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
51.0ms
0.009407423950070513
108193310.68921037
Compiler

Compiled 810 to 443 computations (45.3% saved)

bsearch2.0ms (0%)

Memory
2.0MiB live, 2.0MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
0.009407423950070513
108193310.68921037
Compiler

Compiled 470 to 373 computations (20.6% saved)

bsearch11.0ms (0.1%)

Memory
11.1MiB live, 11.1MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
9.0ms
0.009407423950070513
108193310.68921037
Samples
5.0ms80×0valid
Compiler

Compiled 500 to 393 computations (21.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-div: 1.0ms (25.7% of total)
ival-mult: 1.0ms (25.7% of total)
ival-hypot: 1.0ms (25.7% of total)
ival-sqrt: 1.0ms (25.7% of total)
ival-add: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

simplify77.0ms (0.9%)

Memory
6.7MiB live, 53.9MiB allocated; 2ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
087658
1124654
2200654
3316654
4461654
5617654
6840654
71160654
81641654
91748654
102010654
114673654
Stop Event
1×node limit
Calls
Call 1
Inputs
(if (<=.f64 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 (pow.f64 (+.f64 (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)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #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 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64))))) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 5854679515581645/4503599627370496 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)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 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 x #s(literal 3422735716801577/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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)))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
#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 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 (pow.f64 (+.f64 (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)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 #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 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.f64 #s(literal 1/8 binary64) x) x (*.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)) (pow.f64 x #s(literal 4 binary64))))) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1))) (fma.f64 (*.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)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 5854679515581645/4503599627370496 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)) #s(approx (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 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 (- (pow (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1) -1) (/ (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 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 x #s(literal 3422735716801577/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #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)))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (*.f64 #s(approx (+ (* -11/128 (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
#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)))

derivations1.2s (14%)

Memory
10.8MiB live, 668.9MiB allocated; 51ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0206845
1633767
21960714
37820714
08462676
043271
070271
1243250
21702250
08528249
03241312
19991194
232151117
083851069
052372
078372
1328296
22441296
08619292
04402750
113922412
253632346
087382284
047332
078294
1299294
22153288
08731274
0943
01833
18233
260933
3635833
0824330
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 724 to 93 computations (87.2% saved)

preprocess135.0ms (1.6%)

Memory
-7.8MiB live, 50.8MiB allocated; 11ms collecting garbage
Compiler

Compiled 1 732 to 296 computations (82.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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