sqrtexp (problem 3.4.4)

Time bar (total: 8.0s)

analyze3.0ms (0%)

Memory
2.8MiB live, 2.8MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample878.0ms (11%)

Memory
22.5MiB live, 898.3MiB allocated
Samples
458.0ms8 256×0valid
146.0ms2 571×0exit
Precisions
Click to see histograms. Total time spent on operations: 394.0ms
ival-expm1: 129.0ms (32.8% of total)
ival-mult: 97.0ms (24.6% of total)
ival-div: 77.0ms (19.6% of total)
ival-sqrt: 73.0ms (18.5% of total)
ival-true: 8.0ms (2% of total)
exact: 6.0ms (1.5% of total)
ival-assert: 4.0ms (1% of total)
Bogosity

preprocess463.0ms (5.8%)

Memory
-7.8MiB live, 357.6MiB allocated
Algorithm
2×egg-herbie
Rules
15 394×accelerator-lowering-fma.f32
15 394×accelerator-lowering-fma.f64
2 850×--lowering--.f32
2 850×--lowering--.f64
2 458×*-lowering-*.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01941
14439
27039
311339
419220
534018
667218
7257018
01012
12212
22812
34012
4667
51195
61955
75935
829045
967435
081565
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Call 2
Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(sqrt (+ 1 (exp (neg x))))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
(neg (sqrt (+ 1 (exp (neg x)))))

explain135.0ms (1.7%)

Memory
12.2MiB live, 167.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1770-0-(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1770-0-(-.f64 (exp.f64 x) #s(literal 1 binary64))
20-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
01(295.197229555907)0-(exp.f64 (*.f64 #s(literal 2 binary64) x))
00-0-#s(literal 1 binary64)
00-0-(*.f64 #s(literal 2 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
00-0-#s(literal 2 binary64)
00-0-(exp.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (exp.f64 x) #s(literal 1 binary64))cancellation1770
-.f64(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))cancellation1770
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o20
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow2
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow2
↳(exp.f64 x)overflow2
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow2
exp.f64(exp.f64 (*.f64 #s(literal 2 binary64) x))sensitivity10
Confusion
Predicted +Predicted -
+1780
-276
Precision
0.9888888888888889
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+17800
-2076
Precision?
0.9888888888888889
Recall?
1.0
Freqs
test
numberfreq
076
13
2177
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
39.0ms512×0valid
Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-exp: 7.0ms (28.5% of total)
ival-expm1: 6.0ms (24.4% of total)
ival-div: 3.0ms (12.2% of total)
ival-mult: 3.0ms (12.2% of total)
ival-sqrt: 3.0ms (12.2% of total)
exact: 1.0ms (4.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶34.3%
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify392.0ms (4.9%)

Memory
9.9MiB live, 402.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(*.f64 #s(literal 2 binary64) x)
✓cost-diff192
(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓cost-diff192
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓cost-diff7104
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Rules
15 394×accelerator-lowering-fma.f32
15 394×accelerator-lowering-fma.f64
2 850×--lowering--.f32
2 850×--lowering--.f64
2 458×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
12245
22845
34045
46635
511931
619531
759331
8290431
9674331
0815627
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(- (exp (* 2 x)) 1)
(exp (* 2 x))
(* 2 x)
2
x
1
(- (exp x) 1)
(exp x)
Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(* 2 x)
(+.f64 x x)
2
#s(literal 2 binary64)
x
1
#s(literal 1 binary64)
(- (exp x) 1)
(expm1.f64 x)
(exp x)
(exp.f64 x)

localize32.0ms (0.4%)

Memory
-2.9MiB live, 35.9MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
✓accuracy99.3%
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓accuracy37.7%
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓accuracy37.5%
(-.f64 (exp.f64 x) #s(literal 1 binary64))
Samples
21.0ms256×0valid
Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-exp: 3.0ms (25.1% of total)
ival-expm1: 3.0ms (25.1% of total)
ival-div: 2.0ms (16.7% of total)
ival-mult: 2.0ms (16.7% of total)
ival-sqrt: 2.0ms (16.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
6.4MiB live, 6.4MiB allocated
Counts
5 → 60
Calls
Call 1
Inputs
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
Outputs
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
Calls

15 calls:

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

rewrite363.0ms (4.5%)

Memory
-23.2MiB live, 350.2MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 562×accelerator-lowering-fma.f32
4 562×accelerator-lowering-fma.f64
3 484×*-lowering-*.f32
3 484×*-lowering-*.f64
2 734×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01036
15622
242122
3498522
0809318
Stop Event
1×iter limit
1×node limit
Counts
5 → 711
Calls
Call 1
Inputs
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* 2 x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Outputs
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(+.f64 (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 (+.f64 x x))) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(+.f64 (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 (+.f64 x x))))
(+.f64 (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 x)))
(+.f64 (*.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))
(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x))) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (/.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
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(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 (+.f64 x x))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 (expm1.f64 x) (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(*.f64 (*.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(*.f64 (*.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 6 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))
(*.f64 (*.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 4 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x) (neg.f64 (expm1.f64 x)))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))) (exp.f64 (*.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x)))
(log.f64 (exp.f64 (+.f64 x x)))
(+.f64 x x)
(+.f64 (+.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 x x))
(+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (log.f64 (exp.f64 (*.f64 x #s(literal 1 binary64)))) (log.f64 (exp.f64 (*.f64 x #s(literal 1 binary64)))))
(+.f64 (log.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (log.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 x x) x)) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (expm1.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) #s(literal 1 binary64)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))

simplify414.0ms (5.2%)

Memory
9.7MiB live, 483.3MiB allocated
Algorithm
1×egg-herbie
Rules
15 504×accelerator-lowering-fma.f32
15 504×accelerator-lowering-fma.f64
4 704×*-lowering-*.f32
4 704×*-lowering-*.f64
2 492×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077480
1252446
2663446
31429440
42558360
55941325
08294270
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(* 2 x)
(+.f64 x x)
(* x (+ 2 (* 2 x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

eval95.0ms (1.2%)

Memory
27.1MiB live, 178.5MiB allocated
Compiler

Compiled 17 392 to 2 477 computations (85.8% saved)

prune95.0ms (1.2%)

Memory
-1.3MiB live, 232.0MiB allocated
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New7647771
Fresh000
Picked101
Done000
Total7657772
Accuracy
100.0%
Counts
772 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
70.5%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶69.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶70.8%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶68.8%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶73.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 124 to 92 computations (25.8% saved)

simplify16.0ms (0.2%)

Memory
-9.7MiB live, 27.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(+.f64 #s(literal 2 binary64) x)
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(exp.f64 x)
✓cost-diff0
(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓cost-diff0
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
Rules
400×accelerator-lowering-fma.f32
400×accelerator-lowering-fma.f64
134×*-lowering-*.f32
134×*-lowering-*.f64
132×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02499
15499
210099
318699
423299
523999
023985
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (- (exp x) -1))
(- (exp x) -1)
(exp x)
x
-1
(sqrt 2)
2
(sqrt (+ 2 x))
(+ 2 x)
2
x
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(+ (* x (+ (* x 1/2) 1)) 2)
x
(+ (* x 1/2) 1)
1/2
1
2
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)
x
(+ (* x (+ (* x 1/6) 1/2)) 1)
(+ (* x 1/6) 1/2)
1/6
1/2
1
2
Outputs
(sqrt (- (exp x) -1))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(- (exp x) -1)
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
x
-1
#s(literal -1 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (+ 2 x))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
x
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(+ (* x (+ (* x 1/2) 1)) 2)
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(+ (* x 1/2) 1)
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(+ (* x (+ (* x 1/6) 1/2)) 1)
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)

localize74.0ms (0.9%)

Memory
12.1MiB live, 146.6MiB allocated
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓accuracy100.0%
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓accuracy100.0%
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓accuracy100.0%
(+.f64 #s(literal 2 binary64) x)
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(exp.f64 x)
✓accuracy100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓accuracy100.0%
(-.f64 (exp.f64 x) #s(literal -1 binary64))
Samples
36.0ms181×0valid
12.0ms75×0invalid
Compiler

Compiled 87 to 26 computations (70.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-add: 13.0ms (36.7% of total)
ival-sqrt: 8.0ms (22.6% of total)
ival-mult: 7.0ms (19.7% of total)
const: 3.0ms (8.5% of total)
ival-exp: 2.0ms (5.6% of total)
ival-sub: 1.0ms (2.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory
-13.0MiB live, 25.0MiB allocated
Counts
13 → 144
Calls
Call 1
Inputs
#<alt (sqrt (- (exp x) -1))>
#<alt (- (exp x) -1)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (+ (* x (+ (* x 1/2) 1)) 2))>
#<alt (+ (* x (+ (* x 1/2) 1)) 2)>
#<alt (+ (* x 1/2) 1)>
#<alt (sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))>
#<alt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)>
#<alt (+ (* x (+ (* x 1/6) 1/2)) 1)>
#<alt (+ (* x 1/6) 1/2)>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
Calls

36 calls:

TimeVariablePointExpression
3.0ms
x
@0
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
1.0ms
x
@-inf
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms
x
@0
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms
x
@inf
(sqrt (- (exp x) -1))
1.0ms
x
@-inf
(sqrt (+ 2 x))

rewrite317.0ms (4%)

Memory
12.1MiB live, 441.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 428×accelerator-lowering-fma.f32
4 428×accelerator-lowering-fma.f64
4 328×*-lowering-*.f32
4 328×*-lowering-*.f64
4 210×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02485
114285
2112285
0824071
Stop Event
1×iter limit
1×node limit
Counts
13 → 442
Calls
Call 1
Inputs
(sqrt (- (exp x) -1))
(- (exp x) -1)
(exp x)
(sqrt 2)
(sqrt (+ 2 x))
(+ 2 x)
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(+ (* x (+ (* x 1/2) 1)) 2)
(+ (* x 1/2) 1)
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)
(+ (* x (+ (* x 1/6) 1/2)) 1)
(+ (* x 1/6) 1/2)
Outputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 (neg.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) #s(literal -1 binary64))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (neg.f64 (+.f64 (neg.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (exp.f64 x)))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (*.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (*.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))))
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))) (+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (+.f64 (neg.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x))))
(exp.f64 x)
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) x)
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) x)) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 binary64) x)))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 2 binary64) x))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -4 binary64))) (sqrt.f64 (+.f64 x #s(literal -2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) x))))
(pow.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) x))))
(*.f64 (pow.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+.f64 x #s(literal 2 binary64))
(+.f64 #s(literal 2 binary64) x)
(+.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 x #s(literal -2 binary64))))
(fma.f64 x #s(literal 1 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 2 binary64))
(fma.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (+.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
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(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1/10077696 binary64) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/46656 binary64) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/1728 binary64)))) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/46656 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal -1/8 binary64)) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/46656 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1296 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) #s(literal 1/144 binary64)))) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
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(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))

simplify367.0ms (4.6%)

Memory
-32.9MiB live, 426.2MiB allocated
Algorithm
1×egg-herbie
Rules
11 602×accelerator-lowering-fma.f32
11 602×accelerator-lowering-fma.f64
5 042×*-lowering-*.f32
5 042×*-lowering-*.f64
3 340×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02771514
18811294
229691264
083771149
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(*.f64 x (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(neg.f64 (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* -1 (* x (sqrt 1/2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))) x) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (neg.f64 (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(neg.f64 (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

eval102.0ms (1.3%)

Memory
32.6MiB live, 147.7MiB allocated
Compiler

Compiled 13 943 to 1 908 computations (86.3% saved)

prune93.0ms (1.2%)

Memory
-31.0MiB live, 140.3MiB allocated
Pruning

16 alts after pruning (11 fresh and 5 done)

PrunedKeptTotal
New5779586
Fresh022
Picked055
Done000
Total57716593
Accuracy
100.0%
Counts
593 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶70.5%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
69.6%
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
3.1%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
69.3%
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))
✓69.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓70.8%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶2.5%
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
4.1%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
▶68.8%
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓68.8%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
3.8%
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
▶2.3%
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
▶2.5%
(sqrt.f64 x)
✓73.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 265 to 182 computations (31.3% saved)

simplify18.0ms (0.2%)

Memory
26.5MiB live, 26.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
✓cost-diff0
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 x (*.f64 x x))
✓cost-diff0
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
✓cost-diff0
(+.f64 x #s(literal 1 binary64))
✓cost-diff0
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓cost-diff192
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
✓cost-diff0
(sqrt.f64 x)
✓cost-diff0
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
Rules
408×accelerator-lowering-fma.f32
408×accelerator-lowering-fma.f64
294×*-lowering-*.f32
294×*-lowering-*.f64
118×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027101
164101
2139101
3182101
4216101
5223101
6320101
7341101
8381101
9383101
038392
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
(/ x (sqrt 2))
x
(sqrt 2)
2
(+ (* x 3/16) 1/2)
3/16
1/2
(sqrt x)
x
(sqrt (- (+ x 1) -1))
(- (+ x 1) -1)
(+ x 1)
x
1
-1
(sqrt (* 1/6 (* x (* x x))))
(* 1/6 (* x (* x x)))
1/6
(* x (* x x))
x
(* x x)
(sqrt (+ (* x (* x (+ (* x 1/6) 1/2))) x))
(+ (* x (* x (+ (* x 1/6) 1/2))) x)
x
(* x (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
1/6
1/2
Outputs
(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* x 3/16) 1/2)
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
3/16
#s(literal 3/16 binary64)
1/2
#s(literal 1/2 binary64)
(sqrt x)
(sqrt.f64 x)
x
(sqrt (- (+ x 1) -1))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(- (+ x 1) -1)
(+.f64 x #s(literal 2 binary64))
(+ x 1)
(+.f64 x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(sqrt (* 1/6 (* x (* x x))))
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal 1/6 binary64))))
(* 1/6 (* x (* x x)))
(*.f64 (*.f64 x x) (*.f64 x #s(literal 1/6 binary64)))
1/6
#s(literal 1/6 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(sqrt (+ (* x (* x (+ (* x 1/6) 1/2))) x))
(sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))
(+ (* x (* x (+ (* x 1/6) 1/2))) x)
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
x
(* x (+ (* x 1/6) 1/2))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)

localize79.0ms (1%)

Memory
-6.3MiB live, 149.2MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
✓accuracy100.0%
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓accuracy100.0%
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 x x)
✓accuracy99.9%
(*.f64 x (*.f64 x x))
✓accuracy99.9%
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
✓accuracy89.8%
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
✓accuracy100.0%
(+.f64 x #s(literal 1 binary64))
✓accuracy100.0%
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓accuracy100.0%
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
✓accuracy100.0%
(sqrt.f64 x)
✓accuracy100.0%
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
Samples
31.0ms167×0invalid
16.0ms89×0valid
Compiler

Compiled 104 to 29 computations (72.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-mult: 11.0ms (33.3% of total)
ival-sqrt: 8.0ms (24.2% of total)
ival-add: 6.0ms (18.1% of total)
const: 4.0ms (12.1% of total)
ival-div: 2.0ms (6% of total)
ival-sub: 1.0ms (3% of total)
exact: 1.0ms (3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory
-23.1MiB live, 14.6MiB allocated
Counts
16 → 180
Calls
Call 1
Inputs
#<alt (+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (* x 3/16) 1/2)>
#<alt (sqrt x)>
#<alt (- (+ x 1) -1)>
#<alt (sqrt (- (+ x 1) -1))>
#<alt (+ x 1)>
#<alt (sqrt (* 1/6 (* x (* x x))))>
#<alt (* 1/6 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (sqrt (+ (* x (* x (+ (* x 1/6) 1/2))) x))>
#<alt (+ (* x (* x (+ (* x 1/6) 1/2))) x)>
#<alt (* x (+ (* x 1/6) 1/2))>
#<alt (+ (* x 1/6) 1/2)>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt x) (/ (sqrt -1) (pow (sqrt -1/6) 3))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
Calls

45 calls:

TimeVariablePointExpression
2.0ms
x
@0
(sqrt (+ (* x (* x (+ (* x 1/6) 1/2))) x))
2.0ms
x
@0
(* x (+ (* x 1/6) 1/2))
1.0ms
x
@0
(sqrt (* 1/6 (* x (* x x))))
1.0ms
x
@inf
(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
0.0ms
x
@inf
(/ x (sqrt 2))

rewrite331.0ms (4.1%)

Memory
11.3MiB live, 526.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 352×accelerator-lowering-fma.f32
6 352×accelerator-lowering-fma.f64
3 876×*-lowering-*.f32
3 876×*-lowering-*.f64
3 858×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02788
114888
2120588
0841879
Stop Event
1×iter limit
1×node limit
Counts
16 → 522
Calls
Call 1
Inputs
(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
(/ x (sqrt 2))
(sqrt 2)
(+ (* x 3/16) 1/2)
(sqrt x)
(- (+ x 1) -1)
(sqrt (- (+ x 1) -1))
(+ x 1)
(sqrt (* 1/6 (* x (* x x))))
(* 1/6 (* x (* x x)))
(* x (* x x))
(* x x)
(sqrt (+ (* x (* x (+ (* x 1/6) 1/2))) x))
(+ (* x (* x (+ (* x 1/6) 1/2))) x)
(* x (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
Outputs
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 x (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/16 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (+.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -3/32 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -3/32 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) x))))
(*.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(*.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))

simplify704.0ms (8.8%)

Memory
22.8MiB live, 696.1MiB allocated
Algorithm
1×egg-herbie
Rules
18 390×accelerator-lowering-fma.f32
18 390×accelerator-lowering-fma.f64
5 540×*-lowering-*.f32
5 540×*-lowering-*.f64
2 770×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02091376
16311322
218691285
357591272
080671196
Stop Event
1×iter limit
1×node limit
Counts
180 → 180
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt x) (/ (sqrt -1) (pow (sqrt -1/6) 3))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) x) (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (-.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 x (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) #s(literal 1/4 binary64) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal 1 binary64)) (sqrt.f64 x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(fma.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 5/96 binary64) #s(literal 1/4 binary64))) (sqrt.f64 x))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 x (*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal -3/16 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt x) (/ (sqrt -1) (pow (sqrt -1/6) 3))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -1/6 binary64))))) (neg.f64 x)) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1/6 binary64))))))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

eval78.0ms (1%)

Memory
21.8MiB live, 175.0MiB allocated
Compiler

Compiled 14 208 to 1 837 computations (87.1% saved)

prune132.0ms (1.7%)

Memory
-37.9MiB live, 162.8MiB allocated
Pruning

18 alts after pruning (8 fresh and 10 done)

PrunedKeptTotal
New7134717
Fresh246
Picked055
Done055
Total71518733
Accuracy
100.0%
Counts
733 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓70.5%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶69.6%
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
4.6%
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
▶70.5%
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
▶4.1%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
1.7%
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
▶3.1%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓69.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓70.8%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓2.5%
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓68.8%
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓68.8%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶3.8%
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓2.3%
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
✓2.5%
(sqrt.f64 x)
✓73.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 257 to 181 computations (29.6% saved)

simplify23.0ms (0.3%)

Memory
14.1MiB live, 14.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff1344
(fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff1344
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓cost-diff0
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff128
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
Rules
772×accelerator-lowering-fma.f32
772×accelerator-lowering-fma.f64
286×*-lowering-*.f32
286×*-lowering-*.f64
200×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030179
180179
2197179
3286173
4337172
5381170
6422170
7448170
8455170
9456170
0456153
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(+ (/ (* x (+ (* x 3/16) 1/2)) (sqrt 2)) (sqrt 2))
(/ (* x (+ (* x 3/16) 1/2)) (sqrt 2))
(* x (+ (* x 3/16) 1/2))
x
(+ (* x 3/16) 1/2)
3/16
1/2
(sqrt 2)
2
(* x (sqrt 1/2))
x
(sqrt 1/2)
1/2
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
(* x (* x (+ (* x 1/6) 1/2)))
x
(* x (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
1/6
1/2
(* (/ x (sqrt 2)) (+ (* x 3/16) 1/2))
(/ x (sqrt 2))
x
(sqrt 2)
2
(+ (* x 3/16) 1/2)
3/16
1/2
(+ (* x (+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))) (sqrt 2))
x
(+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))
(+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))
(/ 7/192 (sqrt 2))
7/192
(sqrt 2)
2
(/ 3/16 (sqrt 2))
3/16
(/ 1/2 (sqrt 2))
1/2
Outputs
(+ (/ (* x (+ (* x 3/16) 1/2)) (sqrt 2)) (sqrt 2))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* x (+ (* x 3/16) 1/2)) (sqrt 2))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* x 3/16) 1/2))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
x
(+ (* x 3/16) 1/2)
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
3/16
#s(literal 3/16 binary64)
1/2
#s(literal 1/2 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(* x (* x (+ (* x 1/6) 1/2)))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
x
(* x (+ (* x 1/6) 1/2))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(* (/ x (sqrt 2)) (+ (* x 3/16) 1/2))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* x 3/16) 1/2)
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
3/16
#s(literal 3/16 binary64)
1/2
#s(literal 1/2 binary64)
(+ (* x (+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))) (sqrt 2))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
x
(+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))
(fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/ 7/192 (sqrt 2))
(/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))
7/192
#s(literal 7/192 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 3/16 (sqrt 2))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
3/16
#s(literal 3/16 binary64)
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)

localize112.0ms (1.4%)

Memory
-14.8MiB live, 168.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy100.0%
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.9%
(fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy98.9%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.9%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
✓accuracy99.5%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓accuracy100.0%
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓accuracy72.2%
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy99.6%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
✓accuracy100.0%
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.5%
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
Samples
51.0ms181×0valid
17.0ms75×0invalid
Compiler

Compiled 165 to 32 computations (80.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-div: 18.0ms (35.4% of total)
ival-mult: 15.0ms (29.5% of total)
ival-add: 6.0ms (11.8% of total)
const: 6.0ms (11.8% of total)
ival-sqrt: 5.0ms (9.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory
-16.1MiB live, 21.4MiB allocated
Counts
18 → 168
Calls
Call 1
Inputs
#<alt (+ (/ (* x (+ (* x 3/16) 1/2)) (sqrt 2)) (sqrt 2))>
#<alt (/ (* x (+ (* x 3/16) 1/2)) (sqrt 2))>
#<alt (* x (+ (* x 3/16) 1/2))>
#<alt (+ (* x 3/16) 1/2)>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (sqrt (* x (* x (+ (* x 1/6) 1/2))))>
#<alt (* x (* x (+ (* x 1/6) 1/2)))>
#<alt (* x (+ (* x 1/6) 1/2))>
#<alt (+ (* x 1/6) 1/2)>
#<alt (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (* x (+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))) (sqrt 2))>
#<alt (+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))>
#<alt (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))>
#<alt (/ 7/192 (sqrt 2))>
#<alt (/ 1/2 (sqrt 2))>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 3/16 x)))>
#<alt (* x (+ 1/2 (* 3/16 x)))>
#<alt (* x (+ 1/2 (* 3/16 x)))>
#<alt (* 3/16 (pow x 2))>
#<alt (* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* 3/16 (pow x 2))>
#<alt (* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (/ 3/16 (sqrt 2))>
#<alt (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))>
#<alt (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))>
#<alt (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
Calls

42 calls:

TimeVariablePointExpression
4.0ms
x
@0
(+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))
1.0ms
x
@-inf
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms
x
@-inf
(+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))
1.0ms
x
@inf
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
0.0ms
x
@-inf
(+ (* x (+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))) (sqrt 2))

rewrite388.0ms (4.8%)

Memory
3.9MiB live, 604.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 406×*-lowering-*.f32
4 406×*-lowering-*.f64
4 310×/-lowering-/.f32
4 310×/-lowering-/.f64
3 936×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030148
1188148
21776144
08317128
Stop Event
1×iter limit
1×node limit
Counts
18 → 1 019
Calls
Call 1
Inputs
(+ (/ (* x (+ (* x 3/16) 1/2)) (sqrt 2)) (sqrt 2))
(/ (* x (+ (* x 3/16) 1/2)) (sqrt 2))
(* x (+ (* x 3/16) 1/2))
(+ (* x 3/16) 1/2)
(* x (sqrt 1/2))
(sqrt 1/2)
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
(* x (* x (+ (* x 1/6) 1/2)))
(* x (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
(* (/ x (sqrt 2)) (+ (* x 3/16) 1/2))
(/ x (sqrt 2))
(sqrt 2)
(+ (* x (+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))) (sqrt 2))
(+ (* x (+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))) (/ 1/2 (sqrt 2)))
(+ (* x (/ 7/192 (sqrt 2))) (/ 3/16 (sqrt 2)))
(/ 7/192 (sqrt 2))
(/ 1/2 (sqrt 2))
Outputs
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 x (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/16 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (neg.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) x (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (*.f64 x #s(literal 3/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) #s(literal 1 binary64)) (neg.f64 (*.f64 x #s(literal 7/192 binary64))))) (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64))))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) #s(literal 1 binary64)) (*.f64 x #s(literal -7/192 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
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(/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 7/192 binary64))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 7/192 binary64)))))
(/.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 x #s(literal 7/192 binary64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 x #s(literal 1 binary64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64))))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 x #s(literal -7/192 binary64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 #s(literal 1 binary64) x))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64))))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (*.f64 #s(literal -7/192 binary64) x))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64)) (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 9/512 binary64))) (*.f64 (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))) #s(literal -2 binary64))
(/.f64 (neg.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/16 binary64)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 7/192 binary64))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (fma.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64))))) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) (*.f64 x #s(literal 7/192 binary64))))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 27/4096 binary64))) #s(literal 8 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) (-.f64 #s(literal 9/512 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) #s(literal -9/512 binary64)))) (neg.f64 (neg.f64 (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 9/512 binary64) (*.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(pow.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) (-.f64 #s(literal 9/512 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) #s(literal 2 binary64)))) (/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 27/4096 binary64))) #s(literal 8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) #s(literal -9/512 binary64))) #s(literal -1 binary64))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 27/4096 binary64))) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) (-.f64 #s(literal 9/512 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) #s(literal 2 binary64))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) #s(literal -9/512 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 7/192 binary64) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -7/192 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -7/192 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) #s(literal 1 binary64))))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 192/7 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -7/192 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 3 binary64))))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)))

simplify844.0ms (10.5%)

Memory
40.0MiB live, 544.8MiB allocated
Algorithm
1×egg-herbie
Rules
25 574×accelerator-lowering-fma.f32
25 574×accelerator-lowering-fma.f64
5 514×*-lowering-*.f32
5 514×*-lowering-*.f64
3 352×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01931771
16101754
217371576
348181530
082301397
Stop Event
1×iter limit
1×node limit
Counts
168 → 168
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 1/2 x)
(* x (+ 1/2 (* 3/16 x)))
(* x (+ 1/2 (* 3/16 x)))
(* x (+ 1/2 (* 3/16 x)))
(* 3/16 (pow x 2))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(* 3/16 (pow x 2))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(/ 3/16 (sqrt 2))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(* 7/192 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 7/192 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(* 1/2 (/ x (sqrt 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 3/16 x)))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 3/16 x)))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 3/16 x)))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (pow x 2))
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (pow x 2))
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 3/16 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(*.f64 x (fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(*.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(*.f64 x (fma.f64 x (/.f64 (*.f64 x (*.f64 x #s(literal 1/3456 binary64))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal -1/32 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 6 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal -1/32 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 6 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 #s(literal 1/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal -1/32 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -6 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal -1/32 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -6 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 #s(literal 1/128 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal 5 binary64))))))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/2 (/ x (sqrt 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) x)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 (*.f64 x x) #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 (*.f64 x x) #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/ 3/16 (sqrt 2))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))

eval276.0ms (3.5%)

Memory
-17.1MiB live, 296.9MiB allocated
Compiler

Compiled 34 139 to 3 244 computations (90.5% saved)

prune164.0ms (2.1%)

Memory
21.2MiB live, 411.2MiB allocated
Pruning

22 alts after pruning (13 fresh and 9 done)

PrunedKeptTotal
New1 256101 266
Fresh033
Picked415
Done2810
Total1 262221 284
Accuracy
100.0%
Counts
1 284 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.6%
(fma.f64 (fma.f64 x (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
69.6%
(fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
69.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
69.6%
(fma.f64 x (fma.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) #s(literal -9/512 binary64)) (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
69.5%
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
69.6%
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
4.1%
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
2.7%
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
4.6%
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
3.4%
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
3.0%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
4.0%
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fabs.f64 x))
1.7%
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
✓3.1%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓69.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓70.8%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓2.5%
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓68.8%
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓68.8%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓2.5%
(sqrt.f64 x)
✓73.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 610 to 280 computations (54.1% saved)

regimes32.0ms (0.4%)

Memory
-3.6MiB live, 54.1MiB allocated
Counts
31 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fabs.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (fma.f64 x (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (fma.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) #s(literal -9/512 binary64)) (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
Calls

3 calls:

14.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
9.0ms
x
8.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes26.0ms (0.3%)

Memory
-15.6MiB live, 63.0MiB allocated
Counts
29 → 2
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fabs.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (fma.f64 x (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (fma.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 x #s(literal 7/192 binary64)) (*.f64 x #s(literal 7/192 binary64))) #s(literal 1/2 binary64) #s(literal -9/512 binary64)) (/.f64 (-.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
Calls

3 calls:

9.0ms
x
9.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
7.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
75.4%2x
75.4%2(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
75.4%2(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes23.0ms (0.3%)

Memory
11.2MiB live, 50.4MiB allocated
Counts
27 → 2
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fabs.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (fma.f64 x (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
Calls

3 calls:

8.0ms
x
7.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
7.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
75.4%2x
75.4%2(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
75.4%2(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes34.0ms (0.4%)

Memory
-10.7MiB live, 30.8MiB allocated
Counts
22 → 2
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fabs.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
Calls

3 calls:

21.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
7.0ms
x
6.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
75.4%2x
75.4%2(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
75.4%2(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes12.0ms (0.1%)

Memory
17.8MiB live, 17.8MiB allocated
Counts
12 → 2
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fabs.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
Outputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
Calls

3 calls:

4.0ms
x
3.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
3.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
75.2%2x
75.2%2(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
75.2%2(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes31.0ms (0.4%)

Memory
-24.5MiB live, 15.1MiB allocated
Accuracy

Total -46.0b remaining (-271.9%)

Threshold costs -46b (-271.9%)

Counts
7 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
Outputs
(sqrt.f64 #s(literal 2 binary64))
Calls

3 calls:

25.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
3.0ms
x
2.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
73.6%1x
73.6%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
73.6%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.8MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.9994788952579468
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.9994788952579468
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.9994788952579468
Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.9994788952579468
Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify9.0ms (0.1%)

Memory
20.2MiB live, 20.2MiB allocated
Algorithm
1×egg-herbie
Rules
12×+-commutative_binary64
10×sub-neg_binary64
8×*-commutative_binary64
4×neg-sub0_binary64
4×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042128
153128
260128
368128
469128
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) #s(literal 2 binary64)) (*.f64 x x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))

soundness749.0ms (9.4%)

Memory
-32.9MiB live, 572.5MiB allocated
Rules
15 504×accelerator-lowering-fma.f32
15 504×accelerator-lowering-fma.f64
11 602×accelerator-lowering-fma.f32
11 602×accelerator-lowering-fma.f64
5 042×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02771514
18811294
229691264
083771149
030148
1188148
21776144
08317128
01036
15622
242122
3498522
0809318
077480
1252446
2663446
31429440
42558360
55941325
08294270
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 178 to 84 computations (52.8% saved)

preprocess44.0ms (0.6%)

Memory
-0.2MiB live, 75.0MiB allocated
Compiler

Compiled 284 to 104 computations (63.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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