sqrtexp (problem 3.4.4)

Time bar (total: 10.2s)

analyze2.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated
Algorithm
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)

sample930.0ms (9.1%)

Memory
43.2MiB live, 961.2MiB allocated
Samples
455.0ms8 256×0valid
161.0ms2 620×0exit
Precisions
Click to see histograms. Total time spent on operations: 416.0ms
ival-expm1: 133.0ms (31.9% of total)
ival-mult: 97.0ms (23.3% of total)
ival-div: 91.0ms (21.9% of total)
ival-sqrt: 77.0ms (18.5% of total)
ival-true: 8.0ms (1.9% of total)
exact: 6.0ms (1.4% of total)
ival-assert: 4.0ms (1% of total)
Bogosity

preprocess461.0ms (4.5%)

Memory
-1.6MiB live, 361.8MiB allocated
Algorithm
egg-herbie
Rules
15 394×lower-fma.f64
15 394×lower-fma.f32
2 850×lower--.f32
2 846×lower--.f64
2 458×lower-*.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01229
13227
25527
38927
414313
525013
651313
7203913
8713613
01012
01712
12912
23512
34712
4737
51265
62035
76065
829265
967835
081975
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(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 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

explain134.0ms (1.3%)

Memory
6.2MiB live, 160.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1640-1(0.01132248742408843)(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1640-1(0.025343369726707348)(-.f64 (exp.f64 x) #s(literal 1 binary64))
40-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
01(-150.58615529019949)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))cancellation1633
-.f64(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))cancellation1631
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o40
(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow4
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow4
(exp.f64 x)overflow4
(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow4
exp.f64(exp.f64 (*.f64 #s(literal 2 binary64) x))sensitivity12
Confusion
Predicted +Predicted -
+1661
-287
Precision
0.9880952380952381
Recall
0.9940119760479041
Confusion?
Predicted +Predicted MaybePredicted -
+16610
-2483
Precision?
0.9653179190751445
Recall?
1.0
Freqs
test
numberfreq
088
15
2163
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 (28.1% of total)
ival-expm1: 6.0ms (24.1% of total)
ival-mult: 4.0ms (16.1% of total)
ival-div: 3.0ms (12.1% of total)
ival-sqrt: 3.0ms (12.1% of total)
exact: 1.0ms (4% 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
35.9%
(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)

simplify405.0ms (4%)

Memory
12.3MiB live, 402.8MiB allocated
Algorithm
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×lower-fma.f64
15 394×lower-fma.f32
2 850×lower--.f32
2 846×lower--.f64
2 458×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
01745
12945
23545
34745
47335
512631
620331
760631
8292631
9678331
0819727
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (+.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize48.0ms (0.5%)

Memory
7.4MiB live, 46.3MiB 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))))
accuracy98.7%
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy40.5%
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy40.5%
(-.f64 (exp.f64 x) #s(literal 1 binary64))
Samples
19.0ms256×0valid
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 (24.5% of total)
ival-expm1: 3.0ms (24.5% of total)
ival-div: 2.0ms (16.3% of total)
ival-mult: 2.0ms (16.3% of total)
ival-sqrt: 2.0ms (16.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0%)

Memory
7.0MiB live, 7.0MiB allocated
Counts
5 → 60
Calls
Call 1
Inputs
#<alt (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))>
#<alt (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 x) #s(literal 1 binary64))>
#<alt (*.f64 #s(literal 2 binary64) x)>
#<alt (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
#<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)

rewrite311.0ms (3.1%)

Memory
-39.6MiB live, 293.0MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 562×lower-fma.f64
4 562×lower-fma.f32
3 484×lower-*.f32
3 482×lower-*.f64
2 734×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01036
01736
16322
242922
3499722
0810318
Stop Event
iter limit
node limit
iter limit
Counts
5 → 711
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) x)
(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
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
(+.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))))))
(-.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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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)))
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(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 (+.f64 x x))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.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 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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.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)) (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (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)) (fma.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (neg.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 (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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (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 (fma.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (neg.f64 (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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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)))))

simplify393.0ms (3.9%)

Memory
19.3MiB live, 417.3MiB allocated
Algorithm
egg-herbie
Rules
15 504×lower-fma.f64
15 504×lower-fma.f32
4 704×lower-*.f64
4 704×lower-*.f32
2 492×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077480
1252446
2663446
31429440
42558360
55941325
08294270
Stop Event
iter limit
node limit
Counts
60 → 59
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)))

eval97.0ms (0.9%)

Memory
4.3MiB live, 154.1MiB allocated
Compiler

Compiled 17 383 to 2 477 computations (85.8% saved)

prune91.0ms (0.9%)

Memory
24.0MiB live, 223.8MiB allocated
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New7628770
Fresh000
Picked101
Done000
Total7638771
Accuracy
100.0%
Counts
771 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
65.1%
(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)))
66.0%
(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)))
64.7%
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
64.8%
(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)))
66.2%
(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)))
64.4%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
70.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 142 to 104 computations (26.8% saved)

simplify35.0ms (0.3%)

Memory
-21.6MiB live, 57.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(fma.f64 x (/.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 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
(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
1 172×lower-fma.f32
1 160×lower-fma.f64
478×lower-*.f64
478×lower-*.f32
228×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02092
03992
17692
215692
334292
462992
585092
685592
085592
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#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)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#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)))
x
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#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)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#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))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#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)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#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)))
x
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#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)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#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))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

localize89.0ms (0.9%)

Memory
-8.6MiB live, 159.9MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
accuracy99.9%
(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)))
accuracy99.7%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
accuracy99.4%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
accuracy99.7%
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy98.4%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 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))
accuracy82.2%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
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
49.0ms242×0valid
3.0ms1valid
2.0ms2valid
1.0ms5exit
Compiler

Compiled 94 to 28 computations (70.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-mult: 15.0ms (36.3% of total)
ival-add: 7.0ms (16.9% of total)
ival-sqrt: 6.0ms (14.5% of total)
const: 4.0ms (9.7% of total)
ival-div: 3.0ms (7.3% of total)
ival-exp: 2.0ms (4.8% of total)
adjust: 1.0ms (2.4% of total)
exact: 1.0ms (2.4% of total)
ival-sub: 1.0ms (2.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
21.8MiB live, 21.8MiB allocated
Counts
13 → 132
Calls
Call 1
Inputs
#<alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))>
#<alt (-.f64 (exp.f64 x) #s(literal -1 binary64))>
#<alt (exp.f64 x)>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (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)))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))>
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 (+ (* 1/2 (/ (* 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) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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 (/ 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 (* x (+ 3/16 (* 7/192 x))))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
Calls

33 calls:

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

rewrite506.0ms (5%)

Memory
6.8MiB live, 481.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 414×lower-fma.f32
4 402×lower-fma.f64
4 324×lower-/.f32
4 320×lower-/.f64
3 476×lower-*.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02073
03973
118173
2141771
0829071
Stop Event
iter limit
node limit
iter limit
Counts
13 → 496
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
(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)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1/2 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)))
(/.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))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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))))
(/.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)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (expm1.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)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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 (neg.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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) (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)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.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 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 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) (+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (neg.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)) (-.f64 #s(literal 1 binary64) (exp.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 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 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 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 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 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)))) (sqrt.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal -4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64))) (sqrt.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) (*.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal -4 binary64))) (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))))
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(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (*.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(*.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))

simplify341.0ms (3.4%)

Memory
-33.0MiB live, 415.7MiB allocated
Algorithm
egg-herbie
Rules
10 586×lower-fma.f64
10 586×lower-fma.f32
3 958×lower-*.f64
3 958×lower-*.f32
2 708×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01961199
16521039
22116953
36397949
08336866
Stop Event
iter limit
node limit
Counts
132 → 132
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 (+ (* 1/2 (/ (* 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) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* 1/2 (/ x (sqrt 2)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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))))))
(/ 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 (* x (+ 3/16 (* 7/192 x))))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
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 (+ (* 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 x (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)))) (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 #s(literal 1/2 binary64) (/.f64 x (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 (+ (* -1/4 (/ (* 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 x #s(literal -1/4 binary64) #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 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (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 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (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)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(* 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)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
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 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (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) (* 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)))
(* 1/2 (/ x (sqrt 2)))
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 1/2 (/ x (sqrt 2)))
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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)
(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 (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)))) (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 x (*.f64 (/.f64 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 x (fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (*.f64 (/.f64 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))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* 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 x (*.f64 (/.f64 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) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) 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 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(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))
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)))
(* 7/192 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

eval85.0ms (0.8%)

Memory
32.0MiB live, 147.1MiB allocated
Compiler

Compiled 16 404 to 1 736 computations (89.4% saved)

prune117.0ms (1.2%)

Memory
-30.8MiB live, 126.9MiB allocated
Pruning

18 alts after pruning (14 fresh and 4 done)

PrunedKeptTotal
New67212684
Fresh123
Picked145
Done000
Total67418692
Accuracy
100.0%
Counts
692 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
65.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))
65.1%
(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)))
64.1%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
65.0%
(fma.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (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.f64 #s(literal 2 binary64)))
65.1%
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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)))
64.0%
(/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #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)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
2.6%
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
65.1%
(+.f64 (*.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)))
33.5%
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
3.1%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
3.1%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
64.8%
(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)))
66.2%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
4.4%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
64.4%
(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)))
64.4%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
70.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 489 to 303 computations (38% saved)

simplify34.0ms (0.3%)

Memory
16.5MiB live, 54.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
cost-diff0
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
cost-diff0
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
cost-diff320
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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)))
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 7/192 binary64) #s(literal 3/16 binary64)))
cost-diff0
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
cost-diff0
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
cost-diff0
(+.f64 #s(literal 2 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
cost-diff0
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
cost-diff1664
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))
Rules
1 136×lower-fma.f32
1 124×lower-fma.f64
478×lower-*.f32
468×lower-*.f64
338×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024161
048164
197164
2215156
3510156
4974156
51084156
01084154
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
x
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
#s(literal 1/2 binary64)
(*.f64 x x)
x
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
x
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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)))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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 x (/.f64 (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.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
x
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+.f64 #s(literal 2 binary64) x)
(+.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
#s(literal 1/2 binary64)
(*.f64 x x)
x
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
x
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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 x (/.f64 (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.f64 #s(literal 2 binary64)))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize106.0ms (1%)

Memory
-4.3MiB live, 167.9MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
accuracy100.0%
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
accuracy100.0%
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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)))
accuracy99.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
accuracy99.9%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
accuracy99.8%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
accuracy100.0%
(+.f64 #s(literal 2 binary64) x)
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
accuracy100.0%
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy99.9%
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy99.4%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
Samples
42.0ms157×0invalid
23.0ms98×0valid
1.0ms5exit
Compiler

Compiled 163 to 32 computations (80.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-mult: 25.0ms (50.8% of total)
ival-add: 8.0ms (16.2% of total)
ival-div: 7.0ms (14.2% of total)
ival-sqrt: 5.0ms (10.2% of total)
const: 4.0ms (8.1% of total)
exact: 1.0ms (2% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory
-22.4MiB live, 16.5MiB allocated
Counts
18 → 180
Calls
Call 1
Inputs
#<alt (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))>
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))>
#<alt (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 (+.f64 #s(literal 2 binary64) x))>
#<alt (+.f64 #s(literal 2 binary64) x)>
#<alt (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))>
#<alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)>
#<alt (*.f64 x x)>
#<alt (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))>
#<alt (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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)))>
#<alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))>
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 (+ (* 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 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (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 (+ (* -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 x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<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 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 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)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<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 (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* 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 x)>
#<alt (* x (+ 1/2 (* 3/16 x)))>
#<alt (* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))>
#<alt (* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))>
#<alt (* 7/192 (pow x 3))>
#<alt (* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* 7/192 (pow x 3))>
#<alt (* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
Calls

45 calls:

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

rewrite1.2s (11.8%)

Memory
22.8MiB live, 677.0MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 618×lower-*.f32
4 608×lower-*.f64
4 540×lower-/.f32
4 534×lower-/.f64
3 250×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024126
048129
1207120
21673116
08229114
Stop Event
iter limit
node limit
iter limit
Counts
18 → 1 148
Calls
Call 1
Inputs
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(*.f64 x x)
(*.f64 x (*.f64 (/.f64 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 #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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)))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 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 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.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))))
(+.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(+.f64 (*.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)))
(+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
(+.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) #s(literal 1 binary64) #s(literal 2 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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (/.f64 (-.f64 #s(literal 2 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 (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.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.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))))
(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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.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 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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 (fma.f64 x #s(literal 7/192 binary64) #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 #s(literal 1 binary64) (*.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (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 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
(fma.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (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 (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 (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))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) (*.f64 (*.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x))) #s(literal 1/2 binary64))) (fma.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
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(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
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(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))
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(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
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(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)))

simplify450.0ms (4.4%)

Memory
36.9MiB live, 392.9MiB allocated
Algorithm
egg-herbie
Rules
9 936×lower-fma.f64
9 936×lower-fma.f32
4 018×lower-*.f64
4 018×lower-*.f32
2 272×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02491783
17741742
223051622
356471602
082751497
Stop Event
iter limit
node limit
Counts
180 → 177
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 (+ (* 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))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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 (+ (* -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 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(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)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* 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 x)
(* x (+ 1/2 (* 3/16 x)))
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))
(* 7/192 (pow x 3))
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* 7/192 (pow x 3))
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* 1/2 (/ x (sqrt 2)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (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)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 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 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))))))
(* (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))))))
(*.f64 x (fma.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 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 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) 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 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) x)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.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)))
(/ 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 (+ (* -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 x (/.f64 #s(literal 1/16 binary64) (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 (+.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 (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)))))
(*.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 (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)))))))
(* -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 (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) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x 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 x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/32 binary64))) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
(* 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 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))
(* -1 (* x (sqrt 1/2)))
(*.f64 x (neg.f64 (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 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/4 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 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/16 binary64) (*.f64 x (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* 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)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* 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)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x 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)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 x (*.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) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 x (*.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) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 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) (+ (* 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) (+ (* 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)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 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) (+ (* 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) (+ (* 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)))
(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 (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)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 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 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))))))
(* (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))))))
(*.f64 x (fma.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 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 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) 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 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) x)))
(* 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 (* x (+ 3/16 (* 7/192 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))
(*.f64 x (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 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64))))
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64))))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 7/192 binary64) (/.f64 (+.f64 #s(literal -3/16 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 7/192 binary64) (/.f64 (+.f64 #s(literal -3/16 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
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 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(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))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64)))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 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) (* 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) (* 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)))
(* 1/2 (/ x (sqrt 2)))
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 1/2 (/ x (sqrt 2)))
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))

eval1.9s (18.5%)

Memory
-4.8MiB live, 277.5MiB allocated
Compiler

Compiled 57 349 to 3 219 computations (94.4% saved)

prune411.0ms (4%)

Memory
-38.3MiB live, 350.5MiB allocated
Pruning

27 alts after pruning (20 fresh and 7 done)

PrunedKeptTotal
New1 505161 521
Fresh549
Picked235
Done044
Total1 512271 539
Accuracy
100.0%
Counts
1 539 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
65.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))))
65.1%
(fma.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #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))))
65.1%
(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)))
1.3%
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
65.1%
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
64.1%
(/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
64.1%
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
64.1%
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
64.9%
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
65.1%
(+.f64 (*.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)))
3.1%
(*.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x)
3.1%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
3.1%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
2.6%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64))))
4.3%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))
4.3%
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
2.6%
(*.f64 x (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))))
3.1%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
64.8%
(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)))
66.2%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
4.4%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
64.4%
(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)))
64.4%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
2.7%
(sqrt.f64 x)
70.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 740 to 477 computations (35.5% saved)

simplify341.0ms (3.3%)

Memory
-7.1MiB live, 470.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
cost-diff384
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
cost-diff640
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff960
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff0
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff0
(sqrt.f64 x)
cost-diff128
(-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
cost-diff320
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
cost-diff384
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))
cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))
Rules
10 398×lower-fma.f32
10 388×lower-fma.f64
4 392×lower-*.f32
4 374×lower-*.f64
2 144×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031249
059237
1110231
2246227
3566227
41345227
51944227
62740227
74275227
86608227
08513218
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
x
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))
#s(literal 1 binary64)
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))
(*.f64 x x)
#s(literal 1/8 binary64)
#s(literal -2 binary64)
(sqrt.f64 x)
x
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
x
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
x
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
Outputs
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))))
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
x
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))
#s(literal 1 binary64)
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))
(*.f64 x x)
#s(literal 1/8 binary64)
#s(literal -2 binary64)
(sqrt.f64 x)
x
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 3/16 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
x
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
x
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (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)))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

localize154.0ms (1.5%)

Memory
9.2MiB live, 241.8MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
accuracy100.0%
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy99.9%
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
accuracy100.0%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
accuracy99.9%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
accuracy99.9%
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
accuracy99.9%
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
accuracy99.6%
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
accuracy100.0%
(sqrt.f64 x)
accuracy99.9%
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))
accuracy99.4%
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
Samples
50.0ms157×0invalid
27.0ms80×0valid
6.0ms12×1valid
4.0ms2valid
1.0ms5exit
Compiler

Compiled 251 to 38 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 57.0ms
ival-mult: 28.0ms (49.5% of total)
ival-div: 11.0ms (19.4% of total)
ival-add: 6.0ms (10.6% of total)
const: 4.0ms (7.1% of total)
ival-sqrt: 4.0ms (7.1% of total)
adjust: 1.0ms (1.8% of total)
exact: 1.0ms (1.8% of total)
ival-sub: 1.0ms (1.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory
-2.6MiB live, 35.9MiB allocated
Counts
18 → 192
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))>
#<alt (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))>
#<alt (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))>
#<alt (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))>
#<alt (sqrt.f64 x)>
#<alt (*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))>
#<alt (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))>
#<alt (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))>
#<alt (* 1/4 (* x (sqrt 2)))>
#<alt (* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))>
#<alt (* 1/4 (* x (sqrt 2)))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* -1/4 (/ x (sqrt 2))) (/ 1 (sqrt 2)))>
#<alt (+ (* x (- (* 1/16 (/ x (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (+ (* x (- (* x (+ (* -1/64 (/ x (sqrt 2))) (* 1/16 (/ 1 (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (/ 4 (* x (sqrt 2)))>
#<alt (/ (- (* 4 (/ 1 (sqrt 2))) (* 16 (/ 1 (* x (sqrt 2))))) x)>
#<alt (/ (- (+ (* 4 (/ 1 (sqrt 2))) (/ 64 (* (pow x 2) (sqrt 2)))) (/ 16 (* x (sqrt 2)))) x)>
#<alt (/ (- (+ (* 4 (/ 1 (sqrt 2))) (* 64 (/ 1 (* (pow x 2) (sqrt 2))))) (+ (* 256 (/ 1 (* (pow x 3) (sqrt 2)))) (/ 16 (* x (sqrt 2))))) x)>
#<alt (/ 4 (* x (sqrt 2)))>
#<alt (* -1 (/ (- (* 16 (/ 1 (* x (sqrt 2)))) (* 4 (/ 1 (sqrt 2)))) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 64 (/ 1 (* x (sqrt 2)))) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 256 (/ 1 (* x (sqrt 2)))) (* 64 (/ 1 (sqrt 2)))) x)) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt -2>
#<alt (- (* 1/2 x) 2)>
#<alt (- (* 1/2 x) 2)>
#<alt (- (* 1/2 x) 2)>
#<alt (* 1/2 x)>
#<alt (* x (- 1/2 (* 2 (/ 1 x))))>
#<alt (* x (- 1/2 (* 2 (/ 1 x))))>
#<alt (* x (- 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))>
#<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 (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 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 (* 3/16 x)>
#<alt (* x (+ 3/16 (* 7/192 x)))>
#<alt (* x (+ 3/16 (* 7/192 x)))>
#<alt (* x (+ 3/16 (* 7/192 x)))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))>
#<alt (+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))>
#<alt (* 7/192 (* (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))>
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))>
#<alt (* 7/192 (* (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))>
#<alt (* 7/384 (* (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))>
#<alt (* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))>
#<alt (* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/384 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))>
#<alt (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))>
#<alt (* 7/384 (* (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))>
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))>
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))>
#<alt (* 7/384 (* (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))>
#<alt (/ -2 (sqrt 2))>
#<alt (- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))>
#<alt (- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))>
#<alt (- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt (/ (pow x 2) (sqrt 2))>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
Calls

48 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/ 1 (/ (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) (+ (* (* x x) 1/8) -2)))
2.0ms
x
@0
(/ (- (* (* x 1/2) 1) 2) (sqrt 2))
1.0ms
x
@inf
(+ (* x (/ (+ (* (* x (+ (* x 7/192) 3/16)) (sqrt 2)) (* (sqrt 2) 1/2)) 2)) (sqrt 2))
1.0ms
x
@0
(/ 1 (/ (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) (+ (* (* x x) 1/8) -2)))
0.0ms
x
@-inf
(/ 1 (/ (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) (+ (* (* x x) 1/8) -2)))

rewrite307.0ms (3%)

Memory
8.4MiB live, 443.1MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 324×lower-fma.f32
5 316×lower-fma.f64
4 240×lower-*.f32
4 222×lower-*.f64
4 042×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030158
056148
1212140
21471140
08322133
Stop Event
iter limit
node limit
iter limit
Counts
18 → 862
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(sqrt.f64 x)
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))) #s(literal -1 binary64)))
(+.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(+.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))))
(+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) (*.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal -4 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal -2 binary64))) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 4 binary64) (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)))))
(fma.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))))
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
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(*.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
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(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (*.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
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(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/256 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (*.f64 x #s(literal -7/1024 binary64))))))
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(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -7/192 binary64) #s(literal 3/16 binary64))))
(*.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))

simplify431.0ms (4.2%)

Memory
13.7MiB live, 532.1MiB allocated
Algorithm
egg-herbie
Rules
18 874×lower-fma.f64
18 874×lower-fma.f32
5 652×lower-*.f64
5 652×lower-*.f32
2 040×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02241686
17241639
220571558
353401551
086021444
Stop Event
iter limit
node limit
Counts
192 → 192
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(* 1/4 (* x (sqrt 2)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(* 1/4 (* x (sqrt 2)))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(/ 1 (sqrt 2))
(+ (* -1/4 (/ x (sqrt 2))) (/ 1 (sqrt 2)))
(+ (* x (- (* 1/16 (/ x (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+ (* x (- (* x (+ (* -1/64 (/ x (sqrt 2))) (* 1/16 (/ 1 (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(/ 4 (* x (sqrt 2)))
(/ (- (* 4 (/ 1 (sqrt 2))) (* 16 (/ 1 (* x (sqrt 2))))) x)
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (/ 64 (* (pow x 2) (sqrt 2)))) (/ 16 (* x (sqrt 2)))) x)
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (* 64 (/ 1 (* (pow x 2) (sqrt 2))))) (+ (* 256 (/ 1 (* (pow x 3) (sqrt 2)))) (/ 16 (* x (sqrt 2))))) x)
(/ 4 (* x (sqrt 2)))
(* -1 (/ (- (* 16 (/ 1 (* x (sqrt 2)))) (* 4 (/ 1 (sqrt 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* 64 (/ 1 (* x (sqrt 2)))) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 256 (/ 1 (* x (sqrt 2)))) (* 64 (/ 1 (sqrt 2)))) x)) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
-2
(- (* 1/2 x) 2)
(- (* 1/2 x) 2)
(- (* 1/2 x) 2)
(* 1/2 x)
(* x (- 1/2 (* 2 (/ 1 x))))
(* x (- 1/2 (* 2 (/ 1 x))))
(* x (- 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(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)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (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) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 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))
(* 3/16 x)
(* x (+ 3/16 (* 7/192 x)))
(* x (+ 3/16 (* 7/192 x)))
(* x (+ 3/16 (* 7/192 x)))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(* 7/192 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(* 7/192 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(sqrt 2)
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* 1/4 (sqrt 2))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(/ -2 (sqrt 2))
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))
(* 1/2 (/ x (sqrt 2)))
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))
(* 1/2 (/ x (sqrt 2)))
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(* 1/4 (* x (sqrt 2)))
(*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(* 1/4 (* x (sqrt 2)))
(*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/4 (/ x (sqrt 2))) (/ 1 (sqrt 2)))
(fma.f64 x (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (- (* 1/16 (/ x (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (- (* x (+ (* -1/64 (/ x (sqrt 2))) (* 1/16 (/ 1 (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal -1/64 binary64) #s(literal 1/16 binary64)) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/ 4 (* x (sqrt 2)))
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/ (- (* 4 (/ 1 (sqrt 2))) (* 16 (/ 1 (* x (sqrt 2))))) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x)
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (/ 64 (* (pow x 2) (sqrt 2)))) (/ 16 (* x (sqrt 2)))) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -16 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (* 64 (/ 1 (* (pow x 2) (sqrt 2))))) (+ (* 256 (/ 1 (* (pow x 3) (sqrt 2)))) (/ 16 (* x (sqrt 2))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -16 binary64)) (/.f64 #s(literal -256 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))))) x)
(/ 4 (* x (sqrt 2)))
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (/ (- (* 16 (/ 1 (* x (sqrt 2)))) (* 4 (/ 1 (sqrt 2)))) x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x)
(* -1 (/ (- (* -1 (/ (- (* 64 (/ 1 (* x (sqrt 2)))) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -16 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 256 (/ 1 (* x (sqrt 2)))) (* 64 (/ 1 (sqrt 2)))) x)) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))
(/.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 256 binary64) x) #s(literal -64 binary64))) x) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x)))) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
-2
#s(literal -2 binary64)
(- (* 1/2 x) 2)
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(- (* 1/2 x) 2)
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(- (* 1/2 x) 2)
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (- 1/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(* x (- 1/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(* x (- 1/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -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)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* (pow x 2) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* (pow x 2) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 x (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 7/192 binary64)))
(* (pow x 3) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* (pow x 3) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* (pow x 3) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 x (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 7/192 binary64)))
(* (pow x 3) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* (pow x 3) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(* (pow x 3) (+ (* 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 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64)))))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
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(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
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(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* x (+ 3/16 (* 7/192 x)))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* 7/192 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/192 binary64)))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
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(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
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(* 7/192 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/192 binary64)))
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(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* 1/2 (sqrt 2))
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(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(*.f64 (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))))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(*.f64 (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 2) (sqrt 2)))
(*.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)))
(* 7/192 (* (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))) (*.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)) x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))) (*.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)) x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 3/32 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(fma.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/384 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(*.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(* 7/384 (* (pow x 3) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64)))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(*.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/384 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)) x)))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/384 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64))))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/384 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 7/384 binary64)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x)))
(* 7/384 (* (pow x 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 7/384 binary64)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 7/384 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))) x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 7/384 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))) x))
(/ -2 (sqrt 2))
(/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/ (pow x 2) (sqrt 2))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

eval212.0ms (2.1%)

Memory
20.4MiB live, 291.9MiB allocated
Compiler

Compiled 40 860 to 3 858 computations (90.6% saved)

prune165.0ms (1.6%)

Memory
-24.5MiB live, 327.0MiB allocated
Pruning

22 alts after pruning (16 fresh and 6 done)

PrunedKeptTotal
New1 31681 324
Fresh7815
Picked415
Done257
Total1 329221 351
Accuracy
100.0%
Counts
1 351 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
65.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))))
3.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x)))
65.1%
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))))
65.1%
(fma.f64 (*.f64 x (*.f64 (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)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
1.3%
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
65.1%
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (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)))
64.1%
(/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
64.1%
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
64.9%
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
3.1%
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)))
64.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
2.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64)))
3.1%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
64.8%
(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)))
66.2%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
4.4%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
64.4%
(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)))
64.4%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
2.7%
(sqrt.f64 x)
70.6%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 1 028 to 392 computations (61.9% saved)

regimes37.0ms (0.4%)

Memory
22.3MiB live, 58.7MiB allocated
Counts
45 → 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)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #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)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)))
(*.f64 x (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (/.f64 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))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x)
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #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 (*.f64 (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)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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)))
(+.f64 (*.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 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))))
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (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)))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))
(/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (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.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x)))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))))
(/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #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)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(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:

15.0ms
x
10.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
10.0ms
(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
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)

regimes35.0ms (0.3%)

Memory
19.1MiB live, 55.7MiB allocated
Accuracy

Total -44.7b remaining (-237.9%)

Threshold costs -44.7b (-237.9%)

Counts
43 → 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)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #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)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)))
(*.f64 x (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (/.f64 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))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x)
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #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 (*.f64 (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)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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)))
(+.f64 (*.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 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))))
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (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)))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))
(/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (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.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x)))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))))
(/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #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)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
Outputs
(sqrt.f64 #s(literal 2 binary64))
Calls

3 calls:

13.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
11.0ms
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)))
Results
AccuracySegmentsBranch
70.6%1x
70.6%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))))
70.6%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)

simplify15.0ms (0.1%)

Memory
-28.7MiB live, 10.5MiB allocated
Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
197
2137
3147
4157
Stop Event
saturated
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))

soundness297.0ms (2.9%)

Memory
8.7MiB live, 236.9MiB allocated
Rules
15 504×lower-fma.f64
15 504×lower-fma.f32
4 704×lower-*.f64
4 704×lower-*.f32
4 562×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01036
01736
16322
242922
3499722
0810318
077480
1252446
2663446
31429440
42558360
55941325
08294270
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess22.0ms (0.2%)

Memory
12.1MiB live, 51.0MiB allocated
Compiler

Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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