sqrtexp (problem 3.4.4)

Time bar (total: 7.2s)

analyze2.0ms (0%)

Memory
2.0MiB live, 2.0MiB 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)

sample923.0ms (12.8%)

Memory
48.2MiB live, 927.9MiB allocated
Samples
472.0ms8 256×0valid
139.0ms2 551×0exit
Precisions
Click to see histograms. Total time spent on operations: 391.0ms
ival-expm1: 128.0ms (32.8% of total)
ival-mult: 97.0ms (24.8% of total)
ival-div: 78.0ms (20% of total)
ival-sqrt: 71.0ms (18.2% of total)
ival-true: 8.0ms (2% of total)
exact: 6.0ms (1.5% of total)
ival-assert: 4.0ms (1% of total)
Bogosity

preprocess401.0ms (5.6%)

Memory
-4.1MiB live, 347.5MiB 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)))

explain191.0ms (2.7%)

Memory
-4.4MiB live, 159.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1750-0-(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1750-0-(-.f64 (exp.f64 x) #s(literal 1 binary64))
20-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
01(124.83777898865645)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))cancellation1751
-.f64(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))cancellation1750
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o20
(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow2
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow2
(exp.f64 x)overflow2
(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow2
exp.f64(exp.f64 (*.f64 #s(literal 2 binary64) x))sensitivity10
Confusion
Predicted +Predicted -
+1770
-178
Precision
0.9943820224719101
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+17700
-1177
Precision?
0.9888268156424581
Recall?
1.0
Freqs
test
numberfreq
078
13
2175
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 (28.4% of total)
ival-expm1: 6.0ms (24.4% of total)
ival-mult: 4.0ms (16.2% of total)
ival-div: 3.0ms (12.2% of total)
ival-sqrt: 3.0ms (12.2% of total)
exact: 1.0ms (4.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
31.7%
(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)

simplify393.0ms (5.5%)

Memory
-1.1MiB live, 400.2MiB 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)

localize33.0ms (0.5%)

Memory
3.8MiB live, 41.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(exp.f64 x)
accuracy99.4%
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy36.1%
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy36.1%
(-.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 (24.6% of total)
ival-expm1: 3.0ms (24.6% of total)
ival-div: 2.0ms (16.4% of total)
ival-mult: 2.0ms (16.4% of total)
ival-sqrt: 2.0ms (16.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
5.8MiB live, 5.8MiB 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 (exp.f64 x)>
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 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)>
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
(- (exp (* 2 x)) 1)
0.0ms
x
@0
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms
x
@-inf
(* 2 x)

rewrite306.0ms (4.3%)

Memory
3.3MiB live, 290.3MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 402×lower-fma.f64
5 402×lower-fma.f32
4 492×lower-*.f32
4 490×lower-*.f64
2 532×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0926
01526
15619
237819
3453319
0816115
Stop Event
iter limit
node limit
iter limit
Counts
5 → 656
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)
(exp.f64 x)
Outputs
(exp.f64 (log1p.f64 (exp.f64 x)))
(+.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 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x))) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (/.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
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(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x) (neg.f64 (expm1.f64 x)))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))) (exp.f64 (*.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x)))
(log.f64 (exp.f64 (+.f64 x x)))
(+.f64 x x)
(+.f64 (+.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 x x))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 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 (*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))))) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)) (log.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 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 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 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 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 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 x)
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))

simplify512.0ms (7.1%)

Memory
-9.3MiB live, 501.5MiB allocated
Algorithm
egg-herbie
Rules
18 226×lower-fma.f64
18 226×lower-fma.f32
2 938×lower-+.f64
2 938×lower-+.f32
2 780×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049342
1155342
2335342
3752342
41201302
51536286
62025286
72949286
84633286
08302232
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)
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)
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 #s(literal 2 binary64) (fma.f64 x 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)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #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)

eval89.0ms (1.2%)

Memory
29.3MiB live, 178.8MiB allocated
Compiler

Compiled 16 824 to 2 356 computations (86% saved)

prune80.0ms (1.1%)

Memory
-0.7MiB live, 198.5MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New7105715
Fresh000
Picked101
Done000
Total7115716
Accuracy
100.0%
Counts
716 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
68.7%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
70.2%
(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)))
68.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
74.4%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 70 to 56 computations (20% saved)

simplify16.0ms (0.2%)

Memory
-10.5MiB live, 27.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 13 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01985
03785
16785
211385
320285
424985
525585
025585
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 (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(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)
(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)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 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 (+.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 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)
(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)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)

localize73.0ms (1%)

Memory
24.9MiB live, 139.0MiB allocated
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy100.0%
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy100.0%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy100.0%
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy100.0%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
accuracy100.0%
(+.f64 #s(literal 2 binary64) x)
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
accuracy100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy100.0%
(exp.f64 x)
accuracy100.0%
(-.f64 (exp.f64 x) #s(literal -1 binary64))
Samples
31.0ms179×0valid
16.0ms77×0invalid
Compiler

Compiled 101 to 26 computations (74.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-add: 10.0ms (30% of total)
ival-mult: 8.0ms (24% of total)
ival-sqrt: 8.0ms (24% of total)
const: 4.0ms (12% of total)
ival-exp: 2.0ms (6% of total)
ival-sub: 1.0ms (3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory
-10.9MiB live, 27.4MiB allocated
Counts
13 → 144
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 (+.f64 #s(literal 2 binary64) x))>
#<alt (+.f64 #s(literal 2 binary64) x)>
#<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 (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)))>
#<alt (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))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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 (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
Calls

36 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(sqrt (+ 2 x))
2.0ms
x
@inf
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms
x
@-inf
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms
x
@0
(sqrt (+ 2 x))
1.0ms
x
@inf
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))

rewrite367.0ms (5.1%)

Memory
-2.3MiB live, 448.5MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 428×lower-fma.f32
4 418×lower-fma.f64
4 328×lower-*.f64
4 328×lower-*.f32
4 210×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01971
03771
115571
2113671
0824871
Stop Event
iter limit
node limit
iter limit
Counts
13 → 442
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 (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
(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))
(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)))
(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))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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)) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (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)) (neg.f64 (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) #s(literal -1 binary64))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (neg.f64 (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)) (neg.f64 (expm1.f64 x))))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))

simplify381.0ms (5.3%)

Memory
-39.5MiB live, 419.7MiB allocated
Algorithm
egg-herbie
Rules
11 602×lower-fma.f64
11 602×lower-fma.f32
5 042×lower-*.f64
5 042×lower-*.f32
3 340×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02771514
18811294
229691264
083771149
Stop Event
iter limit
node limit
Counts
144 → 142
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(*.f64 x (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(neg.f64 (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* -1 (* x (sqrt 1/2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))) x) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (neg.f64 (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(neg.f64 (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

eval76.0ms (1.1%)

Memory
25.5MiB live, 139.9MiB allocated
Compiler

Compiled 13 939 to 1 906 computations (86.3% saved)

prune68.0ms (1%)

Memory
-2.8MiB live, 155.7MiB allocated
Pruning

15 alts after pruning (10 fresh and 5 done)

PrunedKeptTotal
New57410584
Fresh000
Picked055
Done000
Total57415589
Accuracy
100.0%
Counts
589 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
68.9%
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
69.9%
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
67.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
3.0%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
68.7%
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)))
68.7%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
70.2%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
2.5%
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
4.1%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
68.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
3.4%
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
2.3%
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
2.5%
(sqrt.f64 x)
74.4%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 273 to 184 computations (32.6% saved)

simplify23.0ms (0.3%)

Memory
1.9MiB live, 40.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
cost-diff0
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
cost-diff0
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
cost-diff0
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
cost-diff0
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
cost-diff0
(*.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
(sqrt.f64 x)
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff1344
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
Rules
588×lower-fma.f32
576×lower-fma.f64
286×lower-*.f32
280×lower-*.f64
164×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024155
047155
183155
2151155
3294154
4383154
5437151
6490151
7490151
0490149
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
x
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 x)
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
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
x
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (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 #s(literal 1 binary64) (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)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
Outputs
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 x)
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
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
x
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (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 #s(literal 1 binary64) (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)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)

localize122.0ms (1.7%)

Memory
-17.0MiB live, 114.6MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy100.0%
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy100.0%
(/.f64 #s(literal 1 binary64) (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)))
accuracy99.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
accuracy100.0%
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy100.0%
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
accuracy83.6%
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
accuracy100.0%
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
accuracy100.0%
(sqrt.f64 x)
accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
accuracy100.0%
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
accuracy100.0%
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
accuracy99.4%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
Samples
59.0ms96×0valid
33.0ms160×0invalid
Compiler

Compiled 181 to 31 computations (82.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 61.0ms
ival-div: 29.0ms (47.8% of total)
ival-mult: 12.0ms (19.8% of total)
ival-sqrt: 8.0ms (13.2% of total)
ival-add: 7.0ms (11.5% of total)
const: 4.0ms (6.6% of total)
exact: 1.0ms (1.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series27.0ms (0.4%)

Memory
1.0MiB live, 37.5MiB allocated
Counts
18 → 180
Calls
Call 1
Inputs
#<alt (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 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 (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))>
#<alt (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))>
#<alt (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (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))))>
#<alt (/.f64 #s(literal 1 binary64) (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)))>
#<alt (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))>
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))>
Outputs
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 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 (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (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 (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 (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 6))>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))>
#<alt (/ 6 (pow x 3))>
#<alt (/ (- 6 (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))>
#<alt (/ 6 (pow x 3))>
#<alt (* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
Calls

45 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(* x (+ (* x 1/6) 1/2))
2.0ms
x
@0
(sqrt (/ 1 (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)))
1.0ms
x
@-inf
(sqrt (/ 1 (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)))
1.0ms
x
@-inf
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms
x
@0
(+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))

rewrite558.0ms (7.8%)

Memory
2.7MiB live, 468.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 676×lower-fma.f32
5 664×lower-fma.f64
3 868×lower-/.f32
3 860×lower-/.f64
3 708×lower-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
024136
047136
1198131
21460126
08257126
Stop Event
iter limit
node limit
iter limit
Counts
18 → 681
Calls
Call 1
Inputs
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 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)
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (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 #s(literal 1 binary64) (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)))
(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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
Outputs
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(+.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/16 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x #s(literal 16/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (neg.f64 (*.f64 x #s(literal 3/16 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x #s(literal -3/16 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(literal -3/16 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (*.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64)))) (/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (fma.f64 (*.f64 x #s(literal 3/16 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (*.f64 x #s(literal 3/16 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 9/512 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64)))))
(/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal 1/8 binary64)) (*.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64))))
(/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64)) (+.f64 #s(literal 1/8 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (*.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (*.f64 x #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))
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(*.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))))
(*.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))

simplify523.0ms (7.3%)

Memory
22.3MiB live, 605.0MiB allocated
Algorithm
egg-herbie
Rules
12 860×lower-fma.f64
12 860×lower-fma.f32
5 710×lower-*.f64
5 710×lower-*.f32
4 296×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04332238
113312124
240892062
083141913
Stop Event
iter limit
node limit
Counts
180 → 179
Calls
Call 1
Inputs
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 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 (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(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)))
(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)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 6))
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(/ 6 (pow x 3))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/ 6 (pow x 3))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
Outputs
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) 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)
(sqrt x)
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(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 x (*.f64 x (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 x #s(literal -1/6 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))))) x) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ 1 (pow x 3))) (sqrt 6))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 6 binary64)))
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)) (*.f64 (/.f64 #s(literal -9 binary64) (sqrt.f64 #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -9 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -9 binary64))) (*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal 81 binary64) (/.f64 x #s(literal 6 binary64)) #s(literal 18 binary64))) (sqrt.f64 #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -6 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -6 binary64))) (*.f64 #s(literal -9 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -9 binary64))) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(/.f64 (-.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -6 binary64))) (*.f64 #s(literal -9 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 #s(literal -6 binary64))))) (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -81 binary64) (/.f64 x #s(literal -6 binary64)) #s(literal 18 binary64))) (sqrt.f64 #s(literal -6 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (*.f64 (sqrt.f64 x) #s(literal -9 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 x (*.f64 x x)))) (neg.f64 x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(fma.f64 x (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/96 binary64) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(/ 6 (pow x 3))
(/.f64 #s(literal 6 binary64) (*.f64 x (*.f64 x x)))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (*.f64 x (*.f64 x x)))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/.f64 (+.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (/.f64 #s(literal -18 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)))
(/ 6 (pow x 3))
(/.f64 #s(literal 6 binary64) (*.f64 x (*.f64 x x)))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(/.f64 (+.f64 #s(literal -6 binary64) (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x)) (neg.f64 (*.f64 x (*.f64 x x))))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
(/.f64 (-.f64 #s(literal -6 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x) #s(literal -18 binary64)) x)) (neg.f64 (*.f64 x (*.f64 x 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))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(*.f64 x (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)))))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (*.f64 x (*.f64 x x)) (neg.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(*.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x)) (neg.f64 (*.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))

eval396.0ms (5.5%)

Memory
-23.3MiB live, 280.7MiB allocated
Compiler

Compiled 23 475 to 3 115 computations (86.7% saved)

prune126.0ms (1.7%)

Memory
12.4MiB live, 253.7MiB allocated
Pruning

21 alts after pruning (15 fresh and 6 done)

PrunedKeptTotal
New92512937
Fresh235
Picked415
Done055
Total93121952
Accuracy
100.0%
Counts
952 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.9%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
69.9%
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
1.3%
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
68.9%
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
68.8%
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
69.9%
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
4.2%
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
67.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
69.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
73.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
69.9%
(+.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
4.0%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
2.7%
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
3.0%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
68.7%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
70.2%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
2.5%
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
68.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
2.5%
(sqrt.f64 x)
74.4%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 448 to 300 computations (33% saved)

simplify35.0ms (0.5%)

Memory
2.3MiB live, 39.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff320
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))
cost-diff640
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff960
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
cost-diff0
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
cost-diff0
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
cost-diff0
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Rules
652×lower-fma.f32
642×lower-fma.f64
574×lower-*.f32
564×lower-*.f64
362×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024134
046134
173128
2118128
3215124
4402124
5513124
6527124
7541124
8541124
9654124
10654124
11683124
12683124
13685124
0685120
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
x
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(*.f64 x x)
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))
(*.f64 x #s(literal 3/16 binary64))
x
#s(literal 3/16 binary64)
Outputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
x
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
x
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(*.f64 x x)
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(*.f64 x #s(literal 3/16 binary64))
x
#s(literal 3/16 binary64)

localize88.0ms (1.2%)

Memory
1.2MiB live, 120.3MiB allocated
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x #s(literal 3/16 binary64))
accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
accuracy100.0%
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))
accuracy99.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))
accuracy100.0%
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
accuracy99.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
accuracy100.0%
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
accuracy100.0%
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
accuracy99.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
accuracy99.5%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
accuracy98.9%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Samples
38.0ms176×0valid
16.0ms80×0invalid
Compiler

Compiled 150 to 31 computations (79.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-mult: 17.0ms (43.6% of total)
ival-sqrt: 7.0ms (18% of total)
ival-add: 6.0ms (15.4% of total)
ival-div: 5.0ms (12.8% of total)
const: 4.0ms (10.3% of total)
exact: 1.0ms (2.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series20.0ms (0.3%)

Memory
0.3MiB live, 39.1MiB allocated
Counts
17 → 168
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))>
#<alt (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))>
#<alt (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))>
#<alt (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 x x)>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))>
#<alt (*.f64 x #s(literal 3/16 binary64))>
Outputs
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (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 (- 1/4 (* 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 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/4))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))>
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 48))>
#<alt (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)>
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)>
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))>
#<alt (* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/48))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48)))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (* 1/48 (pow x 3))>
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))>
#<alt -1/4>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))>
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))>
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (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 (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))>
#<alt (* 3/32 (* (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))>
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/32 (* (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* 3/32 (* x (sqrt 2)))>
#<alt (* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))>
#<alt (* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))>
#<alt (* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))>
#<alt (* 3/32 (* x (sqrt 2)))>
#<alt (* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 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 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
Calls

42 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(sqrt (+ (* x (+ (* (* x x) 1/48) -1/4)) 1/2))
1.0ms
x
@-inf
(sqrt (+ (* x (+ (* (* x x) 1/48) -1/4)) 1/2))
1.0ms
x
@inf
(sqrt (+ (* x -1/4) 1/2))
1.0ms
x
@-inf
(/ 1 (sqrt (+ (* x (+ (* (* x x) 1/48) -1/4)) 1/2)))
1.0ms
x
@inf
(/ 1 (sqrt (+ (* x -1/4) 1/2)))

rewrite340.0ms (4.7%)

Memory
9.8MiB live, 416.0MiB allocated
Algorithm
batch-egg-rewrite
Rules
8 050×lower-fma.f32
8 040×lower-fma.f64
5 606×lower-*.f32
5 596×lower-*.f64
3 276×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024115
046115
1161106
21059106
08385103
Stop Event
iter limit
node limit
iter limit
Counts
17 → 525
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))
(*.f64 x #s(literal 3/16 binary64))
Outputs
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 (*.f64 x (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64)))) (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64))) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/16 binary64) x)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/16 binary64) x)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)))) (/.f64 (*.f64 x (*.f64 #s(literal 1/16 binary64) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)))))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 3/16 binary64) x)
(*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 3/16 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3/16 binary64))) #s(literal 1/2 binary64))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) x)
(*.f64 (*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

simplify384.0ms (5.3%)

Memory
-19.4MiB live, 453.1MiB allocated
Algorithm
egg-herbie
Rules
10 996×lower-fma.f64
10 996×lower-fma.f32
6 268×lower-*.f64
6 268×lower-*.f32
3 494×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03802194
110781989
233451914
369611914
080421825
Stop Event
iter limit
node limit
Counts
168 → 168
Calls
Call 1
Inputs
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(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 (- 1/4 (* 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 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/4))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 48))
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt (pow x 3)) (sqrt 1/48))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48)))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(* 1/48 (pow x 3))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(* 3/16 (* x (sqrt 2)))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (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 (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(* 3/32 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))
(* 3/32 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))
(* 1/4 (sqrt 2))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(* 3/32 (* x (sqrt 2)))
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(* 3/32 (* x (sqrt 2)))
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 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 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
Outputs
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (fma.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (fma.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 x #s(literal -4 binary64) #s(literal 32 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -4 binary64))))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 x #s(literal -4 binary64) #s(literal 32 binary64)) (*.f64 #s(literal 4 binary64) (sqrt.f64 x)))) (*.f64 x (*.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal -1/1024 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt -1/4))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/4 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* 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)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #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 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))))
(* 3/32 (* (pow x 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64)))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(*.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* 3/32 (* (pow x 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64)))
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(*.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64) (/.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (neg.f64 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64) (/.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (neg.f64 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)))
(+ (* 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)))
(+ (* 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)))
(* 3/32 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64)))
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* 3/32 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64)))
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))))
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) 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 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))

eval95.0ms (1.3%)

Memory
15.4MiB live, 166.5MiB allocated
Compiler

Compiled 17 127 to 2 308 computations (86.5% saved)

prune93.0ms (1.3%)

Memory
23.1MiB live, 177.6MiB allocated
Pruning

18 alts after pruning (8 fresh and 10 done)

PrunedKeptTotal
New7235728
Fresh7310
Picked145
Done066
Total73118749
Accuracy
100.0%
Counts
749 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
69.9%
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
1.3%
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
68.9%
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
68.8%
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
67.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
69.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
73.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
68.9%
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2.7%
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
69.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))))
4.2%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64)))
3.0%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
68.7%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
70.2%
(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)))
68.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
2.5%
(sqrt.f64 x)
74.4%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 570 to 261 computations (54.2% saved)

regimes35.0ms (0.5%)

Memory
-15.4MiB live, 55.1MiB allocated
Counts
33 → 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 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #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)))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64)))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 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 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 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)))
7.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
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)

regimes25.0ms (0.3%)

Memory
6.9MiB live, 45.6MiB allocated
Accuracy

Total -47.1b remaining (-287.1%)

Threshold costs -47.1b (-287.1%)

Counts
31 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #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)))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64)))
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 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 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
Outputs
(sqrt.f64 #s(literal 2 binary64))
Calls

3 calls:

9.0ms
x
7.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
7.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
74.4%1x
74.4%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))))
74.4%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)

simplify5.0ms (0.1%)

Memory
11.3MiB live, 11.3MiB 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))

soundness323.0ms (4.5%)

Memory
-8.8MiB live, 205.1MiB allocated
Rules
18 226×lower-fma.f64
18 226×lower-fma.f32
5 402×lower-fma.f64
5 402×lower-fma.f32
4 492×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049342
1155342
2335342
3752342
41201302
51536286
62025286
72949286
84633286
08302232
0926
01526
15619
237819
3453319
0816115
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess36.0ms (0.5%)

Memory
-2.5MiB live, 35.3MiB allocated
Compiler

Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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