ENA, Section 1.4, Exercise 4d

Time bar (total: 10.8s)

analyze16.0ms (0.1%)

Memory
-17.4MiB live, 25.3MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%12.8%87.2%0%0%0%0
0%0%12.8%87.2%0%0%0%1
0%0%12.8%87.2%0%0%0%2
50%6.4%6.4%87.2%0%0%0%3
57.1%6.4%4.8%87.2%0%1.6%0%4
69.2%7.2%3.2%87.2%0%2.4%0%5
75%7.2%2.4%87.2%0%3.2%0%6
82.6%7.6%1.6%87.2%0%3.6%0%7
86.4%7.6%1.2%87.2%0%4%0%8
90.7%7.8%0.8%87.2%0%4.2%0%9
92.6%7.8%0.6%87.2%0%4.4%0%10
95%7.9%0.4%87.2%0%4.5%0%11
96.3%8%0.3%87.2%0%4.5%0%12
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.6s (15.2%)

Memory
71.1MiB live, 1 993.1MiB allocated
Samples
640.0ms4 936×0valid
504.0ms2 722×1valid
143.0ms598×2valid
11.0ms170×0invalid
Precisions
Click to see histograms. Total time spent on operations: 683.0ms
ival-sub: 204.0ms (29.9% of total)
ival-sqrt: 175.0ms (25.6% of total)
ival-mult: 104.0ms (15.2% of total)
ival-<=: 99.0ms (14.5% of total)
adjust: 61.0ms (8.9% of total)
ival-and: 21.0ms (3.1% of total)
exact: 17.0ms (2.5% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

preprocess34.0ms (0.3%)

Memory
-12.9MiB live, 65.2MiB allocated
Algorithm
egg-herbie
Rules
176×accelerator-lowering-fma.f32
176×accelerator-lowering-fma.f64
148×sub-neg
104×*-lowering-*.f32
104×*-lowering-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02154
14952
212549
329049
452249
560949
661749
068
1108
2188
3308
4488
5908
61578
72038
82858
93158
103318
03318
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- x (sqrt (- (* x x) eps)))
Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Call 2
Inputs
(- x (sqrt (- (* x x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- eps (sqrt (- (* eps eps) x)))
Outputs
(- x (sqrt (- (* x x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- (neg x) (sqrt (- (* x x) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(- x (sqrt (+ (* x x) eps)))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(+ x (sqrt (- (* x x) eps)))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- (sqrt (+ (* x x) eps)) x)
(- eps (sqrt (- (* eps eps) x)))

explain118.0ms (1.1%)

Memory
-40.1MiB live, 204.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1040-0-(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
00-0-eps
00-0-(sqrt.f64 (-.f64 (*.f64 x x) eps))
00-0-(-.f64 (*.f64 x x) eps)
00-0-(*.f64 x x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))cancellation1040
Confusion
Predicted +Predicted -
+1040
-0152
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+10400
-00152
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0152
1104
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
43.0ms170×1valid
16.0ms308×0valid
5.0ms34×2valid
Compiler

Compiled 72 to 28 computations (61.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
adjust: 27.0ms (56% of total)
ival-sub: 7.0ms (14.5% of total)
ival-sqrt: 7.0ms (14.5% of total)
ival-mult: 5.0ms (10.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
62.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify29.0ms (0.3%)

Memory
-16.8MiB live, 22.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Rules
176×accelerator-lowering-fma.f32
176×accelerator-lowering-fma.f64
104×*-lowering-*.f32
104×*-lowering-*.f64
64×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0624
11024
21824
33024
44824
59024
615724
720324
828524
931524
1033124
033124
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps
Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps

localize28.0ms (0.3%)

Memory
22.5MiB live, 61.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy62.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Samples
10.0ms85×1valid
8.0ms154×0valid
3.0ms17×2valid
Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-mult: 4.0ms (33.6% of total)
ival-sub: 3.0ms (25.2% of total)
ival-sqrt: 3.0ms (25.2% of total)
adjust: 2.0ms (16.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory
-20.6MiB live, 17.5MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (- (* x x) eps)>
#<alt (* x x)>
Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<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)>
Calls

21 calls:

TimeVariablePointExpression
2.0ms
eps
@0
(sqrt (- (* x x) eps))
1.0ms
eps
@inf
(- x (sqrt (- (* x x) eps)))
1.0ms
x
@inf
(- x (sqrt (- (* x x) eps)))
1.0ms
eps
@0
(- x (sqrt (- (* x x) eps)))
1.0ms
x
@0
(- x (sqrt (- (* x x) eps)))

rewrite344.0ms (3.2%)

Memory
29.7MiB live, 492.5MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 146×accelerator-lowering-fma.f32
4 146×accelerator-lowering-fma.f64
3 310×*-lowering-*.f32
3 310×*-lowering-*.f64
2 470×pow-lowering-pow.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0622
13822
230622
3359522
0855122
Stop Event
iter limit
node limit
Counts
4 → 224
Calls
Call 1
Inputs
(- x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
Outputs
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps)))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) #s(literal -1 binary64)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps)))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps)))))
(fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64) x)
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps)))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps)))))
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (fma.f64 x x eps) (*.f64 x x))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
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(/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (sqrt.f64 (fma.f64 x x eps)))
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(/.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (fma.f64 x x eps)))
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(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)))
(/.f64 (exp.f64 (log.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (exp.f64 (log.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))))
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (exp.f64 (log.f64 (fma.f64 x x eps))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 x x eps)))))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 4 binary64))
(pow.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)))
(*.f64 (fma.f64 x x eps) (*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))))
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))))
(*.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(*.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
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(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (fma.f64 x x eps))))) (fma.f64 (*.f64 eps (fma.f64 x x eps)) (-.f64 (*.f64 eps (fma.f64 x x eps)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (fma.f64 x x eps))))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (fma.f64 x x eps))))
(*.f64 (exp.f64 (log.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))))
(*.f64 (exp.f64 (log.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x eps)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)

simplify369.0ms (3.4%)

Memory
-8.3MiB live, 720.4MiB allocated
Algorithm
egg-herbie
Rules
11 222×accelerator-lowering-fma.f32
11 222×accelerator-lowering-fma.f64
4 906×*-lowering-*.f32
4 906×*-lowering-*.f64
3 416×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02571257
17841238
225941200
369441197
080911129
Stop Event
iter limit
node limit
Counts
84 → 84
Calls
Call 1
Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(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)
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (neg.f64 x) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (fma.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (fma.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x))) x) eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 eps) (*.f64 x x))))) eps)) eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 x (*.f64 x x)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (*.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(neg.f64 (*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(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)

eval56.0ms (0.5%)

Memory
23.8MiB live, 99.2MiB allocated
Compiler

Compiled 9 601 to 1 050 computations (89.1% saved)

prune67.0ms (0.6%)

Memory
-32.3MiB live, 123.8MiB allocated
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New29810308
Fresh000
Picked101
Done000
Total29910309
Accuracy
99.9%
Counts
309 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
41.2%
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
32.9%
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))) x)
43.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
62.0%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
62.5%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
62.4%
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
58.8%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
3.5%
(-.f64 x (neg.f64 x))
4.4%
(-.f64 x x)
26.8%
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 268 to 156 computations (41.8% saved)

simplify199.0ms (1.9%)

Memory
9.0MiB live, 324.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))
cost-diff0
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))
cost-diff0
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
cost-diff320
(fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))
cost-diff0
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
cost-diff0
(sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))
cost-diff0
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
cost-diff896
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
cost-diff0
(neg.f64 eps)
cost-diff0
(sqrt.f64 (neg.f64 eps))
cost-diff0
(-.f64 x (sqrt.f64 (neg.f64 eps)))
cost-diff192
(-.f64 x x)
cost-diff0
(neg.f64 eps)
cost-diff0
(fma.f64 x x (neg.f64 eps))
cost-diff0
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
cost-diff0
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
Rules
2 770×*-lowering-*.f32
2 770×*-lowering-*.f64
2 486×accelerator-lowering-fma.f32
2 486×accelerator-lowering-fma.f64
2 158×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025121
159121
2114121
3193117
4289117
5483117
61364117
73335117
85722117
97419117
08061114
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(- x (sqrt (+ (* x x) (neg eps))))
x
(sqrt (+ (* x x) (neg eps)))
(+ (* x x) (neg eps))
(neg eps)
eps
(- x x)
x
(- x (sqrt (neg eps)))
x
(sqrt (neg eps))
(neg eps)
eps
(- x (sqrt (* eps (+ (* x (/ x eps)) -1))))
x
(sqrt (* eps (+ (* x (/ x eps)) -1)))
(* eps (+ (* x (/ x eps)) -1))
eps
(+ (* x (/ x eps)) -1)
(/ x eps)
-1
(/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x)
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x)))
eps
1/2
(/ (* 1/8 (* eps eps)) (* x x))
(* 1/8 (* eps eps))
1/8
(* eps eps)
(* x x)
x
Outputs
(- x (sqrt (+ (* x x) (neg eps))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (+ (* x x) (neg eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(+ (* x x) (neg eps))
(-.f64 (*.f64 x x) eps)
(neg eps)
(neg.f64 eps)
eps
(- x x)
#s(literal 0 binary64)
x
(- x (sqrt (neg eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
x
(sqrt (neg eps))
(sqrt.f64 (neg.f64 eps))
(neg eps)
(neg.f64 eps)
eps
(- x (sqrt (* eps (+ (* x (/ x eps)) -1))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (* eps (+ (* x (/ x eps)) -1)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(* eps (+ (* x (/ x eps)) -1))
(-.f64 (*.f64 x x) eps)
eps
(+ (* x (/ x eps)) -1)
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(/ x eps)
(/.f64 x eps)
-1
#s(literal -1 binary64)
(/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x)
(*.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x)))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
eps
1/2
#s(literal 1/2 binary64)
(/ (* 1/8 (* eps eps)) (* x x))
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))
(* 1/8 (* eps eps))
(*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))
1/8
#s(literal 1/8 binary64)
(* eps eps)
(*.f64 eps eps)
(* x x)
(*.f64 x x)
x

localize138.0ms (1.3%)

Memory
-0.5MiB live, 132.3MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 eps eps)
accuracy100.0%
(*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))
accuracy99.9%
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
accuracy62.0%
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))
accuracy100.0%
(sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))
accuracy99.9%
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
accuracy99.5%
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
accuracy82.5%
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
accuracy100.0%
(sqrt.f64 (neg.f64 eps))
accuracy100.0%
(neg.f64 eps)
accuracy100.0%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
accuracy100.0%
(-.f64 x x)
accuracy100.0%
(fma.f64 x x (neg.f64 eps))
accuracy100.0%
(neg.f64 eps)
accuracy100.0%
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
accuracy82.5%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
Samples
46.0ms38×1valid
26.0ms153×0valid
9.0ms55×0invalid
5.0ms2valid
1.0ms3valid
Compiler

Compiled 131 to 27 computations (79.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 69.0ms
ival-sqrt: 40.0ms (57.9% of total)
ival-mult: 10.0ms (14.5% of total)
ival-div: 6.0ms (8.7% of total)
ival-sub: 5.0ms (7.2% of total)
ival-add: 4.0ms (5.8% of total)
adjust: 2.0ms (2.9% of total)
ival-neg: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series32.0ms (0.3%)

Memory
-5.8MiB live, 31.4MiB allocated
Counts
16 → 324
Calls
Call 1
Inputs
#<alt (- x (sqrt (+ (* x x) (neg eps))))>
#<alt (sqrt (+ (* x x) (neg eps)))>
#<alt (+ (* x x) (neg eps))>
#<alt (neg eps)>
#<alt (- x x)>
#<alt (- x (sqrt (neg eps)))>
#<alt (sqrt (neg eps))>
#<alt (* eps (+ (* x (/ x eps)) -1))>
#<alt (- x (sqrt (* eps (+ (* x (/ x eps)) -1))))>
#<alt (sqrt (* eps (+ (* x (/ x eps)) -1)))>
#<alt (+ (* x (/ x eps)) -1)>
#<alt (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x)))>
#<alt (/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x)>
#<alt (/ (* 1/8 (* eps eps)) (* x x))>
#<alt (* 1/8 (* eps eps))>
#<alt (* eps eps)>
Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt x>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (pow (sqrt -1) 3))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (pow (sqrt -1) 3)))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt -1>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (/ (pow x 2) eps)>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (/ (pow x 2) eps)>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (/ (pow x 2) eps)>
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)>
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)>
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)>
#<alt -1>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt -1>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (* 1/8 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
Calls

81 calls:

TimeVariablePointExpression
14.0ms
eps
@0
(/ (* 1/8 (* eps eps)) (* x x))
1.0ms
eps
@-inf
(* eps (+ (* x (/ x eps)) -1))
1.0ms
eps
@0
(* eps (+ (* x (/ x eps)) -1))
1.0ms
eps
@-inf
(- x (sqrt (* eps (+ (* x (/ x eps)) -1))))
1.0ms
x
@0
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x)))

rewrite97.0ms (0.9%)

Memory
14.3MiB live, 132.3MiB allocated
Algorithm
batch-egg-rewrite
Rules
898×accelerator-lowering-fma.f32
898×accelerator-lowering-fma.f64
808×*-lowering-*.f32
808×*-lowering-*.f64
630×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025113
1162113
01393105
Stop Event
iter limit
iter limit
node limit
Counts
16 → 250
Calls
Call 1
Inputs
(- x (sqrt (+ (* x x) (neg eps))))
(sqrt (+ (* x x) (neg eps)))
(+ (* x x) (neg eps))
(neg eps)
(- x x)
(- x (sqrt (neg eps)))
(sqrt (neg eps))
(* eps (+ (* x (/ x eps)) -1))
(- x (sqrt (* eps (+ (* x (/ x eps)) -1))))
(sqrt (* eps (+ (* x (/ x eps)) -1)))
(+ (* x (/ x eps)) -1)
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x)))
(/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x)
(/ (* 1/8 (* eps eps)) (* x x))
(* 1/8 (* eps eps))
(* eps eps)
Outputs
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))) (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (neg.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))))
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(/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) x)) (neg.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (*.f64 eps eps)) x)
(pow.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) #s(literal -1 binary64))
(*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)))
(*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x))))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (*.f64 eps eps) x))
(*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x))
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 x x)))
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64))
(*.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) x) (/.f64 eps x))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) eps)
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(neg.f64 (*.f64 eps (neg.f64 eps)))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 #s(literal -1 binary64) (*.f64 eps (neg.f64 eps)))
(*.f64 #s(literal 1 binary64) (*.f64 eps eps))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (*.f64 (neg.f64 eps) #s(literal -1 binary64)) eps)

simplify547.0ms (5.1%)

Memory
-4.4MiB live, 877.1MiB allocated
Algorithm
egg-herbie
Rules
17 934×accelerator-lowering-fma.f32
17 934×accelerator-lowering-fma.f64
6 134×*-lowering-*.f32
6 134×*-lowering-*.f64
3 902×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03393850
110273783
234433687
085853515
Stop Event
iter limit
node limit
Counts
324 → 324
Calls
Call 1
Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
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(* 1/2 (/ eps x))
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(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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x
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
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(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
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(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
0
0
0
0
0
0
0
0
0
0
0
0
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
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(- x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
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(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
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(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
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(+ (* -1 eps) (pow x 2))
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(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
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(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
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(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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x
(+ x (* -1/2 (/ eps x)))
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(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (pow (sqrt -1) 3)))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
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(/ (pow x 2) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
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(- (/ (pow x 2) eps) 1)
(* 1/2 eps)
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(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
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(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
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(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
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(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(* 1/8 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (/.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (/.f64 (-.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 eps) (*.f64 x x))))) eps)) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (/.f64 eps (*.f64 x x)) (*.f64 #s(literal -1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 eps (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (*.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))))) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 (neg.f64 eps) (*.f64 x x)) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 (neg.f64 eps) (*.f64 x x)) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (fma.f64 x (/.f64 (neg.f64 eps) (*.f64 x x)) x))
(pow x 2)
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(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(* 1/8 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)

eval70.0ms (0.7%)

Memory
5.5MiB live, 175.0MiB allocated
Compiler

Compiled 10 100 to 1 145 computations (88.7% saved)

prune49.0ms (0.5%)

Memory
7.1MiB live, 163.1MiB allocated
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New5926598
Fresh415
Picked145
Done000
Total59711608
Accuracy
100.0%
Counts
608 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
34.0%
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x)
41.2%
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
58.4%
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
41.2%
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
24.5%
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))
43.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
62.5%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
62.4%
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
58.8%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
3.5%
x
4.4%
#s(literal 0 binary64)
Compiler

Compiled 222 to 133 computations (40.1% saved)

simplify414.0ms (3.9%)

Memory
14.8MiB live, 242.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
cost-diff0
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
cost-diff0
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
cost-diff0
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
cost-diff0
(*.f64 eps #s(literal 1/2 binary64))
cost-diff0
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
cost-diff0
(neg.f64 eps)
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
cost-diff256
(-.f64 (*.f64 x x) (neg.f64 eps))
Rules
2 808×accelerator-lowering-fma.f32
2 808×accelerator-lowering-fma.f64
1 968×*-lowering-*.f32
1 968×*-lowering-*.f64
1 188×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01891
14489
28889
326689
4103289
5203289
6352789
7482289
8532489
9538389
10539389
11540189
12593389
13622189
14631589
15639189
16648189
17648189
18648189
19648189
20664989
21677989
22678789
23678789
24678789
0678784
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))
(- (* x x) (neg eps))
(* x x)
x
(neg eps)
eps
(+ x (sqrt (neg eps)))
(sqrt (neg eps))
0
x
(/ (* eps 1/2) x)
(* eps 1/2)
eps
1/2
x
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x)
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2))
eps
(+ (* eps (/ 1/8 (* x x))) 1/2)
(/ 1/8 (* x x))
1/8
(* x x)
x
1/2
Outputs
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))
(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(- (* x x) (neg eps))
(fma.f64 x x eps)
(* x x)
(*.f64 x x)
x
(neg eps)
(neg.f64 eps)
eps
(+ x (sqrt (neg eps)))
(+.f64 x (sqrt.f64 (neg.f64 eps)))
(sqrt (neg eps))
(sqrt.f64 (neg.f64 eps))
0
#s(literal 0 binary64)
x
(/ (* eps 1/2) x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
x
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x)
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
eps
(+ (* eps (/ 1/8 (* x x))) 1/2)
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/ 1/8 (* x x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
x
1/2
#s(literal 1/2 binary64)

localize61.0ms (0.6%)

Memory
-30.2MiB live, 124.8MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
accuracy99.8%
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy91.8%
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
accuracy78.6%
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
accuracy100.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
accuracy100.0%
(*.f64 eps #s(literal 1/2 binary64))
accuracy100.0%
(neg.f64 eps)
accuracy100.0%
(-.f64 (*.f64 x x) (neg.f64 eps))
accuracy100.0%
(+.f64 x (sqrt.f64 (neg.f64 eps)))
accuracy99.5%
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
Samples
31.0ms201×0valid
7.0ms55×0invalid
Compiler

Compiled 90 to 20 computations (77.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-div: 10.0ms (39.2% of total)
ival-mult: 8.0ms (31.4% of total)
ival-add: 2.0ms (7.8% of total)
ival-sqrt: 2.0ms (7.8% of total)
ival-sub: 1.0ms (3.9% of total)
ival-neg: 1.0ms (3.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory
7.9MiB live, 47.2MiB allocated
Counts
11 → 216
Calls
Call 1
Inputs
#<alt (- (* x x) (neg eps))>
#<alt (/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))>
#<alt (* x x)>
#<alt (neg eps)>
#<alt (/ (* eps 1/2) x)>
#<alt (* eps 1/2)>
#<alt (/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x)>
#<alt (* eps (+ (* eps (/ 1/8 (* x x))) 1/2))>
#<alt (+ (* eps (/ 1/8 (* x x))) 1/2)>
#<alt (/ 1/8 (* x x))>
#<alt (+ x (sqrt (neg eps)))>
Outputs
#<alt eps>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt eps>
#<alt (* eps (+ 1 (/ (pow x 2) eps)))>
#<alt (* eps (+ 1 (/ (pow x 2) eps)))>
#<alt (* eps (+ 1 (/ (pow x 2) eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt x>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))>
#<alt (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))>
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))>
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))>
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))>
#<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 (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
Calls

54 calls:

TimeVariablePointExpression
3.0ms
x
@0
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))
2.0ms
eps
@-inf
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2))
1.0ms
eps
@-inf
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x)
1.0ms
eps
@inf
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))
1.0ms
eps
@-inf
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))

rewrite1.9s (17.9%)

Memory
9.6MiB live, 705.3MiB allocated
Algorithm
batch-egg-rewrite
Rules
7 072×accelerator-lowering-fma.f32
7 072×accelerator-lowering-fma.f64
5 886×*-lowering-*.f32
5 886×*-lowering-*.f64
4 460×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01774
111266
284366
0840562
Stop Event
iter limit
node limit
Counts
11 → 887
Calls
Call 1
Inputs
(- (* x x) (neg eps))
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))
(* x x)
(neg eps)
(/ (* eps 1/2) x)
(* eps 1/2)
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x)
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2))
(+ (* eps (/ 1/8 (* x x))) 1/2)
(/ 1/8 (* x x))
(+ x (sqrt (neg eps)))
Outputs
(+.f64 (*.f64 x x) eps)
(+.f64 eps (*.f64 x x))
(+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (neg.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))
(+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps))))
(+.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) x) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps)))))
(+.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps))))))
(+.f64 (*.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(+.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(-.f64 (*.f64 x x) (fabs.f64 eps))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x eps)))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps)))
(fma.f64 x x eps)
(fma.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) eps)
(fma.f64 eps #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (fabs.f64 eps) #s(literal -1 binary64) (*.f64 x x))
(fma.f64 (sqrt.f64 (fabs.f64 eps)) (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x x))
(fma.f64 (sqrt.f64 (fabs.f64 eps)) (*.f64 (sqrt.f64 (fabs.f64 eps)) #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) x (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps)))))
(fma.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps))))))
(fma.f64 (neg.f64 x) (neg.f64 x) eps)
(fma.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (neg.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps))))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (fabs.f64 eps) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)) eps)
(fma.f64 #s(literal -1 binary64) (*.f64 (fabs.f64 eps) #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (sqrt.f64 (fabs.f64 eps)) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) eps)
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 x x))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (pow.f64 (fabs.f64 eps) #s(literal 1/4 binary64))) (pow.f64 (fabs.f64 eps) #s(literal 1/4 binary64)) (*.f64 x x))
(fma.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps))) (fma.f64 x x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps))))
(fma.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (fabs.f64 eps) (neg.f64 (fma.f64 x x eps)))) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps))))
(fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 eps (fma.f64 x (neg.f64 x) eps)) (*.f64 (*.f64 eps eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (fma.f64 x (neg.f64 x) eps)) (-.f64 (*.f64 eps (fma.f64 x (neg.f64 x) eps)) (*.f64 x (*.f64 x (*.f64 x x)))))) (neg.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))
(fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (-.f64 (*.f64 x x) eps))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (-.f64 (*.f64 x x) eps))) (neg.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))
(neg.f64 (neg.f64 (fma.f64 x x eps)))
(/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))))
(/.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))
(/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (neg.f64 (fma.f64 x (neg.f64 x) eps)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))))
(/.f64 (*.f64 (fma.f64 x (neg.f64 x) eps) (fma.f64 x x eps)) (fma.f64 x (neg.f64 x) eps))
(/.f64 (*.f64 (fma.f64 x x eps) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (neg.f64 (*.f64 eps (*.f64 eps eps))))) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (neg.f64 x) eps) (fma.f64 x x eps))) (-.f64 (*.f64 x x) eps))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (neg.f64 x) eps) (fma.f64 x x eps))) (neg.f64 (fma.f64 x (neg.f64 x) eps)))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (fma.f64 eps eps (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (fma.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))))))
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(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (fma.f64 x x eps)))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (fma.f64 x x eps)))
(*.f64 (/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (/.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))))
(*.f64 (/.f64 (fma.f64 x x eps) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))
(*.f64 (*.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)))
(*.f64 (*.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))
(*.f64 (*.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (fma.f64 x x eps) (neg.f64 (fma.f64 x x eps))) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))
(*.f64 (/.f64 (fma.f64 x x eps) (-.f64 (*.f64 x (*.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (neg.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (fma.f64 x (*.f64 (/.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (+.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x (*.f64 (/.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (+.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))))))
(*.f64 (/.f64 (fma.f64 x x eps) (fma.f64 x (*.f64 x x) (*.f64 eps (sqrt.f64 (fabs.f64 eps))))) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (*.f64 x x) eps)))
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (fabs.f64 eps) (*.f64 (-.f64 (sqrt.f64 (fabs.f64 eps)) x) (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 x x)))))
(*.f64 (/.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))

simplify1.1s (9.8%)

Memory
-21.4MiB live, 623.6MiB allocated
Algorithm
egg-herbie
Rules
8 308×accelerator-lowering-fma.f32
8 308×accelerator-lowering-fma.f64
3 220×*-lowering-*.f32
3 220×*-lowering-*.f64
2 588×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02172074
16561962
220411828
366131827
082011713
Stop Event
iter limit
node limit
Counts
216 → 216
Calls
Call 1
Inputs
eps
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(pow x 2)
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
eps
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ 1 (/ (pow x 2) eps)))
eps
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))
(/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(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)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
x
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
Outputs
eps
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x))
(pow x 2)
(*.f64 x x)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
eps
(* eps (+ 1 (/ (pow x 2) eps)))
(fma.f64 x x eps)
(* eps (+ 1 (/ (pow x 2) eps)))
(fma.f64 x x eps)
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(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x x))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
x
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(fma.f64 (sqrt.f64 eps) (/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) x) x)
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(fma.f64 (sqrt.f64 eps) (/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) x) x)
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(fma.f64 (sqrt.f64 eps) (/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) x) x)
x
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(fma.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64)) x) x)
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(fma.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64)) x) x)
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(fma.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64)) x) x)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) x)
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) x)
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(fma.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x)
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(fma.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x)
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(fma.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x)

eval274.0ms (2.5%)

Memory
24.7MiB live, 249.2MiB allocated
Compiler

Compiled 28 937 to 2 756 computations (90.5% saved)

prune164.0ms (1.5%)

Memory
-6.1MiB live, 402.4MiB allocated
Pruning

13 alts after pruning (7 fresh and 6 done)

PrunedKeptTotal
New1 18761 193
Fresh112
Picked235
Done134
Total1 191131 204
Accuracy
100.0%
Counts
1 204 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
34.0%
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x)
41.2%
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
43.2%
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
43.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
61.6%
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
62.5%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
62.4%
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
60.1%
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
41.2%
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
41.0%
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
43.5%
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
3.5%
x
4.4%
#s(literal 0 binary64)
Compiler

Compiled 230 to 146 computations (36.5% saved)

simplify407.0ms (3.8%)

Memory
-18.1MiB live, 733.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
cost-diff0
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
cost-diff0
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
cost-diff0
(/.f64 #s(literal 2 binary64) eps)
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff1088
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
cost-diff0
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff0
(fabs.f64 eps)
cost-diff0
(sqrt.f64 (fabs.f64 eps))
cost-diff0
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
cost-diff0
(neg.f64 eps)
cost-diff0
(sqrt.f64 (neg.f64 eps))
cost-diff0
(+.f64 x (sqrt.f64 (neg.f64 eps)))
cost-diff0
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
Rules
19 210×accelerator-lowering-fma.f32
19 210×accelerator-lowering-fma.f64
2 272×*-lowering-*.f32
2 272×*-lowering-*.f64
1 844×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024102
148102
278102
3114102
4165102
5379102
6744102
71510102
83963102
96102102
107617102
117771102
127824102
137844102
0857499
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ eps (+ x (sqrt (neg eps))))
eps
(+ x (sqrt (neg eps)))
x
(sqrt (neg eps))
(neg eps)
(- x (sqrt (fabs eps)))
x
(sqrt (fabs eps))
(fabs eps)
eps
(* (/ 1/2 x) eps)
(/ 1/2 x)
1/2
x
eps
(/ (/ 1 x) (/ 2 eps))
(/ 1 x)
1
x
(/ 2 eps)
2
eps
(* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps)
(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x)
(+ (* eps (/ 1/8 (* x x))) 1/2)
eps
(/ 1/8 (* x x))
1/8
(* x x)
x
1/2
Outputs
(/ eps (+ x (sqrt (neg eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
eps
(+ x (sqrt (neg eps)))
(+.f64 x (sqrt.f64 (neg.f64 eps)))
x
(sqrt (neg eps))
(sqrt.f64 (neg.f64 eps))
(neg eps)
(neg.f64 eps)
(- x (sqrt (fabs eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
x
(sqrt (fabs eps))
(sqrt.f64 (fabs.f64 eps))
(fabs eps)
(fabs.f64 eps)
eps
(* (/ 1/2 x) eps)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
eps
(/ (/ 1 x) (/ 2 eps))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(/ 2 eps)
(/.f64 #s(literal 2 binary64) eps)
2
#s(literal 2 binary64)
eps
(* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps)
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) x)
(+ (* eps (/ 1/8 (* x x))) 1/2)
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64))
eps
(/ 1/8 (* x x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
x
1/2
#s(literal 1/2 binary64)

localize71.0ms (0.7%)

Memory
23.8MiB live, 139.7MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
accuracy99.8%
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy86.7%
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
accuracy78.6%
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
accuracy100.0%
(/.f64 #s(literal 2 binary64) eps)
accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
accuracy99.3%
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
accuracy100.0%
(/.f64 #s(literal 1/2 binary64) x)
accuracy99.7%
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy100.0%
(sqrt.f64 (fabs.f64 eps))
accuracy100.0%
(fabs.f64 eps)
accuracy100.0%
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
accuracy100.0%
(sqrt.f64 (neg.f64 eps))
accuracy100.0%
(neg.f64 eps)
accuracy100.0%
(+.f64 x (sqrt.f64 (neg.f64 eps)))
accuracy99.5%
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
Samples
36.0ms201×0valid
9.0ms55×0invalid
Compiler

Compiled 103 to 26 computations (74.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-div: 13.0ms (44.9% of total)
ival-mult: 6.0ms (20.7% of total)
ival-sqrt: 3.0ms (10.4% of total)
ival-add: 2.0ms (6.9% of total)
ival-fabs: 1.0ms (3.5% of total)
ival-sub: 1.0ms (3.5% of total)
ival-neg: 1.0ms (3.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
17.4MiB live, 17.4MiB allocated
Counts
16 → 288
Calls
Call 1
Inputs
#<alt (/ eps (+ x (sqrt (neg eps))))>
#<alt (+ x (sqrt (neg eps)))>
#<alt (sqrt (neg eps))>
#<alt (neg eps)>
#<alt (- x (sqrt (fabs eps)))>
#<alt (sqrt (fabs eps))>
#<alt (fabs eps)>
#<alt (* (/ 1/2 x) eps)>
#<alt (/ 1/2 x)>
#<alt (/ (/ 1 x) (/ 2 eps))>
#<alt (/ 1 x)>
#<alt (/ 2 eps)>
#<alt (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps)>
#<alt (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x)>
#<alt (+ (* eps (/ 1/8 (* x x))) 1/2)>
#<alt (/ 1/8 (* x x))>
Outputs
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))>
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))>
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))>
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (* -1 (* eps (pow x 3))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) eps)) (* eps x)) eps)))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* (sqrt (/ 1 eps)) (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* -1 (/ x (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (/ eps x)>
#<alt (/ (+ eps (* -1 (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)>
#<alt (/ (- (+ eps (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x)>
#<alt (/ (- (+ eps (* -1 (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) (pow x 3))))) (+ (* -1 (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)>
#<alt (/ eps x)>
#<alt (* -1 (/ (+ (* -1 eps) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x))>
#<alt (* -1 (/ (+ (* -1 eps) (* -1 (/ (- (/ (* (pow eps 2) (pow (sqrt -1) 2)) x) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))>
#<alt (* -1 (/ (+ (* -1 eps) (* -1 (/ (- (* -1 (/ (- (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) x)) (* (pow eps 2) (pow (sqrt -1) 2))) x)) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))>
#<alt (* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))>
#<alt (* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))>
#<alt x>
#<alt (* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))>
#<alt (* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))>
#<alt (* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (- x (sqrt (fabs eps)))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (sqrt (fabs eps))>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (fabs eps)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (/ 2 eps)>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
Calls

72 calls:

TimeVariablePointExpression
1.0ms
eps
@inf
(/ eps (+ x (sqrt (neg eps))))
0.0ms
eps
@0
(/ eps (+ x (sqrt (neg eps))))
0.0ms
x
@inf
(/ eps (+ x (sqrt (neg eps))))
0.0ms
eps
@-inf
(/ eps (+ x (sqrt (neg eps))))
0.0ms
x
@-inf
(/ eps (+ x (sqrt (neg eps))))

rewrite291.0ms (2.7%)

Memory
-15.0MiB live, 417.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 604×*-lowering-*.f32
4 604×*-lowering-*.f64
4 240×accelerator-lowering-fma.f32
4 240×accelerator-lowering-fma.f64
3 782×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02484
113384
290584
0912281
Stop Event
iter limit
node limit
Counts
16 → 847
Calls
Call 1
Inputs
(/ eps (+ x (sqrt (neg eps))))
(+ x (sqrt (neg eps)))
(sqrt (neg eps))
(neg eps)
(- x (sqrt (fabs eps)))
(sqrt (fabs eps))
(fabs eps)
(* (/ 1/2 x) eps)
(/ 1/2 x)
(/ (/ 1 x) (/ 2 eps))
(/ 1 x)
(/ 2 eps)
(* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps)
(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x)
(+ (* eps (/ 1/8 (* x x))) 1/2)
(/ 1/8 (* x x))
Outputs
(+.f64 #s(literal 0 binary64) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))))
(+.f64 (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x)) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))))
(+.f64 (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x)))
(+.f64 (*.f64 (/.f64 eps (fma.f64 x x eps)) x) (*.f64 (/.f64 eps (fma.f64 x x eps)) (neg.f64 (sqrt.f64 (fabs.f64 eps)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))))
(+.f64 (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))))
(+.f64 (*.f64 x (/.f64 eps (fma.f64 x x eps))) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (fma.f64 x x eps))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))
(fma.f64 x (/.f64 eps (fma.f64 x x eps)) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (fma.f64 x x eps))))
(fma.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))))
(fma.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))))
(fma.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))))
(fma.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x)))
(fma.f64 (/.f64 eps (fma.f64 x x eps)) x (*.f64 (/.f64 eps (fma.f64 x x eps)) (neg.f64 (sqrt.f64 (fabs.f64 eps)))))
(neg.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)))
(/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps))))
(/.f64 (fabs.f64 eps) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)))
(/.f64 (*.f64 eps (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))
(/.f64 (*.f64 eps (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (fma.f64 x x eps))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (*.f64 (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))) eps)) (*.f64 (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))
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(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 8 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x #s(literal 8 binary64)))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -8 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x #s(literal 8 binary64)) (neg.f64 x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x (neg.f64 x)))
(/.f64 (/.f64 #s(literal 1/8 binary64) x) x)
(/.f64 (/.f64 #s(literal -1/8 binary64) x) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) x)) (neg.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)) x)
(pow.f64 (*.f64 x (*.f64 x #s(literal 8 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/8 binary64) x))
(*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (*.f64 x (*.f64 x #s(literal 8 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x (*.f64 x #s(literal 8 binary64))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))

simplify269.0ms (2.5%)

Memory
16.3MiB live, 481.9MiB allocated
Algorithm
egg-herbie
Rules
6 716×accelerator-lowering-fma.f32
6 716×accelerator-lowering-fma.f64
4 318×*-lowering-*.f32
4 318×*-lowering-*.f64
1 752×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02022052
15771978
216761916
354671907
083821824
Stop Event
iter limit
node limit
Counts
288 → 288
Calls
Call 1
Inputs
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (* -1 (* eps (pow x 3))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) eps)) (* eps x)) eps)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* (sqrt (/ 1 eps)) (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* -1 (/ x (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(/ eps x)
(/ (+ eps (* -1 (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)
(/ (- (+ eps (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x)
(/ (- (+ eps (* -1 (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) (pow x 3))))) (+ (* -1 (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)
(/ eps x)
(* -1 (/ (+ (* -1 eps) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x))
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (/ (* (pow eps 2) (pow (sqrt -1) 2)) x) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (* -1 (/ (- (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) x)) (* (pow eps 2) (pow (sqrt -1) 2))) x)) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
x
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
x
(* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))
(* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))
(* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))
x
(* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))
(* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))
(* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(- x (sqrt (fabs eps)))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(sqrt (fabs eps))
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(fabs eps)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(/ 2 eps)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
Outputs
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))
(/ eps (+ x (* (sqrt eps) (sqrt -1))))
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))
(fma.f64 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* -1 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))
(fma.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 x (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))
(+.f64 (neg.f64 (*.f64 (sqrt.f64 eps) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 x x) eps))))) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (* -1 (* eps (pow x 3))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) eps)) (* eps x)) eps)))
(-.f64 (-.f64 x (/.f64 (*.f64 (*.f64 x x) (fma.f64 eps x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))))) (*.f64 eps eps))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* (sqrt (/ 1 eps)) (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* -1 (/ x (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 x (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(/ eps x)
(/.f64 eps x)
(/ (+ eps (* -1 (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 x)) eps) x)
(/ (- (+ eps (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x)
(/.f64 (-.f64 eps (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (/.f64 eps x))) x)) x)
(/ (- (+ eps (* -1 (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) (pow x 3))))) (+ (* -1 (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)
(/.f64 (-.f64 eps (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 eps #s(literal 5 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (*.f64 eps eps)) x)) x)) x)
(/ eps x)
(/.f64 eps x)
(* -1 (/ (+ (* -1 eps) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x))
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 x)) eps) x)
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (/ (* (pow eps 2) (pow (sqrt -1) 2)) x) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))
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(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* 1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* 1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* 1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))

eval148.0ms (1.4%)

Memory
11.3MiB live, 319.6MiB allocated
Compiler

Compiled 19 446 to 2 180 computations (88.8% saved)

prune113.0ms (1.1%)

Memory
-2.3MiB live, 313.4MiB allocated
Pruning

16 alts after pruning (6 fresh and 10 done)

PrunedKeptTotal
New1 13141 135
Fresh022
Picked055
Done156
Total1 132161 148
Accuracy
100.0%
Counts
1 148 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
34.0%
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x)
43.2%
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
43.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
61.6%
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
11.3%
(/.f64 eps x)
62.5%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
62.4%
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
60.1%
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
41.2%
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
41.0%
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
39.0%
(*.f64 (/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) eps)
43.5%
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
32.8%
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)) x))) eps)
59.6%
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
3.5%
x
4.4%
#s(literal 0 binary64)
Compiler

Compiled 478 to 211 computations (55.9% saved)

regimes31.0ms (0.3%)

Memory
-3.0MiB live, 71.7MiB allocated
Counts
27 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) eps)
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x)
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)) x))) eps)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))) x)
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
Outputs
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
Calls

3 calls:

11.0ms
eps
8.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
8.0ms
x
Results
AccuracySegmentsBranch
88.2%2x
83.6%2eps
99.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes8.0ms (0.1%)

Memory
21.2MiB live, 21.2MiB allocated
Counts
22 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) eps)
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x)))
Outputs
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)
Calls

1 calls:

7.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes15.0ms (0.1%)

Memory
-43.8MiB live, 17.9MiB allocated
Counts
18 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
Outputs
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))
Calls

1 calls:

6.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes6.0ms (0.1%)

Memory
17.6MiB live, 17.6MiB allocated
Counts
17 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
Outputs
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
Calls

1 calls:

5.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.9%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes6.0ms (0.1%)

Memory
16.3MiB live, 16.3MiB allocated
Counts
16 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
Outputs
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Calls

1 calls:

5.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.8%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes8.0ms (0.1%)

Memory
-23.4MiB live, 15.2MiB allocated
Counts
14 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Calls

1 calls:

7.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.8%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes4.0ms (0%)

Memory
11.5MiB live, 11.5MiB allocated
Counts
10 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Outputs
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Calls

1 calls:

4.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
97.2%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes4.0ms (0%)

Memory
9.5MiB live, 9.5MiB allocated
Counts
9 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
Outputs
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
97.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes13.0ms (0.1%)

Memory
-10.9MiB live, 27.6MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
Outputs
(-.f64 x (sqrt.f64 (fabs.f64 eps)))
(/.f64 eps x)
Calls

3 calls:

6.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
63.2%2eps
62.3%2x
65.8%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes3.0ms (0%)

Memory
8.1MiB live, 8.1MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
Outputs
(neg.f64 (sqrt.f64 (fabs.f64 eps)))
(/.f64 eps x)
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
65.2%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes10.0ms (0.1%)

Memory
-21.3MiB live, 16.6MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
(/.f64 eps x)
Outputs
(/.f64 eps x)
Calls

3 calls:

5.0ms
x
2.0ms
eps
2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
11.3%1x
11.3%1eps
11.3%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes7.0ms (0.1%)

Memory
14.4MiB live, 14.4MiB allocated
Accuracy

Total -0.8b remaining (-1.4%)

Threshold costs -0.8b (-1.4%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(-.f64 x x)
(-.f64 x (neg.f64 x))
Outputs
#s(literal 0 binary64)
Calls

3 calls:

2.0ms
x
2.0ms
eps
2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
4.4%1eps
4.4%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
4.4%1x
Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch0.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-2.0075112324576588e-153
0.0
Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify15.0ms (0.1%)

Memory
-22.2MiB live, 20.1MiB allocated
Algorithm
egg-herbie
Rules
22×*-commutative_binary64
16×+-commutative_binary64
16×sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048272
164272
276272
383272
486272
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x))
(/.f64 eps x)
#s(literal 0 binary64)
Outputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x))
(/.f64 eps x)
#s(literal 0 binary64)

soundness1.5s (13.6%)

Memory
36.9MiB live, 898.4MiB allocated
Rules
17 934×accelerator-lowering-fma.f32
17 934×accelerator-lowering-fma.f64
11 222×accelerator-lowering-fma.f32
11 222×accelerator-lowering-fma.f64
8 308×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0622
13822
230622
3359522
0855122
02022052
15771978
216761916
354671907
083821824
025113
1162113
01393105
03393850
110273783
234433687
085853515
02571257
17841238
225941200
369441197
080911129
02172074
16561962
220411828
366131827
082011713
01774
111266
284366
0840562
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 671 to 306 computations (54.4% saved)

preprocess105.0ms (1%)

Memory
23.3MiB live, 217.6MiB allocated
Compiler

Compiled 592 to 122 computations (79.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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